Think Blue Crew

Rivera's Cutters @ FanGraphs

2010-09-20T15:13:00.001-05:00

I was kindly offered by Dave Cameron to write for FanGraphs after I submitted two articles to their Community Blog. My first post is up, which is a variation of my post on Rivera's cutters based on the count situation a few weeks ago. Check it out!

Comparing Swing-Happy Contact Zones

2010-09-04T09:15:00.001-05:00

Here's a quick look at the contact zones of yesterday's swing-happy hitters, Vladimir Guerrero, Delmon Young, and Jeff Francoeur. Links to plots of their swing zones are right before each picture.

Against fastballs, swing zones vs. contact zones:

Against sliders, swing zones vs. contact zones:

Against curveballs, swing zones vs. contact zones:

And against changeups, swing zones vs. contact zones:

Generally, they look the same as their swing zones, although Francoeur really shouldn't be swinging at so many changeups out of the zone because he doesn't make much contact off of them. Interesting plots, but not necessarily groundbreaking research here. I'm inclined to move on, because it's college football Saturday. Finally.

Comparing Swing-Happy Swing Zones

2010-09-03T11:50:00.007-05:00

In the past few years, the batters who have been among the league leaders in Swing% (percentage of pitches swung at) are the same names every year. Since 2008, Vladimir Guerrero has led baseball in Swing% by swinging at 60.4% of all pitches. Delmon Young is second with 60% while Jeff Francoeur is third with 57.90%.

Let's take a look at the 50% swing zones of each of these hitters by pitch type. First up, fastballs:

Vlad swings at more low RHP fastballs than the other two, but Francoeur takes high LHP fastballs, even swinging at fastballs 1.5 feet above the strike zone 50% of the time. Here's sliders:

Vlad takes a hack at a lot of sliders in the dirt from both handed pitchers, and look at Francoeur again. He also really likes to take a chance at those high sliders too. Let's look at curveballs:

For once, Francoeur doesn't look as vulnerable against curveballs (relatively speaking) compared to Delmon Young and Vlad. All three hitters are righthanders, so you can see the same weakness against LHP curveballs coming low and inside. Finally, here's a look at changeups:

All three hitters don't generally swing at inside changeups from LHP, but Francoeur again likes those high changeups. The RHP plot is particularly interesting, as Delmon Young's swing zone goes up and inside, Francouer's swing zone reaches directly up almost two feet above the strikezone, and Vlad swings at a lot of outside changeups from RHP.

Although Vlad swings at the most pitches, both pitches in the strikezone and outside the strikezone, many of Francouer's 50% swing zones are larger than Vlad's. This means Francouer's outside-the-strikezone swings are more widely distributed than Vlad's. For a professional baseball player who thinks high on-base percentages equates passivity, I don't expect Francoeur's habits to change. I mean, he is the guy who was once quoted as saying, "If on-base percentage is so important, then why don't they put it up on the scoreboard?"

Matt Kemp's Struggles: Fastballs and Breaking Balls

2010-08-31T11:37:00.002-05:00

Kensai over at Memories Of Kevin Malone had a fantastic and exhaustive post on the struggles of Matt Kemp this season. If you haven't read it yet, go read it right now before you continue this post.

A very short Cliff Notes version. Basically, Matt Kemp has been struggling this season, and even if you account for the low BABIP, he is still striking out at a higher rate this season compared to last. What also confounded me that even though he has a higher strikeout rate, he is also setting a career high in walk rate as well. Usually, drawing walks and getting struck out are thought of as tradeoffs, opposite ends of the "patience scale." Kensai also had a meticulous look at the changes in Kemp's swinging mechanics, and he did find a change that hopefully the Dodgers are aware of.

I would like to extend on Kensai's post using PITCHf/x. There are two areas I'd like to investigate: 1) Is Kemp swinging at more strikes in 2010 compared to 2009 and how? and 2) Is Kemp making less contact in 2010 compared to 2009 and how?

To answer these two questions, I'd like to look at Kemp against all fastballs (four-seamers, two-seamers, cutters, and splitters) and against all breaking balls (curveballs, sliders, and changeups). Let's get started with a table of Matt Kemp's plate discipline and swing outcome rates in 2009 vs. that of 2010, broken down between fastballs and breaking balls and by pitcher's handedness:

A lot of numbers in this table. When reading this table, be sure to remind yourself that the blue rows are last year and the white rows are this year. FB stands for fastballs and BB stands for breaking balls. Changes to note between 2009 and 2010: Kemp is swinging less against pitches from RHP but more against pitches from LHP. But in all cases, he is getting more swinging strikes, as well as making less contact, save breaking balls from LHP. This in turn results in less balls in play from Kemp. The last three columns are at a per swing rate (whereas SwStr%, Contact%, and In Play% are per pitch). When Kemp swings, he is whiffing far more in 2009 than in 2010 against BOTH fastballs and breaking balls and RHP and LHP. He is also getting less contact on the ball when he swings in all cases (again, Kemp has performed better in 2010 in In Play% only against breaking balls from lefties).

I have a lot of plots coming up, so I'd like this to be organized and I'll do my best to make concise inferences from the plots. I will be looking at the swinging strike percentages and contact percentages of each combination of fastballs/breaking balls and against righty/lefty. The plots on the left are 2009 and the ones on the right are 2010. There will be four sets of four plots each in the following order:

1) Kemp against RHP fastballs in 2009 vs. 2010 (SwStr% and Contact%)
2) Kemp against LHP fastballs in 2009 vs. 2010 (SwStr% and Contact%)
3) Kemp against RHP breaking balls in 2009 vs. 2010 (SwStr% and Contact%)
4) Kemp against LHP breaking balls in 2009 vs. 2010 (SwStr% and Contact%)

First up is SwStr% and Contact% of Matt Kemp against 1) RHP fastballs:

The red contour lines tell us that Kemp chooses to swing 50% of the time when a ball is thrown within the contour line. This is what I call Kemp's swing zone, so the red circles refer to this. Kemp is swinging at RHP fastballs less in 2010, but is whiffing at a much higher rate as well. He is also making much less contact. The top two graphs show Kemp swinging and missing more, while the bottom two graphs show Kemp making less contact, particularly on high inside fastballs.

Second is SwStr% and Contact% of Kemp against 2) LHP fastballs:

Here in his swinging strike plots, Kemp has actually started to swing more on LHP fastballs down and out of the zone, so his swinging strike rate there is up. But he is also missing a lot more LHP fastballs this year that come down the middle over the plate, ideal pitches for the right-hander to hit out of the park. Looking at his contact plots, we see similar colors in where he makes the most contact, but we see a huge shift. Last year, Kemp made contact off a lot of LHP fastballs down the middle of the plate, but this year, the epicenter of that contact hotspot has shifted a full foot up from the direct middle of the zone to the top of the zone. We can infer that Kemp is making less contact off the sweet spot of his bat, and making more high fastball contact that usually result in pop outs.

What about breaking balls? Third is Kemp's SwStr% and Contact% against 3) RHP breaking balls:

The SwStr% plots don't seem to change much for RHP breaking balls. Kemp is swinging more, however, on inside RHP breaking balls than before. He is clearly making less contact off RHP breaking balls this season compared to last. Last year, it also looks like Kemp made more contact off RHP breaking balls coming to the heart of the plate.

Finally, let's look at the fourth and final set of plots of Kemp's SwStr% and Contact% against 4) LHP breaking balls:

These show Kemp swinging at LHP breaking balls in the strikezone in 2009, but low and inside out of the zone in 2010 in his swing zones. As a result of chasing inside breaking balls, Kemp's SwStr% in 2010 in that lower inside corner has increased dramatically. This also shows in his Contact% plots, as the center of his contact hotspot has also shifted from the very middle of the zone toward the lower inside corner of the zone.

There's a lot of information in the previous 16(!) plots, but here are the Cliff Notes version of what I found about Matt Kemp this season compared to last season:

1) Swinging at less pitches (more walks), but whiffing more on hittable pitches (more K's)
2) Making less contact, but when he does make contact, he also puts the ball in play less
3) Swinging at (and missing) more high fastballs from RHP, resulting in less contact
4) Whiffing on LHP fastballs down the middle of the plate, making more contact on high LHP fastballs and less on down the middle LHP fastballs
5) Swinging at more inside RHP breaking balls and making less contact down the middle
6) Chasing low inside LHP breaking balls more, whiffing a LOT more, and making less contact down the middle

In general, what I present here is what we already know: Kemp is swinging and missing a lot more. But I hope that I was able to demonstrate clearly that Kemp is struggling against both fastballs and breaking balls, and I have shown where he is whiffing on them and where he is making less contact. Whereas Kensai looked at the "why," I'd like to say that I've taken an indepth look at the "how."

There could be plenty of reasons why Matt Kemp's whiffing behavior is so widespread, and this bolsters my belief that Kensai at Memories Of Kevin Malone is on to something with his post on the difference in Kemp's swinging mechanics. It's possible that Kemp started chasing inside sliders, high fastballs, and missing vulnerable pitches that he used to crush for independent reasons all at the same time, but I'm inclined to believe that a difference in mechanics (read Don Mattingly: and approach) is more likely to cause all of this simultaneously. And perhaps there is such a thing as being "too patient."

To evaluate if Kemp has changed his approach, I'd like to look at how Kemp's swinging behavior and outcomes have changed from last year based on count situation. Next time, I'll take a look at Kemp's tendencies and results on the first pitch, when the opposing pitcher is behind in the count (more balls), and when he's ahead in the count (more strikes).

Rivera's Cutters Working the Count

2010-08-30T11:00:00.033-05:00

I've talked about Mariano Rivera and his cutter in the past, but it's always interesting to analyze what I consider to be the greatest pitch in the game. I don't believe that there is any other pitch in the game right now that can be used so exclusively yet so dominantly the way that Rivera uses his cutter.

We know that Rivera has pinpoint control and likes to work the outer and inner edges of the strikezone against both right-handed batters and left-handed batters. We also know that Rivera is great at working the count, rarely getting to 3 balls in a count. Combining both of these ideas, can we figure out how Rivera works the count based on the locations of his cutters?

To do this, let's first look at Rivera's cutters by each count since 2007:

0-0: 218 to RHH, 343 to LHH
0-1: 105 to RHH, 188 to LHH
0-2: 57 to RHH, 42 to LHH
1-0: 80 to RHH, 101 to LHH
1-1: 86 to RHH, 108 to LHH
1-2: 60 to RHH, 55 to LHH
2-0: 24 to RHH, 28 to LHH
2-1: 41 to RHH, 37 to LHH
2-2: 47 to RHH, 53 to LHH
3-0: 2 to RHH, 4 to LHH
3-1: 4 to RHH, 4 to LHH
3-2: 15 to RHH, 19 to LHH

Note that these are cutters used in different pitch counts, not total pitches. Rivera does occasionally use two-seam and four-seam fastballs, and he has used traditional fastballs 16.2% of the time this season so far. However, a quick glance at the above list shows us that Rivera rarely falls behind in the count, or rarely uses his cutter when he has three balls. To analyze how Rivera works the strikezone based on the count, it wouldn't be sensible to do a 12-count plot of Rivera's cutters, as he's only thrown the cutter twice to RHH on 3-0 counts since 2007. Instead, let's combine the counts to different situations to see how Rivera locates his cutters as a result:

Count Situation (Not including full count)
On first pitch: 218 to RHH, 343 to LHH
Behind in the count: 151 to RHH, 174 to LHH
Ahead in the count: 222 to RHH, 285 to LHH
With two strikes: 164 to RHH, 150 to LHH

These sample sizes are much better for our plots and should allow us to accurately see how Rivera's cutters are located in different count situations. Let's take a first crack at Rivera's cutters against right-handed hitters on the first pitch and behind in the count along with the batter's swing zones and contact zones:

On Rivera's first pitch of the at-bat, he likes to throw a strike right away, hitting the outer edge of the zone against right-handed hitters, sometimes outside the zone. Hitters have a low contact rate on the first pitch, and when they do, they are better at making contact when Rivera's cutter is up in the zone. When Rivera is behind in the count, he still likes to get the outside edge of the strikezone, but this time looks to throw a pitch in the zone most of the time. Here, hitters make more contact off of where Rivera tends to throw, where the 50% swing and contact zones both encompass Rivera's hotspot. Note that there are shades of yellow on the inner parts of the zone as well, showing that Rivera does throw inside occasionally when he's behind in the count.

Let's look at the same count situations against left-handed hitters instead:

The first pitch to left-handed hitters is approximately the same location as against right-handed hitters, except Rivera locates up and inside in addition to middle inside. LHH have a much smaller swing zone on the first pitch compared to RHH. However, when they do swing, it is usually where Rivera locates his cutter most frequently. This is to say that Rivera's first pitch to LHH is likely to get swung at if it's placed in his hotspot. LHH also have a larger contact zone than RHH and it's located right in that hotspot, which means LHH make contact on the first pitch more often than RHH. Looking at cutters behind in the count to LHH, Rivera still likes that right edge, but locates to the left (outer edge for LHH) more often than to RHH (inner edge). He also goes inside and out of the zone on LHH in this situation more than he does going outside out of the zone to RHH.

What about his cutters to right-handed hitters ahead in the count and with two strikes? Let's take a look:

Here, Rivera goes outside the zone to RHH more often when he has the upper hand. He also locates inside to RHH sometimes too, but the epicenters of his main hotspot shifts to the right outside the zone when he's ahead in the count or with two strikes compared to when he's behind the count. It also seems as if batters swing more freely, swing zones that encompass much of the strikezone and outside as well.

Let's see if Rivera works left-handed hitters when he's ahead in the count the same way he works right-handed hitters:

Here's something different. Just as Rivera throws his cutters outside to LHH more often than inside to RHH when behind in the count, here we can see hotspots emerging on the left outer edge to LHH. When he's ahead in the count, Rivera works either edge, but goes inside and out of the zone quite often (Rivera's cutter moves in on LHH and away from RHH). On two strikes, it's pretty much anyone's guess whether Rivera wants to come outside and then barely hit the outer zone, or come into the zone and just hit the inside of the zone. The best bet for left-handers is to expect the outside cutter, as this count situation yields cutters in this location more than in other situations. Looking at the swing zones, LHH are pretty much swinging anywhere Rivera throws his cutter.

Finally, let's look at a table of different pitch outcomes and batter reactions based on the count situations we looked at above:

These are percentages of total pitches in those count situations, except for Whiff%. The distinction between SwStr% and Whiff% is that SwStr% is a % of total pitches while Whiff% is a % of total pitches swung at.

On the first pitch, RHH and LHH both swing less than 40% of the time, but LHH are definitely more successful at making contact and putting the ball in play. RHH whiff more in most count situations, but Rivera is able to get LHH to whiff more than RHH on two strikes. RHH put the ball in play 40% of the time when Rivera is behind in the count, but only 28.4% when ahead in the count. LHH put the ball in play about 35% of the time whether or not they are behind or ahead in the count.

To recap(itulate), it would appear that RHH are especially vulnerable on the first pitch, whiffing 28% of the time when they swing. RHH would hope to be behind in the count and expect a cutter inside the zone for their best chance of putting the ball in play. Otherwise, Rivera will paint the outer edge if he is ahead, pitching to the black, a difficult pitch to hit to say the least. For LHH, who make more contact off the right-handed Rivera than RHH, Rivera counters by working both edges of the zone. LHH still get whiff rates as high as 19.4%, and especially don't want to let Rivera get ahead in the count, as he will work either the outside edge or the inside edge.

