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August 16, 2007

Schrodinger's Bat

Putting the Pedal to the Metal

by Dan Fox

"I think we just played the way we thought we should play. We swung it better, we had clutch hitting, we had clutch pitching. If you put all those things together you have a chance to win a few more games and be a little more exciting. That's what we are doing right now."
-White Sox manager Ozzie Guillen commenting after beating the Mariners 5-3 on August 10th

Most readers familiar with the themes of this column, and with sabermetrics in general, will be aware that for 30 years now there has been an ongoing debate over clutch hitting. Whether it exists, and if so how large is the effect, has been the topic of numerous studies over the years, with the consensus being that if it does exist, the effect is small.

"Clutch pitching," however, has not been explored nearly as much. In that realm, the central question is whether certain pitchers have the skill to get more out of their ability in crucial situations, thereby driving down their opponents' run production. Today, we'll make a small contribution to that question by examining what PITCHf/x can tell us about pitchers' efforts with runners on base.

The Effort Externality

The idea of clutch pitching certainly makes more logical sense than does clutch hitting. As Bill James has said, "Pitching is planned. Hitting is reactive. It's much harder to plan a reaction than to execute a plan." As a result, it's more than feasible that having a plan allows pitchers to vary their effort by situation, thereby varying their results. The most well-known current pitcher who fits this mold is Tom Glavine, who by all accounts isn't afraid to give up a walk in a crucial situation if it means preventing an extra-base hit, and who has the numbers to back it up (.303 OBP and .380 SLG with nobody on, as opposed to .353 OBP and .345 SLG with runners in scoring position). This general effect was discussed in a study done on the "protection effect" by J.C. Bradbury and Doug Drinen back in 2004, and summarized in Bradbury's recent book, The Baseball Economist. In short, what Bradbury and Drinen found was that contrary to the conventional baseball wisdom, better on-deck hitters negatively impact the current batter. Although the effect is small--a standard deviation's difference in OPS for the on-deck hitter yields a four percent difference in the likelihood that the current hitter will get an extra-base hit--in their estimation this is because pitchers make an extra effort in these situations, in order to minimize the damage that a good on-deck hitter might do when he gets to the plate. While it could be the case that the "protection externality" (to use their term) exists, it is simply swamped by the "effort externality."

What I found most interesting in the Bradbury and Drinen study, and where the intersection with PITCHf/x can be tested, is the following description of the effort externality:

Assume that each pitcher has a finite stock of energy from which he can allocate his pitching effort. From this stock the pitcher can vary effort from batter to batter. In baseball, the speed of the pitch is the main determinant of effort; thus, the more speed used per batter, the faster the pitcher depletes his stock of effort and must leave the game. Batters on the opposing team differ in quality; therefore, the pitcher may vary his effort according to the offensive threat imposed by the batting team. As veteran manager Tony La Russa states, "If you have a veteran pitcher who may know what he's doing out there, he may throw 140 pitches--but of the 140, he's only maxing out on 40. The other 100, he's taking a little off, putting a little on. But when the slop is flying, he'll reach back and make his best pitch" (Stark 2004). In the language of La Russa, a better on-deck batter creates more "slop."

Those familiar with the previous analysis we've done using PITCHf/x data will realize that it offers the promise of perhaps being able to measure the effort externality in a more granular fashion than using the outcomes of plate appearances. PITCHf/x includes information on velocity and movement which allows us to quantify the behavior of pitches in different game situations.

A Little Extra

In order to get started we'll first take a look only at fastballs that were tracked from a consistent point on the plane from the mound to the plate (50 feet, which is now the standard value being used as of early July) to see if pitchers do indeed put a little extra on it when faced with a potential run-scoring situation. In order to identify fastballs we're building on the work that Joe P. Sheehan has done, and identifying fastballs as those pitches that are of greater than average velocity for the pitcher overall, have positive vertical movement, and move in to the side from which the pitcher throws--in other words, pitches that tail off.

