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June 7, 2007

Schrodinger's Bat

Gameday Triple Play

by Dan Fox

"Plate discipline though is difficult to measure. Good plate discipline can mean swinging at the first pitch, fouling off the fifth, taking the tenth; it's about hitting when it's possible to do so and walking when not. If it's possible to hit, a walk is a relative failure. Ultimately though, because information as to just how many juicy pitches players swing at and how many unhittable ones they take is non-existent, though walks are an imperfect measure, they will have to do."
--John Hill writing for The Cub Reporter weblog in 2005

"What we want from our hitters is for them to get a good pitch to hit and be a tough out."
--Indians General Manager Mark Shapiro

We've been digging into the data captured by MLBAM's 2007 version of the Gameday application. With each passing week, we're blessed with more data to slice and dice. At this point, we have almost 60,000 data points to analyze, encompassing 23.8 percent of all pitches thrown in the 2007 season. While the results of the analysis become more interesting with each passing day, we're still dealing with a subset of a subset of one season. Most of the analysis you find here at Baseball Prospectus encompasses aggregate data stretching back over 40 years, and so the conclusions we reach and the trends we see here are necessarily more tentative. That said, we do have enough observations to generate some statistically significant results where it concerns overall trends.

Today we examine the topic of air density and ballparks, take a first crack at determining whether pitchers do indeed try to establish their fastball early in games, and provide the basic framework for taking a closer look at the often mystical topic of plate discipline.

Velocity and Break

The questions from readers regarding the columns of the last couple of weeks have been pouring in. Of particular interest was last week's chart that showed the average deceleration of pitches thrown with little spin at the nine ballparks at which the PITCHf/x system is operating. What the chart revealed was that there is apparently a fairly large difference in how much the ball decelerates on its way to the plate between Arlington on the low end (roughly eight percent) and San Diego at the high end (a little over 13 percent). That span equates to a difference in velocity of an impressive four miles per hour as the pitch reaches the plate.

One would imagine that kind of discrepancy, if real, could clearly make a difference. Because there were lots of questions regarding whether the difference could really be that large, I looked at the starting times for all 859 games in my database, thereby allowing for a classification of each pitch by time of day.

To make this simple, we can break down the starting time of the game into afternoon and evening (I included as evening games those that started at 5 p.m. or later) and use the same criteria as in last week's article looking only at pitches with a break length of less than 5.5 inches. All together that includes 18,288 pitches.


Time       Pitches  PctOfStart
Afternoon     5502       10.2%
Evening      12786       10.5%

The table reflects what we would expect per the theory that in the evening the air density is higher because of lower humidity and temperatures, which in turn creates greater friction on the ball, and slows it down. The difference between the afternoon and evening values may not seem very large, but it is statistically significant at the 99 percent confidence level. In other words, there is almost assuredly a persistent difference between afternoon and evening.

A better way to illustrate this difference is to graph it by release velocity in the same form we did last week:

image 1

At every release velocity between 86 and 98 mph, the ball slows down less in the afternoon than it does in the evening, confirming the overall results. Unlike the difference between parks, however, the difference here is only about three-tenths of one percent all along the curve, which equates to a divergence of less than a half-mile per hour when a pitch released at 95 mph reaches the plate. This result lends credence to the idea that atmospheric effects can be registered with this system, so if they exist, they should also be reflected in differences between parks.

A second, perhaps indirect way of determining whether atmospheric effects are affecting the flight of the ball differently at different parks is to see how the magnitude of the break differs, and how that stacks up against the deceleration we looked at last week. The theory again (well, actually the fact) is that denser air will exert a greater Magnus force (generated by the difference in pressure on the sides of the ball as it spins) on a ball, thereby allowing it to break to a greater degree than air that is less dense. Last week I noted that the pFX value is a measure of the break of the ball (reported in inches) that incorporates both the horizontal and vertical vectors. We'll use this value to examine the average break for a subset of pitches across two different dimensions.

First, we'll slice the data once again by start time, including all pitches with a pFX value greater than eight.


Time      Pitches    pFX
Afternoon   12938    11.8
Evening     29767    12.1

Once again the difference in the two means is statistically significant at the 99 percent confidence level, consistent with the idea that the denser evening air makes for higher Magnus force, and thus better breaking balls.