Just looking at traditional statistics will appropriately show how dominant Rivera has been in his career, with a 2.21 ERA, 1.00 WHIP, .209 opponent's BA, and 1044 strikeouts in 1137+ innings. The plots and analysis above shows how he has achieved such success: by living on the black against both right-handed and left-handed hitters, and being able to consistently hit his various spots so that he gets hitters to swing at difficult pitches no matter the count.

Cliff Lee's Four-Seamer, Curveball, Cutter, and Changeup

2010-08-29T05:40:00.015-05:00

You learn something new every day, and I must confess, as someone who first dabbed his feet in PITCHf/x less than a month ago, I was very excited to get my hands dirty with this data, plotting it, and analyzing it and such. I have talked about a few of the mistakes I've made in the past with some of my plots and models, and I do want to learn from my mistakes from my analysis of the corrected plots as well. I've been referring to Mike Fast's article here from time to time to understand the possible rookie mistakes a PITCHf/x analyst can make. Needless to say, it's been very helpful and definitely should keep me accountable in the future.

Which brings me to this post about Cliff Lee. Various sources (I looked at several articles, Fangraphs, and yes, Wikipedia) tell me that Lee throws five different pitches, armed with a four-seam fastball, a two-seam fastball, a cutter, a changeup, and a curveball. Plenty of past articles have detailed the faultiness and/or suggested better reclassification techniques of MLBAM's pitch type classification where all of the great PITCHf/x data comes from. I would preface this and my future posts with the knowledge that I will use MLBAM's pitch classification for now, as developing my own algorithm to determine a better classification seems like a time-consuming and daunting task to say the least.

But before I dive into plots of Cliff Lee's pitches, I need to look at his pitch types first according to MLBAM. Here's a list of the frequency of his pitches by handedness since 2007, according to MLBAM's classification and my database:

FA to R: 2016 pitches
FA to L: 885 pitches
FF to R: 1585 pitches
FF to L: 773 pitches
FC to R: 301 pitches
FC to L: 79 pitches
CH to R: 1237 pitches
CH to L: 80 pitches
CU to R: 490 pitches
CU to L: 286 pitches
SL to R: 222 pitches
SL to L: 384 pitches

Fangraphs's player page of Cliff Lee tells us that Lee rarely used his slider in recent years (less than 2% of his pitches) but uses his curveball much more. In the list above, the counts for SL (slider) and CU (curveball) are in the same range, so something is definitely fishy here. Fangraphs uses classifications from Baseball Info Solutions, so I am inclined to believe that if Lee does throw a slider, that he throws it rarely as opposed to almost as often as his curveball.

Now a very thorough study would include looking at the release points, spin deflection, and movements of Lee's sliders according to MLBAM to see if they were somehow misclassified as sliders when they were really curveballs that didn't break. I'm not going to do that in this post. Instead, I'll simply ignore the pitches that were classified as sliders and move on.

The same thing with FA (generic fastballs). These are presumably fastballs that could have been four-seamers or two-seamers, so in this analysis, I will ignore FA as well. Which means that I'll be leaving out two-seam fastballs.

Now that we've got that out of the way, let's look at location density plots of Cliff Lee's four-seam fastballs against RHH (1585 pitches) and LHH (773 pitches):

I've added contour lines indicating the area inside which the batter is 50% likely to swing at a pitch, as well as where the batter is 50% likely to make contact on a pitch (hopefully I did them right and interpret them correctly as well, feel free to correct me when you settle down from the PITCHf/x Summit, Jeremy). I also decided to use this color scheme because it contrasts well with the red and blue contour lines and also makes a yellowish contour line to show where Lee tends to locate his four-seam fastballs the most.

Here, Lee throws his four-seamer all over the zone against right-handed hitters, but throws them mostly to the outer (left) part of the zone against left-handed hitters. It would appear that Lee gets called strikes often in this area against LHH. This means that left-handed hitters are more likely to swing when the fastball comes up and inside and down the middle. Both RHH and LHH seem to make contact off of Lee's fastballs when they do swing, even when the four-seamer is up and out of the zone.

Here's a look at Cliff Lee's curveballs and opposing hitters' swing zones and contact zones (490 pitches to RHH, 286 pitches to LHH):

Lee distributes his curveballs very similarly against RHH and LHH, but hitters react differently depending on handedness. It would appear at first that LHH have the advantage by making more contact, but remember that these contour lines represent where the batter swings 50% of the time. This means that right-handed hitters are making better and solid contact in the sweet spots of the zone against Lee than left-handed hitters do, as the LHH 50% contact zone encompasses the upper and lower parts outside the zone. The RHH contact zone is much smaller than the RHH swing zone compared to the LHH contour lines, but that doesn't necessarily mean that RHH are getting more swinging strikes than LHH. Even if they did, making contact on low curveballs out of the zone usually results in a routine ground out. Basically, the larger the contact zone, the worse the contact being made, so the left-hander's curveballs are more successful against LHH than RHH, which is expected.

Finally, let's look at Cliff Lee's cutters (301 pitches) and his changeups (1237 pitches) against right-handed hitters (I'm not including cutters and changeups against LHH because Lee rarely throws these to them, less than 100 times for either since 2007):

Lee likes to throw his cutter all over the middle parts of the zone against RHH, and interestingly likes to locate his changeups to the outer parts of the zone. What's interesting is that the contact zone is smaller against changeups than against cutters but the swing zones are about the same size, albeit in different locations. To me, this means that Lee is able to get more swinging strikes against RHH with changeups, a precondition being that the swing zones are similar-sized.

These plots are definitely interesting to look at and analyze, but they are also in a beta stage. I hope to make "visual scouting reports" like these in the future for both batters and pitchers, similar to what Jeremy Greenhouse did last year (to borrow his terminology). Having a good understanding of the relationship between the swing zone and contact zone will be important (and possibly even the swinging strike zone and balls in play zone). Hopefully I was able to interpret them correctly here, but I am ready to go back to the scatter plots to see if some of my analysis is confirmed there as well.

Density Plots of Rivera's Cutters

2010-08-28T13:03:00.005-05:00

A few weeks ago, I took a first look at Mariano Rivera's cutters, and saw that Rivera locates his cutters so accurately and so effectively by painting the left and right edges of the strikezone without hitting the middle much. To recall what these scatter plots looked like, check this out.

Now I've learned quite a lot of interesting things since then, including a technique called kernel density estimation, a simple method to estimate the frequency/density of x,y coordinates. I wanted to take a look at Rivera's cutters again, this time in the form of pretty plots.

I've used hexagonal binning methods before to show Rivera's pitch movement plots, as well as filled contour loess regression plots for other players. Here's some plots of Rivera's cutters against RHH and LHH using bivariate kernel density estimation, a catalog of various colorful schemes:

I've already talked extensively about how Rivera locates his cutters, but it's pretty clear that Rivera still has pinpoint control. Those are just a few of the possible color schemes I can use to display these density plots. The rainbow one in the last plot shows more levels of where Rivera locates his cutter. The second plot uses heat colors while the third plot uses terrain colors. Mind you, these are all plots of the same data, just different color schemes. I'll definitely make use of these density plots in the future (I've made them before for basketball shot locations) in order to show pitch locations and such. I'll probably keep the color schemes consistent though (I think the first plot is the best combination of contrast and color), but for now, these are definitely pretty to look at.

The Best and Worst Fastball Hitters

2010-08-27T11:31:00.015-05:00

There is an awesome leaderboard over at Fangraphs.com where you can check out the best (and worst) hitters by pitch type. What stats like 'wFB,' 'wSL,' and 'wCB' do is that they calculate the number of runs scored above average a hitter attained against that particular pitch. The wFB/C and wSL/C stats look at runs above average per 100 pitches, so wFB/C would be looking at runs above average per 100 fastballs.

If you look at the leaderboard for the past three seasons combined, Albert Pujols, Kevin Youkilis, and Mark Teixeira come out on top as the best fastball hitters in the MLB. In the past three years, Pujols gained 121.6 runs above average against the fastball, while Youkilis and Teixeira gained 99.8 and 94.1 runs above average respectively.

A look at heat maps of run value against the fastball would give the best look at how these hitters fared against the heat. However, I wanted to create plots showing a measure that most readers will understand intuitively. Let's take a look at Pujols, Youkilis, and Teixeira in contact percentage against fastballs (percentage of fastballs they swung and made contact off of):

It looks like Pujols is by far better at making contact against fastballs from right-handed pitchers than the other two. Teixeira is a switch-hitter and it definitely shows in these plots, as he is the better hitter of the three against left-handed pitchers' fastballs. He makes contact on fastballs equally well against both RHP and LHP. Also, notice that the eye of the heat maps for all three hitters against LHP fastballs are relatively the same, but that Teixeira makes contact off of fastballs from RHP that are more to the right (outside for RHH) than Pujols or Youkilis, who make contact off RHP fastballs more inside. Again, this is because Teixeira is a switch-hitter while Pujols and Youkilis are exclusively right-handed. Whereas Pujols and Youk make contact in the left part of the zone against RHP, Teixeira bats left-handed against RHP instead, and so makes more contact in the right part of the zone.

Let's see how these guys' swinging strike percentages look against fastballs:

Remember that these are the best fastball hitters in the game today, so there's just blue all over in terms of swinging strikes. Looks like Pujols and Youk whiff a bit on high fastballs and inside fastballs from RHP, as well as high and outside fastballs from LHP. The switch-hitting Teixeira actually looks like he is more susceptible to swinging at low fastballs against both handed pitchers, but again, these swinging strike zones are very good compared to every other batter.

Now let's look back to the leaderboard to see the worst fastball hitters in the game according to Fangraphs. These turn out to be Jason Kendall, Yuniesky Betancourt, and Kurt Suzuki among qualified players, getting -40.5, -32.1, and -31.4 runs below average against fastballs respectively. Let's take a look at how they fared in terms of getting contact off fastballs:

All right-handed hitters, these look different from the Pujols/Youk/Teixeira plots earlier. The one that stands out the most is definitely Jason Kendall, who just can't seem to make contact off of fastballs, especially from LHP, barely making contact 50% of the time when the fastball is right down the middle of the plate. Betancourt can make some contact off of RHP fastballs while Suzuki has a decent epicenter against LHP fastballs, but bear in mind that contact doesn't necessarily entail that they're making good contact. Fastballs are arguably the easiest pitch in the game to get contact off of, and the best hitters can get around fast enough to make solid contact. Pujols/Youk/Teixeira make a lot of contact, but also get wood on the ball, all three being some of the top power hitters in the game, presumably getting most of their success off fastballs.

Let's take a look at how the worst fastball hitters fared in swinging strike percentages against fastballs:

It looks like part of the reason that Kendall can't make contact off fastballs down the middle of the plate is because he keeps missing them, as you see some lighter blue in swinging strikes down the middle as well as low and inside against RHP. This is different from both Betancourt and Suzuki, who swing and miss at high fastballs out of the zone, where Betancourt is particularly vulnerable against high LHP fastballs and low and inside RHP fastballs.

Admittedly, there are better plots to make in order to capture the effectiveness and ineffectiveness of hitters against certain pitch types. Plots I may experiment with in later posts will almost certainly include slugging percentage per balls in play (SLGBIP as opposed to BABIP) to show how much power the best hitters against a certain pitch get per ball they put in play.

But for now, these plots of contact percentage and swinging strike percentage clearly show who are the better and worse of the fastball hitters among these six. I did keep the swinging strike percentage plots at a lower maximum (which is why you see all the shades of blue) because fastballs typically induce the least amount of swinging strikes compared to other pitches (especially changeups). This will allow you to compare the best and worst hitters in terms of contact% and swinging strike% later between different pitch types if I do other posts for other pitches, as the color scales will remain the same to allow for a fair comparison.

Is the Strike Zone Bigger in August?

2010-08-26T11:28:00.001-05:00

Jeff Zimmerman over at Fangraphs had an interesting post about the expansion of the strikezone as the season goes on. He mentions that there may be evidence to bolster David Ortiz's claim that umpires are calling more strikes and less balls as the season goes on.

I wanted to see this for myself using my own method, so I created a called strike probability model for April 2008 vs. August 2008, April 2009 vs. August 2009, and April 2010 vs. August 2010. What I did was I pulled all called strikes and balls (ignoring all the times when the batter swings) within half a foot from the rule book strikezone, half a foot inside and half a foot outside. I then modeled a surface fit for all called strikes over pitches where the batter didn't swing. I assumed that the middle of the inner 0.5 foot border returned called strikes 100% of the time if the model did not project that far inward, and same with balls way outside the strikezone.

Let's take a look at called strikes in April 2008 vs. August 2008 to see if umpires called more strikes as the season went on in the past, where red indicates called strikes and blue indicates balls (blue balls, snicker). Note that I split the strikezone into nine equal-sized boxes for reference, while the outer border is the approximate rule book strikezone:

It looks like here that the left-right distance is not affected much, but you can see that the upper areas as well as the lower areas show more called strikes in August, if only slightly bulging. Let's take a look at April 2009 vs. August 2009:

Here, it actually looks like April had a higher probability of called strikes in the lower part of the strikezone. There isn't that much change in 2009 though compared to 2008. Now let's compare this year's April vs. the current month of August:

Is Ortiz on to something? At first, I wasn't so sure. Using the grid as reference, you can notice the red extend upwards slightly and downwards a bit more, but it didn't see like much of a difference to me. I'd have to show the numbers to back it up, as the difference in the images produced didn't seem significant enough to me. In the end, the numbers over at Zimmerman's post may well back Ortiz's claims, showing an increase in called strikes per non-swinging pitches increasing from 51.0% in April this year to 53.5% this month of August. That difference of 2.5% could very well be captured by that red dip you see in the lower third quadrants.

How much does this affect each individual batter? There were 55,240 total called strikes and balls in April. Assuming the month of August would have a similar number, that's 1381 balls converted to called strikes, 2.5% of 55,240. A quick query tells me that there were 21,191 total atbats in April, which would mean that approximately 6.5% of all at-bats in the month of August had one more called strike than in April.

Crude calculations there, but it looks like that David Ortiz might be right and that the umpires have expanded the strikezone as a whole, if only a little bit. Probably means that Ortiz had an atbat among the 6.5% of unfortunate souls who were disadvantaged by one less call in favor of the batter.

Ryan Howard's Whiffs by Pitch Type

2010-08-25T11:15:00.013-05:00

I submitted my Mark Reynolds post yesterday to Fangraphs' community blog... and they accepted! Needless to say, I'm getting some site traffic from Fangraphs now, and I thought I'd share some plots of the other prodigious power hitter who strikes out a ton. Let's take a look at Ryan Howard, Mark Reynolds' left-handed counterpart, only 40 pounds heavier.

Ryan Howard has been either second or third in the entire MLB in swinging strike percentage and other strikeout categories since Mark Reynolds' debut in 2007. Fangraphs' stats tell us that Howard has swung and missed on 14.6% of pitches so far in 2010 while posting a swinging strike percentage consistently above 15% in the previous three seasons. Like Reynolds, Howard doesn't actually swing at everything compared to other swing-happy batters, swinging at less than 50% of pitches every season for his career.

Again, I'm going to leave out cutters and just look at four-seam fastballs, sliders, curveballs, and changeups due to sample size. Let's look at four-seam fastballs (987 pitches from RHP, 649 pitches from LHP):

It seems like Howard lets off the high fastball more than Reynolds does (or makes more contact), keeping his whiff rate below 30% against fastballs while Reynolds reached the 40% range. But just as Reynolds falls victim to low and inside fastballs from right-handed pitchers occasionally, Howard whiffs at low and inside fastballs from left-handed pitchers. Take another look at Reynolds' four-seam fastball whiff plots and notice the symmetry based on handedness compared to Howard's.

Here's a look at Howard against sliders (892 from RHP, 817 from LHP):

Looking at Reynolds' whiff rates against sliders, there's that symmetry again, but for both batters, it seems as if the opposite handed pitcher is more successful at getting either batter to whiff on sliders, which suggests that one way a pitcher can counter an opposite-handed batter's platoon advantage is to throw low and inside sliders. Of course, that's based on a sample size of the two most whiff-prone hitters in the MLB, so take that suggestion with a grain of salt.

Let's look at Howard against curveballs (675 from RHP, 518 from LHP):

These look similar to that of Reynolds, except that Howard swings and misses on curveballs more from LHP while Reynolds whiffs on curveballs from RHP, again, because of the opposite handedness.

Finally, and this is good, let's see if Ryan Howard falls victim to changeups the same way that Mark Reynolds does (982 from RHP, 274 from LHP):

Now this is telling (I'll eventually find and use another adjective to describe my amazement at a discovery). Howard swings and misses at over 30% of changeups in nearly all parts within the strikezone while he is particularly weak against low changeups from left-handed hitters at over 40% whiff rate, just like Reynolds' weakness against RHP changeups.

Maybe it's just coincidence that two power hitters with the highest whiff rates, one right-handed and the other left-handed, are weakest against same-handed changeups all over the strikezone but particularly low around the knees. Either way, it's definitely interesting to realize the main weaknesses of Reynolds and Howard. I'd imagine that knowing where to throw a certain pitch and being able to combine them effectively will get Reynolds and/or Howard to continue whiffing at a high rate. I'd also imagine that the difference between a deceptively low and inside slider and a hanging one is minuscule, even for a major league pitcher, just as a high fastball out of the zone could just as easily go down the middle of the plate. Of course, those are the types of pitches that both Reynolds and Howard can and routinely do crush out of the ballpark. To confirm that, we'll have to look at slugging percentage by pitch type another time.

Mark Reynolds' Whiffs by Pitch Type

2010-08-24T22:34:00.010-05:00

Mark Reynolds is perhaps one of the more interesting power hitters heading into his prime this season. He has led the entire league in strikeouts since 2008, holding the all-time record for most strikeouts in a season with 223 K's last season.

This year, he leads the league once again in strikeouts, as well as perennial leader in swinging strike percentage. He has whiffed on 17.3% of all pitches this season, second place being Ryan Howard at 14.4%. Interestingly, Reynolds does not actually swing at everything a la Jeff Francoeur (60.7% swing percentage) and is barely in the top 50 in percentage of pitches he swings at with 46.8%. This makes it even more amazing that Reynolds leads the league in strikeouts and swinging strike percentage regularly without even taking that many swings. That's a lot of whiffing going on, and I do suppose that the rare times he does connect the bat to the ball, he hits it hard.

I wanted to know more about Mark Reynolds' swinging strike percentages to see how he fares against certain pitch types by handedness. Of the five main pitch types, fastballs, sliders, cutters, curveballs, and changeups, Mark Reynolds has seen cutters less than 200 times since his debut, 139 cutters from right-handed pitchers and 41 cutters from left-handed pitchers. He has seen at least 200 pitches for the other pitch types for right-handed pitchers or left-handed pitchers. Ignoring cutters due to small sample size, I will take a look at Reynolds' swinging strike percentages against four-seam fastballs, sliders, curveballs, and changeups.

Let's take a look at Mark Reynolds' swinging strike percentages against four-seam fastballs split by RHP and LHP (1435 pitches from RHP, 468 pitches from LHP):

Here, it looks like Reynolds falls victim to high fastballs from both right-handers and left-handers. For Reynolds, he whiffs on the outside fastball from LHP stick out as well as the low and inside fastball from RHP.

Here's a look at Reynolds against sliders (1542 from RHP, 224 from LHP):

This is interesting. Reynolds strikes out far more against right-handed pitchers than against left-handed pitchers, but he tends to swing at (and miss) sliders coming from LHP more than he does from RHP. LHP sliders come low and inside while RHP sliders go low and outside, but even LHP sliders coming in from low and outside are swung at and missed by Reynolds.

Curveballs against Reynolds are a whole different story (567 from RHP, 228 from LHP):

Here, Reynolds clearly struggles at connecting on curveballs from right-handed pitchers, some in the strikezone and most low and outside the strikezone. Curveballs from LHP also get Reynolds to whiff sometimes on the inside part of the plate as well as the lower part.

Finally, here's a look at Reynolds against changeups, which look like his greatest weakness when it comes to missing pitches (430 from RHP, 338 from LHP):

This is very telling. The splits against changeups are very different, as Reynolds whiffs on over 50% of changeups from right-handers that are located on the edge of the strikezone at the bottom. This is much different from LHP changeups, where any spot doesn't look to cross over 30% whiff rate, except the lower righthand corner of the zone. What's also crazy about this is that when you look at Reynolds against changeups in general, he misses at around 20% of nearly all changeups low outside and nearly all areas within the strikezone as well.

From these plots, there are characteristics of Reynolds' swinging strikes that are similar to conventional thought and common knowledge, such as chasing high fastballs or low breaking balls. But the key to exploiting Reynolds' weakness at missing the ball when swinging is definitely throwing timely changeups, especially from right-handed pitchers, while it seems that Reynolds is less prone to whiff against LHP curveballs the most.

Roy Halladay's Pitches

2010-08-22T21:29:00.007-05:00

Roy Halladay has an array of pitches that he uses, and just got even better this season by modifying his changeup to create a different movement while using it more often. Looking at Halladay's pitch type table at Fangraphs, he is using his new changeup 12% of the time this season compared to less than 5% in previous seasons.

I wanted to take a look at Halladay's different pitches to see which ones he gets the highest percentage of swinging strikes off of. The best step to take in order to compare pitch types would be to generate run value heat maps, but seeing as that I still am experimenting with contour heat maps and local regression models, let's keep it simple first (just in case there are mistakes again). Also, I will be sampling at least 1000 pitches for most of my maps from now on. So instead of looking at his changeups, let's take a look at the swinging strike probability models on Halladay's other great pitches, the four-seam fastball, cutter, and curveball:

Halladay, a right-handed pitcher, gets swinging strikes on high four-seam fastballs against right-handed hitters and high and inside fastballs against left-handed hitters. His cutters go outside on RHH and inside on LHH, getting RHH to whiff on cutters in the zone and LHH to whiff low and inside. Halladay's curveballs are the real meat here in terms of getting batters to whiff, as around 30-40% of curveballs thrown down and away from RHH and down and inside to LHH get batters to whiff.

What can I say? Halladay is one of the best pitchers in our generation, and I haven't even showed the results of his changeup yet. According to Fangraphs' pitch type values for Halladay, his cutter is his most valuable pitch, followed by his curveball, four-seamer, and changeup. But it's his new changeup that's been the most improved since last season, after he made adjustments to the grip on his changeup this offseason.

Corrections to previous Kershaw post

2010-08-22T10:33:00.014-05:00

Long story short, I was fine-tuning the regression methods I've been employing to generate those pitch location heat maps, my first example being Clayton Kershaw's slider and curveball. A couple of hours working on this and I realized that much of what was graphed was incorrect (in fact, disregard my previous post). I'm going to reproduce the swinging strike percentage graphs from my last post, which make a lot more sense now (not as high SwStr% values of 60%, smoother plots, down in the strikezone instead of up in the zone, etc.):

These (hopefully) corrected plots still show that Kershaw's sliders induce more swinging strikes than his curveballs. The differences between these ones and the previous post are that the breaking pitches are inducing swinging strikes down in the zone, not up in the zone (the orientation was off in the first post). Needless to say, I regret that I did not mention this in my first post, although I did find the images very fishy. I'm still fine-tuning these sort of local regression models and turning them into surface-fitted filled contour maps. I had several post ideas following the Kershaw one, including a look at Tim Lincecum's pitches and what went wrong this season compared to last season, but I may have to take some time to fully understand the statistics and the method behind the madness of these heat maps before I make a post and include my interpretations again.

Sample size is a huge issue, and I have been informed that looking at a particular pitcher's pitch type may not be suitable for a local regression surface fitting precisely because the sample size is too small (about 200 pitches seems to be too small, especially when modeling swinging strike probabilities where the number of swinging strikes is in the dozens for this particular situation).

Hopefully I don't make this mistake again, but again, I started this blog in order to explore analytical ways of presenting sports information, including graphically, and I'm glad I'm learning a lot along the way.

Clayton Kershaw's Slider Is Sick-Nasty

2010-08-20T08:58:00.013-05:00

[Edit 2: Since the original post, I found that some of the later plots had incorrect parameters, and therefore, should be ignored. They do not accurately represent Kershaw's swinging strike and contact percentages. You can take a look at the updated swinging strike percentages for his slider and curveball here.]

Sir Clayton Kershaw, he of the curveball nicknamed by Vin Scully "Public Enemy No.1," has been mighty magnificent this season with a 3.03 ERA and 163 K's through 157.1 innings (a side note: I would have linked the Youtube clip of Scully's call of Kershaw's huge curveball striking out a stunned Sean Casey during March 2008, but it was gone a week or so after I saw it over two years ago).

[Edit: Here's a grainy video of Scully's call at metatube, hat-tip to Bill Plaschke's sweater.]

But I believe that it's really been Kershaw's slider that has been helping him so much as an additional new toy for him to fool batters with. It's always great to add another pitch to a tandem arsenal like Kershaw's fastball/curveball combination, and the effectiveness of Kershaw's slider really shows how Kershaw has another weapon to induce swinging strikes. According to Fangraphs, Kershaw threw his slider on 7% of pitches in 2009 but 19% of pitches in 2010 so far.

Let's conduct a closer examination of Kershaw's pitch types since his ML debut by looking at the month-by-month table below to show when Kershaw introduced his slider and how much he's used it since then:

Keen Dodger fans have taken note of Kershaw's use of his new slider, but I didn't know he started using it so much, or significantly more than his famous curveball. If you check this out, you'll notice that he introduced his slider sometime during June 2009. Since then, he's gradually used his slider more and more and his curve ball less and less. This doesn't mean that his slider is more effective than his curve ball, as part of a pitcher's effectiveness is his ability to mix and match and locate different types of pitches given the previous pitch (for what it's worth, Kershaw's pitch type values at Fangraphs show that his above-average slider has been more valuable than his below-average curveball this season, attaining a 1.63 wFB/C and a -0.82 wCB/C, but please ignore those numbers if you don't know what they stand for).

Let's take a quick look at the pitch movement plots of Kershaw's curveball and slider:

Looks like Kershaw gets a lot of movement on both his curveball and slider, but it's the vertical movement of his curveball that sticks out here. That 12-6 break that everyone always talks about has really made his curveball into a filthy moving pitch. The slider isn't too shabby either, with huge horizontal movement to the left (from the catcher's perspective).

This brings up some interesting questions I have about Kershaw. Suppose I want to take a look at the effectiveness of Kershaw's curveball vs. Kershaw's slider (and yes, I do). For a few weeks now, I've been playing with my PITCHf/x database and learning to make pitch location plots, including the hexagonal binning plots you see above. However, it's difficult to compare between two types of pitches for the same criterion, say, swinging strikes on Kershaw's curveball vs. swinging strikes on Kershaw's slider, especially for normal scatter plots, because all you see are a bunch of dots (see my recent post about Jonathan Broxton and you'll know what I'm talking about). You can get information about where Kershaw locates his two pitches to induce swinging strikes, but you can't compare how well Kershaw does it with his curveball vs. his slider just by simple scatter plots. I suppose I could just show a table of Kershaw's swinging strike percentage by pitch and by month, but it's more telling and effective (and fun) to see the pitches in the strikezone for yourself.

Enter Dave Allen and Jeremy Greenhouse. I believe the idea of plotting PITCHf/x data in the form of heat maps was first popularized by Allen, and Greenhouse has also done fantastic work with heat maps of his own. With the help of both of these guys, I was able to figure out how to fit a surface model and plot them on filled contour plots. In this case, instead of plotting the actual curveballs that Kershaw pitched that caused a swinging strike, I ran a model to predict swinging strike percentage based on location, looking at all of Kershaw's curveballs and how often those pitches caused a batter to swing and miss. Creating a filled contour plot, much like what you see in infrared imaging and topographical elevation mapping, allows me to smooth out the data in order to see if there are any trends.

It's fitting that I make my first of these images for the Dodgers' best (read: best) starting pitcher, Clayton Kershaw. Let's take a look at the first of them, shall we? Here's Kershaw's swinging percentages on curveballs:

Note that there were 901 curveballs against RHH and 235 curveballs against LHH. I scaled the colors on the graph to range from 0% to 60% (shown as 0.0 to 0.6 in the legend) so that you can compare these with the slider graphs later, red being a very high swinging strike percentage, blue being near zero swinging strike percentage. I suppose the scale would be better read if I put them in percentages, but I'll discuss these values in 0-100% terminology rather than 0.0-1.0.

Let's discuss Kershaw's curveball. First of all, recall that Kershaw has great negative vertical movement as well as negative (left in the catcher's view) horizontal movement. As a left-handed pitcher, curveballs will go down and toward right-handed hitters and down and away from left-handed hitters. If you take a look at the bottom lefthand corner for left-handed hitters, you'll notice a green "hill," showing that Kershaw gets up to 30% of LH batters to swing and miss out of the zone when he throws his curveball there. The middle of the zone and low outside the zone actually get left-handed hitters to swing and miss the most. And as expected, LHH whiff more often overall than RHH on Kershaw's curveball.

However, the most interesting part is where you see a shade of green in the middle of the strike zone for right-handed hitters, where about 45-50% of RH batters whiff. But there's a blue spot to the immediate left of Kershaw's "hot spot," which looks like the spot where right-handed hitters get the sweet spot of the bat (or at least, contact). With a curveball as huge of a vertical break as Kershaw has, sometimes there's not much a hitter can do when he sees it coming toward the strikezone but to swing and hope it connects with the ball. In this case, that blue spot might just be where the batter swings and connects most often (and where Kershaw should avoid with his curveball).

Let's compare this with the swinging strike percentage of Kershaw's newest pitch, his slider, again looking at handedness splits:

Note that there were 473 sliders against RHH and 188 sliders against LHH. There's a lot more color in this plot, which tells us right away that Kershaw's sliders are getting more batters to swing and miss than his curveballs. The entire outside edge for lefties has up to 60% swinging strike percentage when batters are fooled and swing and miss, while the middle of the strikezone causes even more whiffs for righties. Low sliders also look like they fool both RHH and LHH.

Remember that these are models, not the actual pitches themselves, and that in order to get this graph to look smooth, the model may have overemphasized some hot spots. This is due to sample size. Still, it's very clear from these graphs that hitters swing and miss on a higher percentage of Kershaw's sliders than his curveballs.