The second way we can slice the data is to do so by park. The following table shows the average pFX value and the average percentage of velocity decrease at all parks for all pitches ordered by pFX:


Park         Pitches    pFX  PctOfStart
San Diego       4974    13.0     13.0%
Chicago (AL)    4617    12.4     11.3%
Los Angeles     4903    12.2     10.8%
Anaheim         5300    12.0      9.4%
Toronto         4879    12.0     10.5%
Oakland         4630    11.7     10.0%
Seattle         4849    11.5     10.3%
Atlanta         4098    11.5      8.6%
Texas           4243    11.4      8.2%

Just eyeballing the table reveals a healthy correlation (with a correlation coefficient of 0.90) between pFX and the percentage velocity decrease, supporting the idea that there is probably a link between the two. Although it's possible that a calibration problem with regards to velocity may also affect the break value accounting for that link, it would seem highly unlikely. This data provides evidence that the system is indeed picking up atmospheric affects, and that the differing air density both in terms of time of day and park influences both the deceleration and the break of the pitch.

Establishing the Fastball

A second question that several readers entertained after last week's piece was triggered by the graph that showed that pitchers lose their velocity in a fairly uniform way throughout the game. What the questioners wanted to know was whether the data showed that pitchers, as the common wisdom dictates, do indeed attempt to establish their fastballs early in the game in an effort to set up hitters for breaking balls in subsequent at-bats.

To take a first shot at this question, we can produce the following table which shows the number of "straight and fast" pitches thrown by inning for starters who threw 80 or more pitches in a game, along with their percentage of the total. The moniker "straight and fast" is used since only pitches that averaged 83 or more miles per hour with a horizontal break of less than 10 inches were chosen. (The data actually records this value as negative for a pitch that breaks into a right-handed hitter, and positive for a pitch that moves into a left-handed hitter, so the absolute value was used.) Obviously this conservative filter may miss fastballs for a minority of pitchers who don't throw as hard and for others who have more movement (the "tail" on the fastball), but it should give us an idea of whether there is any truth to the old saw.


Inning  Pitches     SF   AvgVel   AvgHB    Pct
1          5137    2965    87.2    -2.5   57.7%
2          4851    2608    87.1    -2.6   53.8%
3          4925    2595    87.1    -2.6   52.7%
4          4535    2275    87.2    -2.7   50.2%
5          4501    2228    87.1    -2.7   49.5%
6          3794    1784    87.1    -2.4   47.0%
7          2176    1056    87.0    -3.3   48.5%
8           677     328    86.8    -3.6   48.4%
9           206     103    86.7    -3.5   50.0%

To explain, SF is the number of straight and fast pitches, and AvgHB is the average horizontal break. The chart shows that pitchers do indeed throw a greater percentage of straight and fast pitches in the first inning (58 percent) than in any other inning. That percentage declines as the game goes along.

Because we're using average velocity in our filter it is true that we've introduced some selection bias, since pitchers lose velocity as the game moves along. However, the average speed that hovers around 87 miles per hour through the first six innings indicates that it is probably the case that pitchers rely on their fastball more early in the game. However, the differences are not as great as I would have thought, especially given the vehemence to establish your fastball early is promoted.

Plate Discipline

As discussed two weeks ago, one of the fascinating aspects of the PITCHf/x data is the ability to examine the location of each pitch. The fact that a customized strike zone is also available for each batter for each plate appearance makes the data even more useful, since it allows us to fairly accurately determine (within an inch, according to MLBAM) whether the pitch was actually in the strike zone or not. This information can be used for many purposes, but to round out today's column we'll begin an examination of just one.

Recently, an interesting article written by Russell Carleton and titled "Is Walk the Opposite of Strikeout?" appeared in the February 2007 issue of SABR's By the Numbers newsletter. The article deals with developing two new metrics based on signal detection theory in order to measure plate discipline. Discussion of the article and an explanation of the underlying math can be found on Russell's blog.

At its heart, the technique he developed combines the ability to properly discern whether pitches are in the strike zone (signaled by swinging) with creating a proper balance between swinging too much and swinging too little. For the study he uses Retrosheet data, but as some readers may be aware, Retrosheet contains pitch sequence and outcomes going back to around 1988, but does not contain pitch location data. Using the location data provided by PITCHf/x, we should be able to more directly measure the concept of plate discipline.