Swinging and missing a lot means less contact. Let's take a look at hitters' contact percentage on Kershaw's curveballs and sliders, seeing if they agree with the previous swinging strike percentage plots:

Some good stuff here. Not sure what to make of the long red streak down the middle of the RHH graph, but perhaps that's where right-handed hitters make contact (fouling off pitches possibly?). Right-handed hitters make contact throughout much of the strikezone, around 30% to 45%, while left-handed hitters make contact mainly in the middle and/or up in the zone or out of it. I believe the red spot (50-60%) out of the zone is where many left-handed hitters foul off hanging curveballs. Either way, hanging curveballs that are up in the zone, even out of the zone, do not bode well for Kershaw, as they cause both righties and lefties to make decent contact.

Let's compare this with the contact percentage of Kershaw's slider, again with handedness splits:

At first glance, it looks like that hitters get more contact off Kershaw's sliders due to the red. But notice that most of the red for both RHH and LHH is out of the zone, likely meaning that although hitters make contact 60% of the time or more, they are probably mostly foul balls or pop-ups. Still, it's a vulnerable spot to leave a hanging slider. But notice that there is very little contact in most of the strikezone (the lucky ones who do get hits off Kershaw's best-placed sliders are drowned out by the many many more unlucky ones who don't). At the very least, Kershaw's sliders do not draw as much contact, and presumably hard contact from hitters as compared to his curveballs.

Remember how I mentioned earlier that Kershaw's curveball this season has been more valuable than his slider, according to Fangraph's run values? All of the plots seem to agree that Clayton Kershaw's newest pitch is even more effective than the one he is most known for. Not only does Kershaw's slider cause more batters to whiff than his curveball, but hitters are less likely to make contact off his slider as well. Maybe there is a new Public Enemy No.1 that less people are talking about. I prefer to call it Kershaw's sick-nasty slider.

What's Wrong With Jonathan Broxton?

2010-08-18T21:37:00.012-05:00

Never mind that the Dodgers are 4th in the NL West and over 11 games behind the Padres. Jonathan Broxton, known early on as "The Ox," has lost his closer role due to three blown saves in July and August. He has been wild, uncharacteristically wild. While he's still striking out a ton at 11.4 per 9 IP, he has walked more batters than struck out since the All-Star Break, resulting in a post-All-Star 8.10 ERA and 2.10 WHIP.

Every pitch ends in five distinct outcomes: ball, called strike, foul, in play, and swinging strike. I wanted to take a month-by-month look at these five outcomes of Broxton's fastballs and sliders since 2007. If we take a look at the percentages that each outcome occurred by month, maybe we can glean some information about what's wrong with Broxton. But I realized that the sample size for each month got pretty small, so instead, let's take a look at the average velocity and result of Broxton's fastballs by two-month periods (October games included with August and September) since April/May 2007:

First of all, take note Broxton's fastball outcome breakdown is not the end-all, be-all of his troubles. Command issues and being hit hard can be separate things, as struggling with command could be due to injuries and the like while being hit hard could be the result of a high BABIP, just plain bad luck. Still, this information should tell us something about Broxton's recent struggles as well as the dominant months of his career. First thing to notice is that Broxton's average velocity is consistently down compared to recent years. His fastball was hovering around 95.6 MPH during the first two months of this season after consistently averaging above 97 MPH in the previous two seasons. It seems to have gotten worse as the season has gone on (and the walks and runs started piling up), and Broxton is averaging a flat 95 MPH in August. This is a significant loss of velocity for his standards of hitting 98 MPH on the gun consistently.

The second thing I notice is Broxton's swinging strike percentage vs. his ball percentage. It's particularly off so far in August, with Broxton throwing balls 55% of the time compared the 30-35% in previous two-month periods. His swinging strike percentage is low, as well as his foul ball percentage. Batters are actually making less contact off Broxton this month, but that is misleading due to the high number of balls he's been throwing outside the strikezone. Sure, Broxton has only allowed 9.1% of balls in play in August thus far, but compare this to the other period that he allowed less than 10% of pitches to be put in play, and you'll recall that during that period in April/May of 2009, Broxton had 39 K's in 20 IP with a 1.44 ERA and holding batters to a .096/.200/.145 line. This is very different from the 6.75 ERA and .259/.394/.426 line recently since the beginning of July. Broxton's high ball% on fastballs has allowed runners to get on base, and his loss in fastball velocity suggests that hitters are able to get more solid contact off his pitches when they do.

Let's look at the average velocity and % of outcomes of Broxton's sliders now:

Broxton throws about 2/3 less sliders than he throws fastballs, which decreases the two-month period sample sizes by a lot, returning the volatile results you see above. Still, it's plain to see that Broxton's slider velocity is also down, around 86-87 MPH rather than the norm of 88-89 MPH. This is concerning, because Broxton's slider is effective and fools hitters into swinging out of the zone when it has the most movement, and his decrease in speed might indicate that he's also lost movement. As a result, since June, Broxton's slider has resulted in swinging strikes only 15% of the time, compared to the usual 25-28% when he is on top of his game. It may be interesting to note that 30% of Broxton's sliders in August were put into play and only 5% were fouled off, but the sample size here only consists of 20 sliders, so take that with several grains of salt.

Finally, let's just take an overall look at the pitch locations and movements of Broxton's four-seam fastballs and sliders this year vs. previous years:

Lots to digest here and some interesting stuff going on. First of all, I'm definitely still in "experiment mode" with R plotting, as you can tell by the paint splatter all over the legend in the fastball location plot. Also still trying to figure out how to get hexbin plots on the same graph, in order to show a gradient color scale instead of just a blotch of singular-colored paint.

Aside from that, let's focus on the pitch movement plots instead of the pitch location plots (there are just too many pitches in the pitch location plots to glean any meaningful information from non-splits data except, maybe, that Broxton throws his slider low and away from right-handed hitters). The four-seam fastball movement plot is very very telling. I noted earlier that Broxton's velocity has decreased this season compared to previous seasons, and this plot shows that Broxton's fastballs are not moving as much as well. It's a pretty significant difference. If Broxton's loss in velocity can affect his "rising effect" movement on his fastball that much, it makes it that much easier for hitters to get around in time AND to make solid contact on this pitch.

The slider movement plot is similar. There is less vertical movement on the 2010 sliders (blue) than all of the other sliders from 2007 to 2009 but similar horizontal movement. It's clear to me that both Broxton's four-seam fastballs and sliders have been more ineffective this 2010 season than previous seasons, largely because of their loss in speed and hence movement. This resulted in the disparity we saw in swinging strike percentage this year and previous years, and is a precursor to the hard hits off Broxton. Along with the loss of control that Broxton has had this season, throwing more balls than ever before, this has resulted in Broxton's ineffectiveness this season (at least compared to the stellar campaigns of previous years).

Frankly, Broxton just hasn't been the same pitcher, and it's pretty blatantly showing up in both of his main pitches, his four-seamer and the slider (I didn't look at changeups because he doesn't throw that many). There are all sorts of reasons for why this has happened, and to be honest, I think it's on the coaches and pitching coach Rick Honeycutt to figure out what's wrong with Broxton's pitches. If there was an internal mechanics change from spring training or something, they have to recorrect it back if they want Broxton to be a top NL closer again. Maybe he's nursing an injury and Broxton and/or the Dodgers are hiding it. Sure, taking Broxton out of the closer role and putting him in the time-out chair might help him settle down, but fundamentally, Broxton has been a different pitcher as of late and needs to correct whatever it is that's wrong. I feel that these location and movement issues are what the Dodgers and the media should focus on, rather than his "makeup" or his "fear of Carlos Ruiz" or that "he isn't a winner" and "doesn't have what it takes" etc. etc. etc.

The Anatomy of a Block: Points Created (Part 5)

2010-08-16T01:33:00.017-05:00

In case you missed it, check out Parts 1, 2, 3, and 4 in this series on "The Anatomy of a Block": Introduction, By Shot Location, By Shot Type, and Repeatable Skill.

This is a long post coming up, but I hope you try to read it to the end, as I believe I uncovered the most interesting findings so far in this study. I mentioned last post that I would be doing a summary of my findings and concluding with improvements and possible future study ideas on the value of a block. Turns out that there is a lot more to work on and a lot more ahead, but for the time being, this will be the last post in this series on "The Anatomy of a Block," which will almost certainly be re-continued sometime in the future.

It's amazing what social media and the strong online basketball community has been able to help me with in terms of understanding the merits of this study, but much more so the limitations and areas for improvement. In the end, I believe the analysis on the value of blocks based on shot location and shot type may be worth it, but that it is limited in assessing the defensive value of players, and even assessing the value of a block itself. There are a host of other factors that go into determining the quantitative value of a block and its effects on the game, not just shot location and shot type. I suppose this is a consequence of every area of research, in that an examination of one part of the analysis will never be complete and always has room for improvement.

Before I go into the other components to take into account when evaluating the value of a block, let me first address a few problems from my previous posts, thanks to the critical evaluations of readers. My initial idea of assigning a number to a block based on shot location and shot type eventually came up with an average value of a block for each shot-blocker, and hence, my main analysis revolved around measures in the units of PPS (points per shot). To recall, I looked at points saved per block by shot location and points saved per block by shot type. I did not give credit to the actual quantity of blocks amassed by the Marcus Cambys and the Dwight Howards when discussing the PPS values, and I realize that I should not have neglected it. Even if Dwight Howard does not get as high value per block (based on location or type) as Amare Stoudemire (both with over 10,000 minutes played since 2007), it would be misguided to suggest that Stoudemire was more valuable from the shot-blocking perspective than Howard when Howard's 791 blocks since 2007 (2.43 per game) is much greater than Stoudemire's 413 blocks (1.40 per game).

Here's a tabular reproduction of the top 25 shot-blockers in total blocks since 2007 with additional columns of points saved per 36 minutes played for shot location and shot type as well as a look at the top and bottom shot-blockers in that category (minimum of 200 blocks and 1.00 blocks per game since 2007):

I sorted by shot location in the top and bottom points saved per 36 MP because it's generally the same as by shot type (and also because I found R2 values of 0.40 and 0.18 respectively for season-by-season fluctuations, meaning that shot location seems like the more reliable measurement for points saved by block). Factoring in the total number of blocks given the amount of minutes a player plays changes our evaluation of who attains the most value from blocks on a per unit time basis. Marcus Camby is one of the noticeable top shot-blockers in this measurement, as well as Alonzo Mourning and Chris Anderson, two players I talked about in previous posts. Take note that Dwight Howard, despite averaging 2.43 BPG, was 10th in points saved per 36 MP. Looking at the bottom guys, guys like Chris Bosh who had high value per block get penalized for only getting just over 1 block per game, while guys like Pau Gasol, Amare Stoudemire, and Elton Brand post low points saved per 36 MP while averaging around 1.40-1.70 BPG.

Now here's the real meat of this exercise, something I've only touched briefly on previously. To summarize what we've looked at thus far, we tried to figure out the value of a block based on shot location and on shot type, forming a "Points Saved" model. However, there are several problems and possible areas of future research I see:

Probability of shot-blocker to commit a shooting foul
Probability of shot-blocker to commit a goaltending violation
Blocks per block attempt and/or block opportunity
Altering a shot without recording a block
Keeping a player away from the basket and forcing tough shots

The first two are definitely possible to take into account for each shot-blocker. The last three, however, must be noted when using the shot location and shot type models in this series. Some players may block low percentage shots precisely because it is better to force a tough shot in the first place. This includes forcing the shooter to take a shot out of position as well as altering the shot type (turning an open jump shot into a fade away, or turning an easy layup into a reverse layup).

Ideally, the numbers presented in this series should be taken with a grain of salt, and combined with what you see when you scout video with your own eyes. If a defensive player is very good at keeping the guard out of the paint, he is doing his job of forcing the guard to find other opportunities for points rather than taking the high percentage shot. And if the guard goes up for a difficult shot, and the player blocks it, this is the preferred defensive strategy than to block a high percentage shot, even though he is penalized by the shot location and shot type models.

The other side of blocks that I mentioned in the introduction of this series (and also a part of John Huizinga and Sandy Weil's work) is the "points created" part, which is the effect of a block on the shot-blocker's own team's expected points during the next possession. This part may be perhaps the most valuable side of a block that I haven't accounted for, in that blocks that lead to turnovers and create fastbreak points from transition baskets (known as "Russells") are more valuable than blocks that end up back in the offense's hands. Probably the part of the points created side that affects the value of blocks the most because of both its per block value and its total value is number of changes in possession, or possessions gained.

I'd like to take a preliminary look at points created by looking at who has possession after a block. The way I see it, the immediate post-block situation after any blocked shot falls into three categories in terms of possessions:

Possessions gained by the defense (the shot-blocker's team)
Possessions recovered by the offense
Jump ball

If we consider that possessions gained as one possession, no change in possession as zero, and a jump ball as 0.5 possessions (50% chance for either team to get possession on a jump ball), we can formulate the average possessions gained per shot-blocker and per block.

Let's look at the top 25 block totalers as well as the top 15 and bottom 15 shot-blockers in possessions gained per block between 2007-2010, along with their season values to see if these numbers are consistent (consider that 57% is the average possessions gained per block):

Lots of revealing stuff going on here. Remember how I touted Chris Anderson for his points saved per block numbers? Looks like he'd be among those in the bottom of the league for a points created per block model, as his blocks resulted in a possession gained only 51.39% of the time, the worst value since 2007 for the players sampled. Lamar Odom tops it off with 65.84% since 2007, while the best season was Joel Przybilla in 2007 with 70.90%. Andris Biedrins had the worst season with a low value of 42.22% this past season, and was mainly average in his previous three seasons. The other player I noted who performed poorly in the points saved model was Brendan Haywood, and he's among the league leaders in possessions gained per block with 61.89% (again, compare this with the league average of 57%).

Finally, how do we combine the points saved model (using shot location and ignoring shot type) with the points created model, which is in the form of possessions gained? Using the league points per possession values for each season between 2007 and 2010, I calculated points created for each possession gained, then added it to the points saved. Let's take a look at some of these numbers since 2007 (minimum of 200 total blocks and 1.00 blocks per game since 2007):

Alonzo Mourning may be the best shot-blocker in the past 5 years, if not one of the best in our generation as his blocks are worth 6.528 points per 36 minutes played. Even though he averaged less blocks per game (2.16 BPG) in this last two seasons, he beat Marcus Camby (2.79 BPG) by over 1.5 points per 36 MP (6.528 pts/36MP vs. 4.920 pts/36MP). Chris Anderson is second, who more than makes up for his low possessions gained per block with 2.12 blocks per game, reaching a block value of 6.138 points per 36 MP. Guys like Joel Anthony and Ronny Turiaf also have high block value given their minutes. For the players sampled, the lowest points saved and points created yields players like Chris Bosh, Kevin Garnett, Amare Stoudemire, and Pau Gasol, players who averaged total block values less than 2.5 points per 36 MP since 2007.