Remember that we don't have full data for all hitters, since there are only nine parks in which PITCHf/x is installed, and those are heavily biased to the American League West. We also are only looking at a subset of one season. Despite these limitations, we can create a few metrics including:

  • Swing (S): Defined as the percentage of pitches the batter swung at, this information is available in many other places. Obviously, high values here are indicative of aggressive hitters, or hitters who see a greater percentage of pitches out of the strike zone.
  • Fish (F): Defined as the percentage of pitches out of the strike zone that the hitter swung at. A higher percentage here indicates that the hitter may have trouble recognizing pitches, since he is offering at pitches that would likely otherwise be called balls. It should be noted that the strike zone as defined for this analysis is 17 inches wide (the standard) and uses the actual height customized for the player. No buffer room was added here, since we're not concerned with giving the umpire the benefit of the doubt.
  • Bad Ball (BB): Defined as the percentage of pitches out of the strike zone that were swung at where contact was made. This includes foul balls, although there is an argument to be made that a foul ball is not the intended outcome, and so should be discounted in some way. A higher value in this category indicates that, when swinging at bad pitches, the hitter is at least able to get the bat on the ball.
  • Eye (E): Defined as the percentage of pitches in the strike zone on non-three and zero counts that were taken for strikes. A smaller value in this metric indicates a player who recognizes strikes and aggressively offers at them. I excluded 3-0 counts, since a hitter is much more likely to let a strike go by in this situation, and we don't want to penalize them for that behavior. However, some readers will see where this idea could be extended to each of the eight possible counts, and a system could be devised where a smaller penalty is credited to hitters who take at 3-1 than those that do so at 0-2.

We can now apply these measures to the 174 hitters who have seen 100 or more pitches with PITCHf/x watching. First, a quick look at the leaders and trailers in each as shown in the following tables.

Sorted By Swing
Name                 Pitches   Swing  Fish  BadBall  Eye
Ivan Rodriguez           103   .631   .585   .868   .263
A.J. Pierzynski          357   .602   .469   .813   .117
Jason Smith              103   .592   .516   .424   .205
Joshua Barfield          115   .583   .474   .704   .241
Alfonso Soriano          103   .583   .571   .600   .303
Victor Diaz              123   .569   .433   .621   .196
Scott Thorman            196   .566   .514   .730   .255
Tony Pena                130   .562   .500   .718   .288
Jose Molina              157   .561   .462   .698   .206
Matt Diaz                152   .559   .444   .773   .189
------------------------------------------------------------
Maicer Izturis           179   .352   .263   .871   .377
Esteban German           126   .333   .188   .667   .391
Andy Laroche             127   .331   .160   .538   .283
Reggie Willits           274   .328   .219   .818   .455
Wilson Betemit           208   .327   .155   .700   .282
Travis Hafner            138   .319   .232   .545   .381
Jack Cust                294   .310   .175   .563   .342
Reggie Willits           135   .304   .186  1.000   .400
Nick Swisher             149   .302   .236   .810   .483
Dan Johnson              387   .282   .148   .737   .346

Sorted By Fish
Name                 Pitches   Swing   Fish BadBall  Eye
Ivan Rodriguez           103   .631   .585   .868   .263
Alfonso Soriano          103   .583   .571   .600   .303
Jason Smith              103   .592   .516   .424   .205
Scott Thorman            196   .566   .514   .730   .255
Tony Pena                130   .562   .500   .718   .288
Robinson Cano            155   .510   .475   .723   .327
Joshua Barfield          115   .583   .474   .704   .241
A.J. Pierzynski          357   .602   .469   .813   .117
Garret Anderson          260   .515   .467   .750   .350
Jose Molina              157   .561   .462   .698   .206
------------------------------------------------------------
Julio Lugo               196   .378   .206   .714   .337
Marco Scutaro            183   .377   .204   .850   .369
Jim Thome                330   .358   .203   .545   .239
Esteban German           126   .333   .188   .667   .391
Reggie Willits           135   .304   .186  1.000   .400
Bobby Abreu              203   .374   .185   .545   .274
Jack Cust                294   .310   .175   .563   .342
Andy Laroche             127   .331   .160   .538   .283
Wilson Betemit           208   .327   .155   .700   .282
Dan Johnson              387   .282   .148   .737   .346