This is my longest post yet in this series, but if you made it this far, I'm glad that you did and I hope you enjoyed what I found. I believe that this is only the starting point to analyze the value of blocks better, and this at least provides more information than total blocks or blocks per game in determining who are the best shot-blockers in the NBA. One thing of note is that I found very little season-by-season correlation in the possessions gained stat, which indicates that points created from blocks may fluctuate too greatly from year to year to be attributed fully to a player's shot-blocking skill. Still, these numbers can help us understand the value of blocks from past seasons better. I would still like to reiterate that numbers in measuring block value are not enough, and that they should be evaluated in conjunction with professional video scouting, especially in a dynamic team game like basketball where defense is many things other than blocks.

That's it for this series on the value of a blocked shot, at least, for the time being. If there is something you like (or didn't like), I welcome you to leave a comment or two. I'd like to put this project to rest (or on hold) for awhile, as there are other things in sports that I would like to write about. Nevertheless, I hope you enjoyed this series as much as I have.

The Anatomy of a Block: Repeatable Skill? (Part 4)

2010-08-13T09:01:00.008-05:00

In case you missed it, check out Parts 1, 2, and 3 in this series on "The Anatomy of a Block": Introduction, By Shot Location, and By Shot Type.

In this post, I'll take a look at whether or not value of blocks as measured by shot location and value by shot type is a repeatable skill. The premise is that if a skill in sports is measured effectively, then there should be reasonable expectations that the statistic measuring the skill will remain consistent from year to year, making the skill repeatable. One of the tests of the value of a statistic in objective evaluation is looking at how much that statistic varies with time for each player. Essentially, if a set of numbers fluctuates from year to year for not just one but most players, then that provides evidence that a certain skill (such as blocking certain shots based on location or type) may not be repeatable. This type of analysis looking at the correlation between what a player does one year with what a player does the next year is used in preliminary studies before determining the existence of the hot hand, clutch hitting in baseball, and how much control a pitcher has over the number of hits he allows.

Here's a look at the block value by shot location of the top 25 shot-blockers in total blocks since 2007 along with their season-by-season values to see if they fluctuate:

The color scale of the cells should give you an idea of how much points saved per block by shot location vary from season to season for these 25 players. For instance, if you look at the '2007' column and the '2010' column from left to right, you can see the colors of the cells change or stay the same, particularly for players with high value blocks such as Andrew Bogut, Emeka Okafor, and Josh Smith as well as players with low value blocks such as Andris Biedrins and Brendan Haywood. You can also notice some players with a little bit higher statistical fluctuation in their season-by-season value per block numbers, such as Ronny Turiaf. The standard deviation column on the far right is a measure of how spread out these numbers are, and captures a sense of how much the numbers fluctuate. A further discussion on the validity of this measurement gets into a statistical discourse covering other stats terms that I won't get into right now, but for the most part, these standard deviation values are relatively small and speak that the data is uniform from season to season (more likely that blocking shots based on location is a repeatable skill) more than it is volatile (less likely that the numbers are affected too greatly by random fluctuations).

Now here's a look at the block value by shot type of the same top 25 shot-blockers in total blocks since 2007 with their season-by-season values:

Again, the color scale of 2007, 2008, 2009, and 2010 shows mostly consistency from left to right, save for a few players. This time, Jermaine O'Neal has the most fluctuations in his values by season, ranging from 0.903 PPS in 2009 to 1.102 PPS in 2007. Other than O'Neal, however, it seems to me that shot-blockers with high value per block tend to have high values for all four seasons, and vice versa with shot-blockers with low values. Brendan Haywood did attain a 1.011 PPS by shot type in 2007, but followed that with some of the lowest PPS numbers with 0.839 in 2008 and 0.847 in 2009.

All of this brings me into another thought about whether or not block value by shot location is correlated with block value by shot type. Let's look at a scatter plot of value by shot location against value by shot type using all 122 players I sampled:

R2 value of 0.3952 is decent, which is a measure of how correlated the two sets of data are, ranging from 0 to 1 where 0 is completely unrelated. However, shot location and shot type may speak to different types of blocks and skills needed in order to attain those blocks, even if different shot types are precisely defined by where they are taken on the court (all dunks and layups are at rim and 3-pointers are at a distance, for instance). Also, I believe a more intrinsic evaluation on the interaction effects between types of shots and where they are on the court would need to be conducted in order to properly assess how the block value models affect one another and combine both models.

I'm sure many of you think a lot of this is just statistical blabber jabber, and I do too, so I'll just leave it at that for part 4. In my next and last post on this rather long series, I will be concluding with a summary (in words, not tables and charts and numbers) on what I found and detailing an exhaustive list I have compiled on the limitations of the study on blocks as well as possible future improvements and extensions. I hope to be getting back to doing more posts on what I've been working on with shot location heat maps, baseball PITCHf/x, and football play-by-play data, so in a sense, I'm rushing along to get this series done ;).

The Anatomy of a Block: By Shot Type (Part 3)

2010-08-11T10:00:00.008-05:00

In case you missed it, check out Parts 1 and 2 in this series on "The Anatomy of a Block": Introduction and By Shot Location.

In this post, I'll take a look at the value of a blocked shot based on the shot type. The first thing to figure out is what type of shot types are recorded in the PbP dataset provided by Basketball Geek (I really can't stress enough how thankful I am that Ryan J. Parker provided this data). I grouped every shot with a recorded shot type from the 2007-2010 seasons and found the number of shots taken as well as the total points scored in order to figure out points per shot by shot type (there are 63 different types of shots in the PbP data). Let's look at several lists of shot types: 1) Most shots taken, 2) Highest points per shot, and 3) Lowest points per shot.

Big top 15 tables there. I've added effective field goal percentage (eFG%) which is just field goal percentage taking 3-pointers into account (however, I will be talking in terms of PPS rather than eFG% in order to remain consistent throughout this study). Most shots are categorized generically, for example, jump or layup or dunk instead of the more specific like jump bank hook or turnaround finger roll or putback reverse dunk. It's definitely interesting to see how many driving layups and reverse layups are distinguished from the generic layup.

In the second table, clearly dunks and layups of the eclectic variety return the most points per shot, with several thousand slam dunks averaging 1.956 points per shot (note here that an alley oop dunk averaged 1.814 PPS through four seasons of data, so next time your team messes up an alley oop dunk, it's alright to throw a tantrum). In the third table, generic jump shots (0.692 PPS) and hook shots (0.907 PPS) are the least efficient shots by this measure, but it's also important to note that the generic layup (0.914 PPS) is a close third. In addition to the 118,804 generic layups recorded, there are more than 69,000 other categorized layups as well, all of them being high value shots within 1.3-1.7 PPS.

Now let's take a look at which shot types result in or avoid being blocked the most: 1) Most shots blocked, 2) Highest % of shots blocked, and 3) Lowest % of shots blocked:

The second and third tables are the truly interesting ones here. 19.73% of all generic layups were blocked in 2007-2010, while 13.65% of all driving jump shots were blocked. Several other types of layups were also blocked more than 5% of the time. For these driving and reverse layups as well as the generic dunk, having efficient point values ranging from 1.345 PPS to 1.749 PPS are more important numbers than the block percentages. For instance, even though a guard driving in only to get blocked can be infuriating, keep in mind that a successful driving layup attempt goes in 73% of the time even if it is blocked 7.57% of the time (by successful, I mean successfully penetrating the defense up until the shot). Check out the end of this post to see the entire list of shot types.

Now let's go back to the players. Similar to the blocks by shot location post from yesterday, I took the points per shot for each shot type and multiplied that by the number of blocks of a particular shot type for each player. Summing it up, I found the total number of points saved by shot type and the points saved per block. Let's take a look at the top 25 shot-blockers in terms of total blocks since the 2007 season and see how they fared in points saved per block:

The values for points saved per block by shot type here actually vary more than the values by shot location I looked at yesterday. Here, Josh Smith (1.027 PPS) and Erick Dampier (1.022 PPS) saved the most points per blocked shot based on shot type in this top 25 list, while Andris Biedrins (0.860 PPS) and Brendan Haywood (0.875 PPS) saved the least, just like the table by shot location. Moving along, let's look at both the top 10 and bottom 10 shot-blockers in points saved per blocked shot based on the shot type (minimum of 200 blocks since 2007):

Chris Bosh (1.119 PPS), Joel Przybilla (1.112 PPS), and Chris Anderson (1.090 PPS) come out on top again, all three being among the top 10 in value by shot location. Andris Biedrins (0.860 PPS) and Andray Blatche (0.865 PPS) were also in the bottom 10 in value by shot location, but it's guys like Biedrins, Haywood (0.875 PPS), Roy Hibbert (0.876 PPS), and Shaq (0.879 PPS) who are noteworthy. The four appear in the bottom 10 of the other table, indicating that they are not as valuable to their teams for their shot-blocking abilities as we may have thought in the past by both measures.

Finally, and mostly just for fun, let's take a look at the players who tallied the most blocks since 2007 for different shot types:

Whew, hope you're still with me. Marcus Camby blocked the most generic layups, reverse layups, and running jump shots since 2007, second most for driving layups. To me, this says that Camby is very good at knowing when and where the shooter is just about to release his shot, whether it's off the dribble, a reverse, or a running jumper. Meanwhile, Dwight Howard blocked the most generic jump shots and hook shots since 2007. This tells me that Howard benefits greatly from a huge vertical leap in order to swat away these type of shots. (Diversion: A quick look online tells me that Howard has a 40-inch vertical jump. Current players with higher verticals include LeBron James, Shannon Brown, Vince Carter, Nate Robinson, and Gerald Green. Retired players with higher verticals include Spud Webb, Michael Jordan, Dee Brown, Shawn Kemp, and Dominique Wilkins. Definitely no surprises here.). Finally, Andre Iguodala, Tayshaun Prince, and Kevin Durant blocked the most 3-pointers since 2007.

Alright, that's part 3 of this series. As always, feel free to leave a comment if you found anything interesting or if you think there's a better way I can look at things. In my next post, I'll take a look at how block value by shot location relates with block value by shot type and whether or not these values fluctuate from season to season for different players.

The Anatomy of a Block: By Shot Location (Part 2)

2010-08-10T10:55:00.008-05:00

In case you missed it, check out Part 1 in this series, The Anatomy of a Block: Introduction.

In this post, I'll take a look at the value of a blocked shot based on the shot location. The conventional wisdom is that big men down low find plenty of shot-blocking opportunities in the painted area and that perhaps forwards and more athletic guards get blocks at the 3-point line and in the jump shot range. Each location on the grid of a basketball court can be assigned a point value based on the expected point value of a shot in that specific location. These assigned point values can then be totaled by the number of blocks in each location in order to come up with "points saved per block by shot location" for each player.

To do this, I looked at four seasons' worth of PbP data with over 750,000+ shots and their X,Y coordinates to indicate their locations. If you can imagine yourself standing behind the offense's basket, the X-axis runs from left to right along the baseline (the range of X values is 0 to 50, or 51 possible values) and the Y-axis runs from bottom to top toward and beyond the 3-point line (the range of Y values is 1 to 35, or 35 possible values). This forms the basis of a half court, where the center of the hoop is located at (25, 5.25).

For the 51*35 = 1785 shot location coordinates I looked at, I noted the total number of shots taken in each coordinate over the past four seasons and stored it in a matrix. Here's what the shot location frequency for the NBA in that time period looks like (excuse the color scheme and note that approximately 28% of the shots were taken at rim):

I then found the number of points scored in each coordinate over the past four seasons, and multiplied that by each element from the shot location frequency matrix. Basically, this shows me where the average NBA player was efficient with his shots, giving the expected point value for each shot location. Here's what the shot location efficiency for the NBA looks like (statistical noise shmatistical shmoise):
As you would expect, the high value shots (not necessarily high percentage) are either at rim or along the 3-point line, particular the corner 3s coming at 1.1 to 1.4 points per shot, or PPS. Jump shots just outside the key and near the baseline are low value shots, going down to 0.8 PPS. To give you a general idea of points per shot based on location, here's points per shot by distance from the basket in 2007-2010 according to Hoopdata.com:

Similar to the shot location efficiency heat map, at rim shots return the most points per shot at 1.208 PPS, with threes at 1.081 PPS and long twos at 0.801 PPS.

Taking the expected point values of each shot location coordinate multiplied by the number of blocks by a player in each coordinate, I found the total number of points saved by location and the points saved per block. Let's take a look at the top 25 shot-blockers in terms of total blocks since the 2007 season and see how they fared in points saved per block:

A quick glance at this table sorted by total blocks shows that although the top shot-blockers in block count nearly matches the number of points saved per block by location (notice how the column "Pts by loc" fades from green to yellow pretty consistently), the value of a player's blocks in terms of points saved per block varies. With the knowledge that the average is about 1.075 PPS, Andris Biedrins (0.982 PPS, or points saved per block if you prefer) and Brendan Haywood (0.987 PPS) clearly save the lowest in value per blocked shot on this top 25 list, while Andrew Bogut (1.152 PPS), Emeka Okafor (1.118 PPS), Tyrus Thomas (1.118 PPS), and Josh Smith (1.116 PPS) come out on top.

But do these shot-blockers, among the league leaders in most blocks, also lead the entire league in points saved per block? Let's take a look at the top 10 shot-blockers in value per blocked shot (minimum of 200 blocks since 2007):

Gerald Wallace comes out as the player with the most points saved per block at 1.163 PPS, despite averaging just under 1.00 block a game. Paul Millsap, Lamar Odom, and Shane Battier are other notable players that you wouldn't expect to get good value for each block, at least, according to shot location (perhaps this could be an extension to Battier's underappreciated defensive value to the Rockets). The most notable player on this list has got to be Chris Anderson. Not only has Anderson blocked 2.12 shots per game since being reinstated in 2008 from expulsion due to positive tests for abusive drugs, but he has also saved 1.130 PPS for each block. Whether this makes up for his relatively lacking presence on offense, that's for another study, but Anderson certainly may be one of the best shot-blockers in the NBA today. Bogut, Okafor, and Thomas are the only players on this list to also appear in the previous top 25 total blocks list.

What about the "overrated" shot-blockers in terms of points saved per blocked shot? Let's take a look at the bottom 10 (minimum of 200 blocks since 2007):

Andris Biedrins and Brendan Haywood appear again at the bottom with the least points saved per block, despite averaging 1.46 and 1.64 blocks per game since 2007. Dwyane Wade, Shawn Marion, and Kevin Durant are notable players who don't get as much value for each block they get, but this is likely due to their guard/forward position and the fact that they defend jump shots more often than the traditional shot-blocker. I lowered the minimum blocks to 100 and found there were other guards/forwards with low PPS saved by block as well, such as Baron Davis, Francisco Garcia, Grant Hill, and Stephen Jackson, the type of players you don't find in the high value points per block list.

Finally, here's a look at 15 notable players we haven't seen yet, sorted by blocks per game. I selected 15 of the younger and up-and-coming shot-blockers in the NBA from my spreadsheet. Let's see if we can spot any value in their shot-blocking ability by location:

So I lied, sue me. Alonzo Mourning and Dikembe Mutombo aren't exactly young and up-and-coming, currently aged 40 and 44 respectively. But for the years that this data was available for, Mourning (1.080 PPS) and Mutombo (1.124 PPS) weren't too shabby at blocking high value shots while approaching retirement when compared to the NBA average of 1.075 PPS. Hasheem Thabeet (1.119 PPS), Taj Gibson (1.115 PPS), and Serge Ibaka (1.084 PPS) are notable rookies from the past season with high value blocks based on location as well.