Sorted By Bad Ball
Name                 Pitches   Swing   Fish BadBall  Eye
Brian Roberts            134   .440   .306  1.000   .344
Reggie Willits           135   .304   .186  1.000   .400
Luis Castillo            119   .395   .257   .944   .354
Ramon Martinez           124   .419   .258   .941   .345
Ken Griffey Jr.          109   .440   .366   .923   .289
Juan Pierre              431   .480   .385   .916   .302
Mark Grudzielanek        186   .462   .352   .895   .308
Luis Gonzalez            428   .395   .236   .889   .256
Kenji Jojima             270   .522   .389   .878   .217
Josh Bard                283   .470   .292   .878   .177
------------------------------------------------------------
Derrek Lee               108   .454   .254   .533   .224
Howie Kendrick           164   .488   .396   .528   .347
B.J. Upton               225   .431   .269   .528   .227
Rocco Baldelli           135   .541   .441   .512   .190
Elijah Dukes             193   .399   .252   .500   .175
Rob Bowen                110   .400   .302   .474   .383
Craig Wilson             105   .410   .250   .471   .143
Royce Clayton            227   .515   .348   .457   .194
Jason Smith              103   .592   .516   .424   .205
Russ Branyan             139   .547   .344   .419   .061

Sorted By Eye
Name                 Pitches   Swing  Fish BadBall   Eye
Nick Swisher             149   .302   .236   .810   .483
Reggie Willits           274   .328   .219   .818   .455
Darin Erstad             372   .398   .318   .797   .413
Reggie Willits           135   .304   .186  1.000   .400
Esteban German           126   .333   .188   .667   .391
Rob Bowen                110   .400   .302   .474   .383
Travis Hafner            138   .319   .232   .545   .381
Mark Ellis               440   .409   .302   .851   .380
Maicer Izturis           179   .352   .263   .871   .377
Jason Kendall            405   .432   .325   .870   .373
------------------------------------------------------------
Albert Pujols            108   .417   .313   .760   .143
Craig Wilson             105   .410   .250   .471   .143
Vladimir Guerrero        403   .524   .421   .771   .142
Milton Bradley           135   .489   .260   .550   .140
Nomar Garciaparra        436   .557   .388   .800   .132
A.J. Pierzynski          357   .602   .469   .813   .117
Derek Jeter              178   .427   .246   .857   .111
Jorge Posada             121   .463   .247   .722   .104
Jeffrey Francoeur        337   .546   .425   .775   .094
Russ Branyan             139   .547   .344   .419   .061

Many inclusions on these lists should come as no surprise. Ivan Rodriguez is aggressive, as indicated by his high Swing (.631), and he swings at a lot of bad balls (a Fish of .585), but he also makes contact with a goodly number of those bad pitches he swings at (Bad Ball of .868); if the latter were not the case, he would strike out a lot more than he does. On the other end of the spectrum, Jack Cust (along with his A's teammates Nick Swisher and Dan Johnson) swings at only 31 percent of all pitches, and only 17.5 percent of the pitches out of the strike zone.

What's more interesting is to look at two primary metrics which together reflect two important components of plate discipline, Fish and Eye, and plot them together as shown in the graph below. Some players who fell in the middle have been left out of the chart in order to make it slightly more readable:

image 1

As you can see, the graph is split into four quadrants, and we've added a possible interpretation to each quadrant. Starting in the upper left, this quadrant contains players who don't swing at bad pitches out of the strike zone, and who end up taking more than an average percentage of pitches in the strike zone. Players like Nick Swisher, Reggie Willits (both right- and left-handed, as you see him listed twice), Jack Cust, and Bobby Abreu all could therefore be said to be overly conservative in their approach, and may benefit from offering at more strikes.

Moving clockwise to the right, the next quadrant contains players who swing at a large number of pitches out of the strike zone, while also somehow managing to take a lot of pitches in the zone. Players who nonetheless perform well are typically bad-ball hitters (Alfonso Soriano, Ivan Rodriguez), while those who don't manage to put the ball in play will struggle, as Garrett Anderson and Robinson Cano are doing thus far.

Moving to the third quadrant, we see players who chase a lot of pitches, but also take advantage of pitches in the strike zone. Classically aggressive and good hitters like Vladimir Guerrero and Nomar Garciapara can be found here.

Finally, we move to the sweet spot of the lower left quadrant, where players who don't chase pitches and who offer at pitches in the strike zone can be found. It's not surprising that Derek Jeter, Jorge Posada (against right-handed pitchers), Barry Bonds, David Ortiz, Magglio Ordonez, and Chipper Jones can be found here.

Once again, keep in mind that this is just a small snapshot at this point, and doesn't include all hitters. As we gather more data, this can be refined further, and the two metrics combined into a single number that more accurately reflects the concept of plate discipline.

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