Looking at Greg Oden's 1.077 PPS and 1.43 BLK/G being above average, there is little doubt that his shot-blocking ability along with Camby (1.103 PPS, 2.79 BLK/G) and Przybilla (1.141 PPS, 1.29 BLK/G) will give the Portland Trail Blazers multiple defensive weapons to frustrate opposing offenses in the paint. If the Blazers ever need to go big, they could conceivably have two of three of these shot-blockers on the court at any given time along with LaMarcus Aldridge. They will take away minutes and block opportunities from one another, but no matter which way you slice it, it will be a force that could lead to many defensive stops if they spread out the defense effectively. The Camby/Przybilla/Oden combination does sound enticing, but the Blazers must allocate minutes and usage rate to their shot-blockers efficiently in order for the three-headed tandem to be effective.

That's it for part 2 of this series. If there is something you like (or didn't like), please feel free to leave a comment! In my next post, I will take a look at blocks based on shot type, with an interesting look at which players blocked the most dunks, jump shots, layups, etc.

The Anatomy of a Block: Introduction (Part 1)

2010-08-09T02:24:00.022-05:00

Blocks are a fundamental statistic in basketball. Along with steals, the number of blocks is often recorded and cited by fans and writers in order to evaluate a basketball player's defense. Generally, fans attribute steals to small and fast guards with quick hands, while blocks are a contribution by tall, high-flying centers and power forwards who can get off the ground quickly. No doubt, such qualities are assets on the defensive end of the basketball court, and racking up steals and/or blocks force the worst kinds of turnovers for the opposing offense, as many of them result in fast break opportunities for the defensive team in transition.

Yet, the number of blocks a player gets is but a summation of a general defensive weapon, and says nothing of the value that the actual block gave to the defense by preventing a basket opportunity on a shot attempt. Sure, players like Hakeem Olajuwon racked up hundreds, even thousands of blocks in their careers to make cases for themselves as one of the best defensive centers in NBA history. And this study is not trying to take away from those exceptional centers who were able to gain much for their teams by swatting away multiple balls on a nightly basis.

However, when it comes down to it, fans look at the number of blocks in a given season and use that as a ranking basis for the best defensive big men in the league. This is under the incorrect assumption that all blocks are the same. Are all blocks created equal? Does blocking a lay-up bring the same value as blocking a jump shot?

A study by a professor at the University of Chicago Booth School of Business named John Huizinga (you may know him as Yao Ming's agent) shows that, no, not all blocks are equal. At this year's MIT Sloan Sports Analytics Conference, Huizinga presented a paper titled "The Value of a Blocked Shot in the NBA: From Dwight Howard to Tim Duncan." In it, Huizinga explains how he and Sportsmetricians Consulting's Sandy Weil developed a database called Chances, using data provided by STATS, LLC. to compile the context of each event for the past 7 years, events such as blocks. The idea for this database is simple: instead looking at box scores, look at play-by-play accounts of the game in order to ascertain individual offensive opportunities. As Sandy Weil explains at his website, the two believe that "chances" are a very useful unit of account for many types of analysis of basketball. It allows you to easily sort and filter the context of an event, for instance, what happened before a shot attempt or what happened after a steal.

One of the key concepts that Huizinga presented about in order to understand the value of blocked shots was the preblock situation. This is basically what happened before the block occurred. As Sebastian Pruiti explains at NBA Playbook, this allows the analyst to differentiate between a block of a layup coming off a fast break opportunity vs. a block of a long off-balanced two-point jump shot, understanding that the former is more valuable than the latter. The idea that these two types of blocks are different comes from the fact that all shots taken have its own values, whether the shot was a slam dunk or a turnaround jumper. This leads us to expected point value, and since every block is attributed to a shot, the value of a block is naturally related to the expected point value of the shot attempt.

Looking at Pruiti's recap of the presentation, Huizinga closed his thoughts by going over what he calls "block value." To quote Pruiti, "to determine block value, Huizinga used the formula Points Saved + Points Created where Points Saved equals the effect of a Block on Opponents Expected Points during this possession and Points Created equals the effect of a Block on Own Team’s Expected Points during the next possession." This formula allowed Huizinga to determine overall block value, a better indicator of who was the best "shot blocker" in any given season.

Without having the benefit of the same database and viewing of Huizinga's paper (I can't seem to find it on Google, if it is online), I decided to take the idea Huizinga hatched and to do my own analysis with Basketball Geek's PbP data from the past four seasons. Thanks to Ryan J. Parker's hard work, there is a wealth of shots data in this PbP dataset, from the location of each shot to the shot type (ranging everything from turnaround fade away to driving reverse layup to putback dunk).

Whereas Huizinga looked at both points saved and points created (blocks that lead to fast break points, for instance), I looked at only points saved. I've developed two models for estimating the value of blocked shots (I will dedicate one post to each):

Points saved per block by shot location
Points saved per block by shot type

For the first model, this distinguishes blocked shots at rim (layups or dunks) vs. blocked 3-pointers or long 2s. Based on shot location, we can look at the value of a shot in any X and Y coordinate on the basketball court based on four seasons of data, and attribute each block to its corresponding value based on shot location. Adding this all up, we can determine which players saved the most points per block based on their shot location.

For the second model, this distinguishes blocked shots based on shot type, so dunks from layups, turnaround jumpers from pullup bank shots, driving reverse layups from tip-ins. Each block is attributed to a corresponding shot type value for which the shot was blocked. Adding this all up, we can determine which players saved the most points per block based on their shot type (with the added bonus of which players were the best at blocking dunks, layups, 3s, or mid-range jumpers).

In my next few installments of (at least) two parts, I will look at some of the findings I found from each block value model.

Finally, as an ode to the work that has been done by John Huizinga and Sandy Weil, here are some of their findings from what I could gather up that I may refer back to in my next posts (paraphrased from NBA Playbook and Peter Keating on ESPN Insider):

A jumper has an expected point value of 1.04.
A layup has an expected point value of 1.54.
69% of Brendan Haywood's blocks were jumpers (31% layups).
91% of Jermaine O'Neal's blocks were layups (9% jumpers).
Tim Duncan saved 1.12 points per block in 2008 (best season).
Dwight Howard saved 0.53 points per block in 2008 (worst season).

This introduction post is dedicated to Huizinga's work with Weil. Hopefully my findings will agree with and add on to theirs.

Holy Morrow

2010-08-09T01:18:00.008-05:00

So Brandon Morrow struck out 17 Rays yesterday, while having his no-hitter broken up with 2 outs in the 9th inning. Hopefully the novelty of striking out 17 hitters doesn't wear off and the near no-hitter doesn't take away from the fact that... well, Brandon Morrow has some sick stuff.

I'm still figuring out how to sync my pitch database for the 2010 season... which means I won't be able to take a look at my own PITCHf/x plots of Morrow's game just yet. Fortunately, there are some awesome PITCHf/x tools on the web, such as Joe Lefkowitz's website, Brooks Baseball, and TexasLeaguers.com. I will use those sites in the mean time if I want to take a look at current season pitch data, and just would like to give them lots of credit for the great work they've done for the baseball community (especially those like me who are not as well-versed in SQL and Perl).

Anyway, I pulled Morrow's 17 K's game from Brooks Baseball just to take a look at how he did. Of the 137 pitches he threw, 97 went for strikes, 63 were four-seam fastballs, 34 were splitters, 38 were sliders, and 2 were curveballs.

Of the 20 swinging strikes Morrow threw, 14 of them came on sliders while the other 6 came on four-seamers or splitters. On the other hand, of the 25 called strikes Morrow threw, 10 came on four-seamers, 11 came on splitters (amazingly, 10 of them fooled lefties), and only 4 came on either sliders or curveballs. The Rays made contact on four-seamers more than 60% of the time, as 33 four-seamers (52.4% of all 4FBs), 6 splitters (17.6% of all FSs), and 13 sliders (34.2% of all SLs) put the ball in play (only one of them resulted in a hit, obviously).

Morrow averaged 93.3 MPH on his four-seam fastball all game, including 93.4 MPH in the first three innings, 93.5 MPH in the middle three, and 93.1 MPH in the last three, indicating that he kept his fastball velocity up the entire game, going as high as 97 at one point.

I'd talk about the movement of Morrow's sliders, since they were the most responsible for those strikeouts today, but since it'd be a bit too tedious to plot their movements without the numbers inside my database, I'll link the video instead:

Rivera's Fastballs

2010-08-08T21:23:00.015-05:00

So, Mariano Rivera is pretty good. I thought I'd take a look at some of his PITCHf/x plots from 2007-2009. Before we go on, keep in mind that the pitch database that I have does not necessarily accurately categorize every fastball as cutter, sinker, four-seam fastball, etc. It is a well-known fact that Rivera throws only two pitches, well, three I suppose: the cutter and occasionally a four-seam fastball and a two-seam fastball. In the PITCHf/x database, FA, FC, and FF come up, which are generic fastballs, cutters, and four-seam fastballs respectively. Rivera's pitches between 2007-2009 break down and are categorized as follows:

FA: 897 pitches (28.7%)
FC: 1907 pitches (61.1%)
FF: 320 pitches (10.2%)

So bear in mind that some of his cutters which didn't have movement (intended or unintended) may have been categorized as generic fastballs, while some of them may also be two-seam or four-seam fastballs. Now let's take a look at some of his PITCHf/x plots from 2007-2009, split up by fastball type and batter handedness. Again, this is the catcher's POV, right-handed hitters standing on the left and left-handed hitters standing on the right:

The generic fastballs are all over the strikezone, and since these are likely just uncategorized cutters and four-seamers instead of exclusively two-seamers or four-seamers, there's not much to tell from the location plot there. Rivera's cutters, on the other hand, show Rivera hitting all over the strikezone, but consistently painting the outer edge for right-handed hitters and the inner edge for left-handed hitters, some up in the zone and some down and out of the zone. Since we know that Rivera's cutters and their locations are everything to his success in striking out hitters, these plots bolster Rivera's profile that his pitch locations are accurate. Four-seam fastballs (at least 10.2% of his pitches against RHH) are used to go on the inside of righties, but Rivera rarely throws them against lefties. Without a hexagonal binning plot or a filled contour, we can only see that he throws his four-seamer more frequently against RHH than LHH. Let's take a quick look at his pitch breakdown by opposing hitter handedness:

Against RHH:
FA: 497 pitches (31.8%)
FC: 842 pitches (53.9%)
FF: 222 pitches (14.3%)

Against LHH:
FA: 400 pitches (25.3%)
FC: 1083 pitches (68.5%)
FF: 98 pitches (6.2%)

Looks like even if you look at percentages, Rivera throws four-seamers a higher percent of the time against RHH than against LHH, throwing it at least 14.3% of the time against RHH and at least 6.2% of the time against LHH. Rivera's cutters are effective against both RHH and LHH, as they go away from righties and cave in on lefties in order to jam them. However, the use of a four-seamer to paint the inside edge and go toward righties as an additional weapon (the same way that the cutter works against lefties) makes sense, as such a pitch that comes toward lefties from the outside could be more vulnerable.

All this talk of direction and movement begs for movement plots of those pitches. Here they are:

You can see a problem of sample size here. The cutters definitely show consistent positive horizontal movement (movement to the right, away from righties, towards lefties) and that putting that pitch on the right edge of the strikezone is ideal for both righties and lefties. The few four-seamers there are shows some pitches with lots of negative (left) horizontal movement and some with little positive (right) horizontal movement. All of his fastballs have a rising vertical movement effect, with the cutters consistently 5-7 inches higher than a pitch with no spin-induced movement.

Finally, let's look at Rivera's cutters by called strikes and by swinging strikes:

Again, since my database only contains years 2007-2009, the sample size gets smaller and smaller as we get more and more specific. Still, it looks as though Rivera gets more called strikes than swinging strikes against both RHH and LHH. RH hitters whiff more when the cutter is in the zone, while LH hitters are fooled more into swinging on cutters on the inside out of the zone. For both RHH and LHH, Rivera gets the umpire to call strikes when he has cutters coming toward the strikezone and narrowly missing.

That's it for Mariano Rivera. I'm still figuring out the best ways to use hexagonal binning plots. Figuring out the kinks of filled contour plots is still in the works. Hopefully before long, I can make interesting filled contour plots for pitch location heat maps and even spray chart heat maps to show hitters' balls in play tendencies as well as evaluating team defenses on a whole. After mastering graphical techniques for PITCHf/x data, I would love to start doing pitching and hitting scouting reports much like these. Look out for those in the coming weeks.

Carmelo's Shots Blocked

2010-08-08T10:27:00.005-05:00

I've been out of town for the weekend. It's amazing what a few days cut off from the Internet leaves in your Google Reader and RSS feeds, especially this breaking news that Kendrick Perkins signed with Boston for less than $800K.

What's also amazing is how a largely objective article in the sports world causes readers to scream for the firing of a writer as well as the boycott of the world leader in sports. Tom Haberstroh over at ESPN Insider had a great article a few days ago about Carmelo Anthony being an inefficient offensive player and not worthy of a max contract (in a Joe Johnson-less world). He presented pretty strong evidence that Carmelo is at least not one of the top 5 current players in the NBA, if you take his offensive ratings, the Nuggets' pace factor, and his sheer number of shots taken (wasted?) into account. Sure, Haberstroh's article may come across as written in order to belittle some of the conventional statistics that Carmelo Anthony has piled upon himself since 2003, but it's not like he's claiming that Carmelo should be riding the bench, just that he isn't as elite as fans and the media glorify him to be. It's pretty disconcerting how many readers can get offended by a statistical look at things so easily, but that is a barrier that we have to break in order to get a larger portion of the sports world to understand the usefulness of new, perceptive statistics that take context into account. It adds to our understanding of sports from what we watch through our eyes, not replaces it.

One of the things that Haberstroh mentioned about Carmelo was that he "got his shot blocked a whopping 109 times last season, which ranks as the second-highest total in the league, according to Hoopdata.com." I've been looking at blocks data in quite a bit of detail, and I thought I'd take a look at Carmelo's blocked shots on the offensive end.

A quick look at the 2006-2010 dataset shows that Carmelo got his shot blocked (at least) 373 times, which, as Haberstroh mentioned for the past season, is second-highest in the league during the past four years. That's 1.35 blocks per game. Only 31 players have averaged at least 1.35 blocks per game on the defensive end since 2006, so Carmelo is almost doing opposing defenses a favor by allowing his shots to be easily blocked. Considering that many of the players on the top 10 list of shots blocked include power forwards or centers, who understandably take a lot of shots at rim, Carmelo gets his shots blocked at an abnormally high rate for a high usage small forward.

I looked at my blocks by shot location model as well as my blocks by shot type model to take a deeper look at Carmelo's shots that were blocked (if anyone knows a less awkward way of wording this stat in order to differentiate it from its defensive counterpart, let me know). Carmelo lost 405.26 points by blocks based on shot location, which comes out as 1.09 points lost per block. If you consider that of the top 20 players with the most blocked shots on the defensive end in the past four years, 13 of them saved more than 1.09 points per block, not only does Carmelo have the second most shots allowed to be blocked, but he may have also been among the league leaders of points lost per block allowed.

Looking at blocks by shot type might be even more telling. According to Basketball Geek's PbP dataset, Carmelo had 3 threes blocked, 8 dunks blocked, 109 jump shots blocked, and a whopping 253 layups blocked in the past four years. It all totals out to approximately 1.00 lost points per shot blocked based on shot type (most of the top shot blockers also save approximately 1.00 points per shot). However, Carmelo's had 59 driving layups blocked, good for second most in the NBA. With driving layups worth about 1.46 points per shot, that's quite a bit of high percentage shots that Carmelo allowed to get away. Carmelo is one of three players to be both in the top 11 of jump shots blocked and layups blocked, with the generic jumper worth 0.69 PPS and the generic layup being worth 0.91 PPS. Carmelo only had 6 dunks blocked though, a category of blocked shots that goes as high as 25 in the past four years (Emeka Okafor). Finally, Carmelo is one of four players in the top 10 of shots being blocked on the offensive end without even ranking in the top 120 in blocks on the defensive end.

Carmelo may do a lot of things well on the offensive end because of his athleticism, durability (at least in a minute-by-minute basis), and points-scoring. But he is most definitely not among the league leaders in offensive efficiency, and has several teammates in Denver who shoot the ball more efficiently than he does. If Carmelo can take better and more efficient shots (which includes getting blocked less), he may yet become one of the stars in the NBA. Until then, the team that gives him a long-term max contract in 2011 may regret it if they're basing it on Carmelo's past performance and if he continues to heave a high volume of inefficient shots.

Looking at Pitch Movements

2010-08-05T19:03:00.008-05:00

Here's a look at horizontal pitch movement against vertical pitch movement. The units are in inches, and is compared to a "theoretical pitch thrown at the same speed with no spin-induced movement." And since I'm on the subject of swinging third strikes, here are the movements of four-seam fastballs, changeups, curveballs, and sliders on those types of pitches between 2007-2009:

I used the hexbin plotting function in order to group the pitches by hexagonal points. I put the LHPs and RHPs together, so if you take a look at fastballs, changeups, and curveballs, you can see two focal points. Fastballs seem to have "rising movement," so there is positive vertical movement here for pitches that get pitchers to swing. On the other hand, swinging strike-inducing curveballs drop, showing negative vertical movement.

Update on Value of Blocked Shots

2010-08-04T11:32:00.007-05:00

I do have an update on my research on the value of blocked shots. I made two preliminary rankings lists of the value of blocks by the leading blockers in the NBA between the 2006-2010 seasons. For the first list, I calculated points saved per block based on the shot location. I found that Brendan Haywood and Andris Biedrins (394 and 370 total blocks in 2006-2010, respectively) saved 0.987 and 0.982 points per block while Andrew Bogut (382), Chris Anderson (322), and Paul Millsap (319) saved 1.152, 1.130, and 1.131 points per block respectively, based solely on the location of the shot (so the value of blocking a running slam dunk is the same as that of a reverse layup in this model).

For the second list, I calculated points saved per block based on shot type. This is where I ran into problems, as although every shot is categorized with a specific shot type (no blanks or uncategorized shots), there are many idiosyncratic shot types such as running finger roll layups vs. driving finger roll layups. I've kept these for now (they should have negligible effect on the final values), and have not generalized the categorizations as of yet (say, into 3pts, dunks, layups, jump shots, etc.), but there is no question that dunks produce the most points per shot (PPS) of all the generic shot types, ranging from putback dunks at 1.81 PPS to running slam dunks at 1.97 PPS. Blocking dunks appears to be the most valuable skill for blocking any type of shot (all while earning a spot on Top 10 Plays on Sportscenter), while 'risky' jump shots such as the running jump, driving jump, and turnaround jump go down toward 1.06 PPS.

Anyway, more details for points saved per block based on shot type are to come, but Chris Anderson comes near the top again for the second model, saving 1.09 points per block based on shot type, while Andris Biedrins is near the bottom again, saving only 0.86 points per block based on shot type.

After fine-tuning both models of points saved per block (PSPB?) by shot location and PSPB by shot type, my plan is to compare them with a basic statistical report, then combine the two models, either with a straight up average or something to that effect. I'm also interested in looking at the results in a season-by-season format rather than all four seasons to see if blockers tend to retain their shot-blocking ability in certain shot locations or against certain shot types.

Hopefully, I can share some of my research with John Huizinga to see if our rankings agree. For now, I'll be searching for a way to combine shot location data with shot type data (the sample size becomes too small if I try to calculate PPS by shot location AND by shot type simultaneously), but I'll be sure to post a finalized rankings list as well as my complete methodology based on Ryan J. Parker's PBP data when I'm done.

Called Strike Three

2010-08-04T10:45:00.007-05:00

Yesterday, I took a look at swinging strike threes on four-seam fastballs, changeups, curveballs, and sliders. To summarize, I found what most baseball fans expect, that many swinging third strikes come on high pitches for four-seamers, low pitches for breaking balls, and low and away or sometimes just outside of the zone for sliders. These findings were expected for all four combinations of handedness.

Today, I'll look at called strike threes. Here's what I've got:

Not that I expected to find anything particularly enlightening from a sample of several thousand called third strike pitches (to reiterate, I am learning the elementary art of PITCHf/x graphing as I continue to tackle filled coutour heat map plots, while also trying to figure out how to fetch 2010 PITCHf/x data for new analysis).

Four-seam fastballs paint the outer parts of the strikezone for same handedness matchups, while opposite handed matchups tend to the fool the batter with both inside and outside pitches (and the proverbial called strikes that are out of the zone).

Changeups tend to hit the strikezone, except for the RHP vs. LHH matchup where several changeups hit the outside of the plate as they "come towards the batter." (One thing that I didn't note previously: The LHP vs. LHH matchup does not feature many changeups on swinging third strikes OR called third strikes. I realize that the changeup is rarely thrown in same handedness matchups in general, but I don't recall the exact reason why they are rarely used to get the third strike).

Similar to changeups (both breaking balls), curveballs painted most of the zone, except in the RHP vs. LHH matchup where many curveballs hit the outer part of the strikezone, sometimes even missing it. It's one of those pitches when you see the batter's eyes follow the ball all the way to the end of its path, and he slightly bends and looks at the catcher's mitt before looking up at the umpire's call for a third strike. Many of these batters proceed to argue the call, but that's another story. THOSE pitches occur in this particular matchup with the curveball.

Finally, the slider acts much like the curveball on called third strikes. Fools the batter nearly everywhere in the zone, but for the RHP vs. LHH matchup, most of the sliders come toward the outside.

Spray Charts and Defensive Shifts

2010-08-03T22:44:00.009-05:00

Here's my first look at plotting spray charts. I look at every batted ball in 2007-2009 of a few of the more famous pull-heavy left handed hitters, favorites for inducing defensive shifts. The cloud of hits obscures the baseball diamond behind it, but if you look closely, you can determine approximately where the infielders should ideally set up in order to pick up the most grounders:

I included Justin Morneau despite him not being a shift candidate because of an interesting study on batted ball distributions for "shifted" batters and non-shifted batters against trajectory angle of a groundball. Basically, what Jeremy found was that shifted LH batters have a higher BABIP when they hit opposite grounders toward the regular shortstop position, due to the absence of a shortstop because of the defensive shift. The non-shifted LH batters have higher BABIP up the middle and to the right.

He then made a model to predict BABIP with a defensive shift and without a defensive shift for several batters based on the batted ball distribution of grounders, average batted ball angle, and actual BABIP. Justin Morneau was found to be one of the hitters to benefit from a shift than without a shift.

My question (and possible future research idea) is, why not take the distribution of the batted ball angles for each hitter instead of the average? Some LH hitters (like Morneau) spread their grounders out much more than other LH hitters who are shifted do. But by nature of being a lefthanded hitter, Morneau's average batted ball angle is going to go towards the right of second base no matter the data, despite hitting the ball to the left and up the middle far more frequently than guys like Ryan Howard. The designated "shift" and "no shift" batters in order to create the BABIP on groundballs graph is a great idea, but is not perfect, as it also requires the researcher to select actual shift candidates.

Until defensive alignments on each at-bat are actually recorded (Baseball Info Solutions probably does, I'd have to check), I suppose that determining how a hitter would theoretically perform against a defensive shift will be an inexact science, especially when it depends on a groundballs model that is highly affected by the batter's foot speed. Still, definitely food for thought and awesome work by Jeremy.

Strike Three Swinging

2010-08-03T09:43:00.015-05:00

It took awhile, but I'm going to finally get to post about baseball (it is, after all, by far my favorite sport). I was able to read values from the PITCHf/x database and plot pitch charts directly from R. Somehow, reading articles about PITCHf/x these past few years, though exciting, is not the same as actually being able to do my own PITCHf/x analysis. So it's definitely amazing to finally get into the game.

Batters getting fooled swinging on strike 3 appear on Sportscenter all the time it seems, whether it's a high fastball out of the zone or if it's a slider low and away. Whatever the case, a swinging strike on strike 3 is one of the most exciting plays in baseball, and I wanted to take a look at all of the swinging strike 3 pitches (strike 3 swinging pitches?) on four-seam fastballs, changeups, curveballs, and sliders. Let's take a look at all swinging strike 3 pitches from 2007-2009, categorized by pitch and by handedness (from the catcher's perspective):

Here's four-seam fastballs on strike 3 swinging. As expected, many of the pitches lie up in the zone, blowing hitters away out of the strikezone, the type of pitches batters like to call "rising fastballs." Batters also whiff a lot on pitches from righthanded pitchers painting the upper lefthand side of the strikezone away for righthanded batters (righthand side for lefthanded batters), and vice versa from lefthanded pitchers.

Changeups are offspeed pitches, and they're shown here as low and out of the zone as well, sometimes low and away. Compared with fastballs, changeups seem to drop when they're not supposed to, and so are ideal pitches to induce a swinging strike, most of the time after a fastball. Whereas the four-seam fastball is mainly used to blow a hitter away even when the hitter sometimes knows it's coming, changeups are usually used as deception pitches, acting like they rise and come quickly as fastballs, but actually drop and slow down, causing batters to swing much too early.

Much like changeups, curveballs tend to get the batter out on strike 3 while low and away. In this case, the "away from the batter" factor kicks in, especially in the same handedness matchups of RHP vs. RHH and LHP vs. LHH.

Finally, sliders have the most horizontal movement of all of the above pitches, and therefore, can paint the outer sides of the strike zone and beyond it in order to get a batter to whiff on strike 3. It looks like righthanded pitchers love to use the slider to get the final strike on a righthanded batter, locating the slider low and away sometimes, but most of the time just away. And vice versa, the low-and-away slider works well for lefthanded pitchers against lefthanded hitters, while a slider coming towards the batter in an opposite handedness matchup does not seem to favor the outside of the strikezone as much as a same handedness matchup.

Once I figure out how to produce filled contour plots for pitches like the basketball shot location heat maps (with Dave Allen and Jeremy Greenhouse as prime examples), the differences between different plots will be more resounding. Until then, straight up scatter plots of pitches will have to do.

Time Splits, FG%, and eFG%

2010-08-02T10:17:00.007-05:00

Came up with a couple more basketball shot location visualizations. I can see more and more how this data can be used in addition to visualizing hot zones for players, teams, and etc. but it's always fun to see more basketball graphics.

It's definitely been an exciting week taking more and more of an indepth look at visualizing some of the data out there. All of that and I've only just scratched the surface of the PITCHf/x data. I hope to do much more PITCHf/x visualization analysis in the future, perhaps after I've exhausted all my questions concerning the NBA and NFL PBP data.

Something to look for in the future: I've been thinking more and more about John Huizinga's paper/presentation at the MIT Sloan Sports Analytics Conference about the value of a blocked shot. Sebastian Pruiti's summary of Huizinga's work was indeed very helpful for those of us who weren't fortunate enough to attend the conference back in March. You can check it out over at his acclaimed blog, NBA Playbook. Anyway, I've been looking at using Basketball Geek's data (under the alias Ryan J. Parker) to see how I could use points per shot by location to assign a value to each block between 2006-2010, since most of the blocks are attributed to their corresponding shot locations. My preliminary calculations show ranges from Brendan Haywood saving 0.987 points per block to Andrew Bogut saving 1.152 points per block, which seems to agree with Huizinga's conclusion that Haywood is not as valuable a shot blocker as traditional numbers indicate. Still, my preliminary estimates aren't that promising, but I'll continue to dig into it. Huizinga did have access to more crucial data (such as turnovers leading to blocks, etc.) but I believe that he did not use shot locations to determine expected values of shots blocked. Instead, he used preblock situations and shot types, which probably is more effective. Anyway, I'm going to continue some work on this, and hopefully I'll publish my findings on Think Blue Crew soon (with a look at players who were blocked the most as well).

Here are the time splits of NBA shot location frequencies for 1st quarter, 2nd quarter, 3rd quarter, 4th quarter, first two minutes of 1/2/3/4 quarters, and last two minutes of 4th quarter plus overtime. And here... we... go.:

The following two graphs are of FG% and eFG% by shot location. Here, I hope to emulate what Eli Witus did over two years ago at Count The Basket, when he compiled his own play-by-play data to produce heat maps of FG% and eFG% by shot location. Check them out here and here. The color schemes and scales are a little different, but the idea is the same. For those of you who don't know, eFG% is effective field goal percentage, which takes the value of 3 pointers into account by adding an additional 0.5 for each 3pt made ((FGM + 0.5*3PTM)/FGA). Take a look:

Anyway, having the titles, axes labels, and more contrasting color schemes adds to the visualizations.

This is probably the end of the mass posts of different looks at shot location heat maps. If I use heat maps and filled contours again in the future, I will probably do studies on different players and different teams, but hopefully, this gave you a good idea of the sheer amount of information contained in Ryan J. Parker's dataset and the amount of exciting basketball analysis that can be done.

Scat backs vs. power backs, inside run vs. outside run

2010-08-01T21:28:00.006-05:00

In football, there is a great diversity of running backs. Many of the most exciting players are the smaller and faster players, backs who use their speed and agility to elude defenders and make outside runs while dodging tacklers (Barry Sanders comes to mind). These are known as "scat backs." On the other extreme are bigger, stronger backs who are usually slower (but not always) than the smaller more agile scat backs. These are called "power backs."

In order to ascertain which backs are categorized to which type of running back and to what degree, I used the run direction data to look at running backs between the 2007-2009 seasons to roughly figure out which players were the "most extreme scat backs" and which were the "most extreme power backs" (but not necessarily the best or most successful). Here's what I came up with:

Although sorting the running backs by percentage of rushes they ran up the middle is simple enough, it produces names that match the characteristics for the running backs. However, it's curious to see guys like Brandon Jacobs and Jamal Lewis listed among the likes of Reggie Bush and Willie Parker, but when you see that Lewis runs toward the guards a high percentage of the time and rarely runs on the outside like the other scat backs, it looks like that his place in least used backs up the middle is dubious. For the power backs, Maurice Jones-Drew and Fred Taylor come out as the only running backs in the past three years to rush up the middle over 50% of the time, the most extreme power backs in the NFL today.

At the same time, the listings of Brandon Jacobs and the like as well as the absence of Adrian Peterson indicates that there is a third type of running back: the hybrid power-scat back. Here are the top 10 running backs with the lowest standard deviations of run direction (an admittedly quaint measurement to determine the best combo backs):

There's Purple Jesus. Looks like standard deviation may not be the best method to figure out which running backs represent a power-scat back inside-outside run distribution as Bradshaw, Bush, and Jacobs are listed in the top 3.

Anyway, looking at run directions for individual running backs definitely could use additional research. But what about run directions against certain defenses? Which defenses tend to allow the run up the middle and which ones on the outside?

Again, though this may look like interesting information, it looks like I'll have to do further research. For now, I'll leave the team defenses allowing runs up the middle vs. runs on the outside as is.

Assists, blocks, and team shot location frequencies

2010-08-01T11:20:00.004-05:00

Since the play-by-play data records which shots are assisted and blocked, I filtered the 2006-2010 data in order to see where shots are assisted (locations of the shot made after an assist) and where shots are blocked:

Where Assisted Shots Are Made (2006-2010)

Where Blocked Shots Are Missed (2006-2010)

Hmm... these visualizations aren't very telling. It's clear that most shots are blocked near or at rim, while the assisted shots location frequency looks distributed almost exactly the same as the NBA total shot location frequency. Counting statistics don't tell the full story about assisted shots vs. unassisted shots, since a high percentage of them will be at rim anyway. Looking at percentages per field goal per location would return a more interesting plot. I plotted the same graphs, except with assists / field goals made and blocks / field goals missed to see the percentages of field goals made that were assisted as well as the percentage of field goals missed that were blocked:

Assists/Field Goals Made by Location (2006-2010)

Blocks / Field Goals Missed by Location (2006-2010)

Interestingly enough, a very high percentage of 3 pointers are assisted, and almost 100% of all corner 3s are assisted. If you consider that the basket is at (25, 5.25), the locations with the lowest percentage of shots that are assisted are around the top of the key. (Note: changes to make in the future include the color scheme of the color palette and an outline of the 3 pt line, the key, and the basket. This is possibly the first graph so far that the basketball court is not apparent).

For the blocks per field goals missed graph, looks like a high percentage of shots near the basket are blocked, which makes sense. Notice the blips of yellow/green in the top left corner of the graph, about 30-35 feet from the basket. It seems that someone or a few players were blocked trying to take a long 3, and it just so happened to be in the same location. I looked it up. Two shots were missed at that particular location, and one of them was blocked (Donyell Marshall on Kevin Martin at 4,30). Another note for the future: remove statistical noise wherever possible.

Next, I took a look at the shot location frequencies of different teams:

LAL Shot Location Frequency (2006-2010)

PHX Shot Location Frequency (2006-2010)

ORL Shot Location Frequency (2006-2010)

HOU Shot Location Frequency (2006-2010)

CHI Shot Location Frequency (2006-2010)

ATL Shot Location Frequency (2006-2010)

IND Shot Location Frequency (2006-2010)

NJN Shot Location Frequency (2006-2010)

This time, I tried to standardize the scales (made the maximum of any # of shots in any location to be 150) but again, it's not completely standardized because different teams took a different number of shots over the course of four seasons. Still, there are some trends you can see here. The Lakers, Suns, Magic, and Rockets distribute shots across the floor pretty well, taking a high percentage shots at high percentage locations such as at rim and the corner 3. The Bulls, on the other hand, do take a lot of long 2-pointer shots in comparison, an inefficient location to make buckets. The Hawks post up quite a bit as well as lay up and dunk at rim, as do the Pacers. The difference is that the Pacers take a higher percentage of 3 pointers, and the Hawks take a lot of long 2s. The Nets also tend to take a lot of long 2s, but look more or less like the average NBA shot distribution.

Looking at the shot location frequencies of teams over a 4-year period does have its limitations. It might be more interesting to see those shot location frequencies change over time for a team, after standardization. Next time, it'd be more interesting to compare shot efficiencies by team to determine which teams are locating their shots in efficient locations and how successful they are, but for now, this is what I've got.

A first look at shot location visualizations

2010-07-31T10:14:00.002-05:00

On the subject of investigating play-by-play data for the first time, Ryan J. Parker over at www.basketballgeek.com has provided the NBA stats community with great NBA play-by-play data between the 2006-2010 seasons. I downloaded that data this past week for the first time (even though I've known about it for awhile now), and I've become inspired to take a deeper look at the entire dataset.

Using a macro that I found via Google called "Merge CSV files," I was able to combine all of the play-by-play data in single spreadsheets, one for each of the four seasons that Basketball Geek has available.

I then filtered each of the spreadsheets by etype, and chose shot, in order to return all plays in each season that were shots. I took each of these filtered datasets combined them into a fifth Excel file to list all shots that happened in the past four regular seasons of the NBA (turns out to be 763,444 shots, which unfortunately does not agree with Basketball-Reference.com's 796,617 shots, something that I will ignore for now due to the sheer amount of entries here).

This shots data has everything from players on the court at the time, who the assist went to, who blocked the shot if it was, the result (made or missed) type of shot (ranging from 3pt to driving layup to pullup jumper to running bank shot), and, get this, the X and Y coordinates of each shot. And with a general knowledge of filter and pivot tables and the like, I've come up with a lot of interesting findings.

Using the same data that I've compiled, Jeremy Greenhouse over at The Baseball Analysts was able to chart visualizations of shot locations. I decided to give this a try myself, knowing a little bit of R from class.

With the help of Jeff Zimmerman's Advanced Graphing Techniques series over at Beyond the Box Score, I was able to write the R code to map contours and heat maps based on data.

Here's some of the preliminary images I came up with (without axes labels and titles, mind you. I've just tried these last night, and this is my first look):

Carmelo Anthony Shot Location Frequency (2006-2010)

Danny Granger Shot Location Frequency (2006-2010)
Dirk Nowitzki Shot Location Frequency (2006-2010)

Dwyane Wade Shot Location Frequency (2006-2010)

Kobe Bryant Shot Location Frequency (2006-2010)

LeBron James Shot Location Frequency (2006-2010)
Tim Duncan Shot Location Frequency (2006-2010)

NBA Shot Location Frequency (2006-2010)

NBA Shot Location Heat Map and Expected Points per Shot (2006-2010)

Please note that the scales are all off (except the last one) so you probably shouldn't compare the colors between player graphs (the color palette scale actually refers to a raw count of number of shots taken, so it's not standardized by minutes played or whatever. The last one refers to expected points per shot that I calculated). The X and Y axes are in feet, so consider that the center of the basket is at coordinates (25, 5.25).

However, you can definitely make sense of the graphs and tell the tendency of where some of these superstars/stars tend to shoot. Carmelo and D-Wade fans know that they love their hot spots, and these graphs confirm their tendencies. Dirk and Kobe basically can shoot anywhere on the court, while Granger loves to go at rim or take 3s not on the baseline. Tim Duncan is your classic post-up player, so he hangs out near the bottom of his frequency graph there.

Some things to add on to these graphs when I make them in the future:

title and xlabel and ylabel and etc.
Superimposed outline of 3 pt line and key lines and etc.
Legend for made and missed shots possibly?

And other graphs to take a look at in the future:

Some way to standardize shot location frequency scale (shot percentage? as a fraction of total NBA shots in that location? or as compared to the league average tendencies?)
Home vs. Away splits
1st, 2nd, 3rd, 4th quarters, last two minutes of regulation + overtime
Field goal % and effective field goal %
Expected points per shot for players (are players taking shots where they are successful at?)
Types of shots, by NBA and by player
Assisted shots (Nash-assisted shot locations, NBA assisted shot locations)
Offensive rebound locations (need X-Y coordinates of shot in previous play before offensive rebound)
Any additional suggestions

Anyway, I have a short rest of the summer ahead of me to generate more of these graphs and take a look at some of these in greater detail. There's definitely a lot more stuff and analysis to do with a huge database of NBA play-by-play data categorized by a lot (but not everything). But right now, generating heat maps and these visualizations interest me the most. Should be fun.

More graphs: Play call% by yard line for each down

2010-07-29T02:39:00.003-05:00

Yesterday, I looked at pass locations, run directions, field goal distances, and FGA% vs. Punt% by yard line. The following graphs, however, are far more interesting. They show the play call %s on each yard line, and there's a graph each for 1st down, 2nd down, etc.

For the 1st down graph, the first thing to notice is that rushes tend to be called much more than passes on 1st down when you start off with terrible field position. This is probably due to the fact that your QB is set up in the end zone and in order to avoid a safety, teams always run the ball first and play it safe. Consistent with conventional thinking. The second thing to see is that passes on 1st down occur more often than rushes mainly between the 50-70 yardline range. Interesting.

For the 2nd down graph, things are a little bit more desperate here, so pass% is > than rush% for nearly every yard line EXCEPT when you're stuck in your own end zone or when you're 2nd and goal. In only those situations do NFL teams, on the aggregate, tend to rush the ball at a higher % of the time. This is also consistent with conventional thinking.

For the 3rd down graph, pass% is >>> than rush% in nearly all cases, except when you're 3rd and goal and short in the redzone. It's your 'last' chance to get a 1st down, so passing the ball in order to get more yards is the most common play here. This is also consistent with conventional thinking.

The 4th down graph is very interesting, it's similar to the FGA% vs. Punt% graph I posted yesterady. It seems that at around the 35 yard line, 4th down plays are a toss up between punt, FG, and "go for it" pass/rush play, and likely depending on the game situation, such as time left on the clock or yards to go.

A few things to note: None of these graphs indicate yards to go, and that is obviously a huge determining factor on whether the offense decides to pass, rush, punt, etc.

Finally, an interesting thing I found. There are three occurrences in 2008 in which the offense elected to punt on 3rd down (haha).

Dec. 18, NE@BUF
(5:16) (Shotgun) M.Cassel punts 57 yards to BUF 2 Center-D.Koppen downed by NE-S.Morris. Quick kick.

Dec. 18, NE@BUF
(1:18) (Punt formation) C.Hanson punts 41 yards to BUF 19 Center-L.Paxton. F.Jackson pushed ob at BUF 49 for 30 yards (M.Slater).

Nov. 3, PIT@WAS - (2:39) M.Berger punts 48 yards to WAS 25 Center-J.Retkofsky. A.Randle El pushed ob at WAS 30 for 5 yards (An.Smith).

All three happened in the 4th quarter with a few minutes left in the game. The Patriots did it twice in the game against the Bills when the Dolphins won on the same day and kicked the Pats out of a playoff berth: http://sports.espn.go.com/nfl/recap?gameId=281228002 and one of the punters was Matt Cassel.

The Steelers were leading the Redskins 23-6 with 2:39 in the 4th qtr when they punted on 3rd down.

First graphs: Pass locations, rush directions, field goals, and punting

2010-07-28T02:22:00.002-05:00

As promised, here's a first look at some of the graphs from Burke's PBP dataset, specifically the 2008 spreadsheet. The first graph here looks at the distribution of pass locations in the 2008 NFL season. Passing up the middle, short or long, occurs less frequently than passing left or right. Passing right occurs more frequently than passing left, due to the fact that most quarterbacks are right-handed. Throwing over your shoulder requires more arm strength and gives the defense more time to adjust and get a good look to get a pick. In short, throwing left is common but is a slightly more risky play for a right-handed quarterback.

Edit: Wow, didn't realize I mixed up the guards and the tackles. Oh well.
This graph shows the distribution of run directions in the 2008 NFL season. This time, running up the middle occurs more than twice as often as any other direction, likely also because it is a "safe" direction to run the ball (behind the protection of the full force of your offensive line). Short yard attempts are usually the least risky plays, but also do not gain as much reward as an outside run if executed correctly.

Here is a graph showing field goals by distance (I used yard line and added 17 yards to each). Few field goals are blocked or no good at the 44-yard distance, but once you go beyond there, the number of successful field goals drop faster and faster.

Here is a graph showing the field goal and punt percentages on 4th down. This shows that the 36 or 37 yard line is approximately the breakeven point in NFL teams deciding whether to punt or to go for a field goal (which is around 53 or 54 yards for field goal distance). What might be more interesting to see in 4th down situations is how often NFL teams tend to go for it on 4th down depending on yard line, relative to punting and field goals, etc.

Next time, I'll take a look at play calls in the 2008 NFL season and see how they stack up against one another (pass vs. rush vs. punt vs. field goal vs. etc.) depending on yard line and on what down it is.

A first look at NFL PBP data

2010-07-27T04:22:00.003-05:00

I will use this blog to present, discuss, and archive some of my thoughts on research into sports, particularly baseball, basketball, and football.

Thanks to Brian Burke of Advanced NFL Stats, we now have freely available play-by-play data for NFL seasons 2002-2009. I've taken the 2008 data set and added additional columns to capture other characteristics of each play, categorizing things like pass/rush plays, fumbles, types of penalties, types of scores, even run direction, pass location, intended receiver on complete/incomplete/intercepted passes, etc. This is thanks to the help of the valuable comments left by contributors at Burke's website.

Here are the original columns in the 2008 spreadsheet:

gameid (example: 20090201_PIT@ARI)
qtr
min (minutes left of regulation, so counts down from 60)
sec
off (who's on offense)
def (who's on defense)
down
togo (yards to go)
description (description of the play)
offscore
defscore (offscore and defscore switches after a change of possession)
season

description is the key attribute here where we can use Excel formulas to figure all sorts of information out. To see how much info description contains, check out this example:

(:18) (Shotgun) K.Warner pass short middle intended for A.Boldin INTERCEPTED by J.Harrison at PIT 0. J.Harrison for 100 yards TOUCHDOWN. Super Bowl Record longest interception return yards. Penalty on ARZ-E.Brown Face Mask (15 Yards) declined. The Replay Assistant challenged the runner broke the plane ruling and the play was Upheld.

Anyway, I've added additional columns to the 2008 spreadsheet. Here are the additional attributes extracted from description I added using the formulas that were posted in the comments (and some of my own and modified ones):

play type (example: pass)
play subtype (example: incomplete)
play call (example: rush, when play type is fumble)
yards gained
fumble?
fumble result (either fum Recov or fum Lost)
penalty?
penalty type
penalty decision
challenge
challenge decision
nullified TD (if TD was reversed because of challenge)
clean description (without formations, time left, etc.)
description w/o reversed plays
score type
passer/runner (who threw the ball or who rushed the ball)
run direction (right end, right tackle, etc.)
pass location (deep middle, deep left, etc.)
pass complete to
intended receiver on incomplete pass
intended receiver on interception

I haven't cross-checked all of the data to see if the formulas are 100% correct (the PBP data itself might have a few errors, missing plays, incorrect entries, etc.) but I am sure the ones highlighted in red have shown faulty results. Still, with this spreadsheet, you can figure out the answers to all sorts of questions if you are pretty savvy with using filter and pivot tables (they're very easy to learn). For instance, you can figure out simple questions such as how often passing attempts vs. rushing attempts for any combination of down, yards to go, and yard line using filter and pivot tables. If you dig even deeper, you can sort by team as well (the spreadsheet needs to be fixed up a bit), and see which teams chose to pass for highest % of plays or chose to rush for highest % of plays. Run direction and pass location are very useful attributes, as you can figure out how run directions are distributed in the average NFL game in 2008. Maybe we can even find out if fumbles occur more often if rushed up the middle, or if less fumbles occur in the shotgun formation than not.

I played around with pivot tables and filtering on Excel, and came up with some preliminary graphs. Nothing substantial or revolutionary here, but definitely interesting to look at and a good initial step to looking more at this data. In my next post, I'll take a look at some interesting graphs from aggregating the data (of course, only for the 2008 season).