Under these rules, we end up with over 43,000 pitches we can analyze, and we find the following results for left- and right-handed pitchers:

Starting Velocity on Fastballs
Hand      Empty   RunnersOn    One Runner   Two Runners   Loaded
Left      88.64     88.89        88.65        88.90        89.01
Right     91.46     91.52        91.41        91.85        91.71

In both cases, what we see is that having runners on base and having more runners on in general correlates with higher velocities, thereby supporting the "effort externality." The differences appear to be fairly slight, however. Left-handers gain just under 0.3 percent when runners are on base; there's a 95 percent chance that the difference is real for pitchers with 100 or more fastballs. Right-handers come in under 0.1 percent in their gains, a result with a 90 percent statistically significance. When the bases are loaded, lefties gain over 0.4 percent and right-handers almost 0.3 percent, with the likelihood of both results being statistically significant clocking in at 95 percent. This result is also worth noting given that the conventional wisdom says that pitching out of the stretch costs a pitcher in terms of velocity since they are not able to use their legs as much in their deliveries. It should be noted that the effect holds even when considering only starting pitchers--who typically use both the windup and stretch--as opposed to relievers many of whom pitch from the stretch exclusively. From this it appears the need to bear down overrides a penalty, if one exists, of pitching from the stretch.

In addition to the velocity increase on fastballs, because of the increased spin on the ball with runners on, we also find the corresponding effect that pitchers get a little more movement on their offerings. Their fastballs tail anywhere from a third of an inch (for lefties) to a full inch (with right-handers) more, and don't drop quite as much during their paths to the plate.

To complete the picture we'll take a quick look at the top and bottom 20 pitchers in terms of gaining and losing velocity on a percentage basis with runners on base among the 265 hurlers with 50 or more fastballs thrown in these situations:


                                            Velocity
Name                  Throws      Pitches   Empty Runners  Loaded    Diff Pct Diff
Paul Maholm              L             65   88.29   90.41   90.39    2.12   2.40%
Joel Hanrahan            R             53   89.24   91.11   91.64    1.88   2.11%
Josh Towers              R             78   88.17   89.95    N/A     1.78   2.02%
Tom Gorzelanny           L            124   88.76   90.38    N/A     1.63   1.83%
Kyle Snyder              R             57   85.55   87.08   92.50    1.53   1.79%
Tom Glavine              L            117   84.00   85.42   85.60    1.42   1.69%
Mike Timlin              R             66   89.10   90.51   87.70    1.41   1.58%
Francisco Cordero        R             86   95.12   96.54   96.98    1.42   1.49%
Ted Lilly                L            356   88.01   89.21   87.75    1.20   1.36%
Jeremy Accardo           R             65   94.97   96.16   98.35    1.20   1.26%
Jose Capellan            R             59   91.72   92.85   91.90    1.13   1.24%
Yovani Gallardo          R            164   91.47   92.53   93.87    1.06   1.16%
George Sherrill          L            105   90.29   91.31   91.27    1.02   1.13%
Jake Peavy               R            473   93.73   94.76   95.99    1.03   1.10%
Dustin McGowan           R            200   95.36   96.41   99.23    1.04   1.10%
Mark Hendrickson         L            323   87.08   88.01   88.26    0.92   1.06%
Ryan Rowland-Smith       L             92   91.36   92.30   92.77    0.94   1.03%
Bob Wickman              R             88   91.46   92.40   93.42    0.94   1.03%
Josh Beckett             R            301   93.27   94.22   92.76    0.94   1.01%
Jamey Wright             R            209   88.40   89.27   88.60    0.87   0.99%
---------------------------------------------------------------------------------
Matt Thornton            L             92   96.11   95.37   95.88   -0.74  -0.77%
Boone Logan              L             66   94.07   93.33   92.96   -0.74  -0.79%
Micah Owings             R            325   90.36   89.61   90.40   -0.75  -0.83%
Randy Messenger          R             77   93.26   92.47   91.68   -0.78  -0.84%
Jose Contreras           R            215   91.69   90.92   90.30   -0.77  -0.84%
Jake Westbrook           R            196   91.80   90.96   91.53   -0.84  -0.91%
Erik Bedard              L            240   91.57   90.70   88.82   -0.87  -0.95%
Tim Stauffer             R             54   91.39   90.47    N/A    -0.92  -1.01%
Braden Looper            R            222   90.60   89.66   89.70   -0.93  -1.03%
Joe Thatcher             L             53   89.01   88.08    N/A    -0.93  -1.05%
Victor Santos            R             51   89.77   88.83    N/A    -0.95  -1.06%
Daisuke Matsuzaka        R            170   92.53   91.37   89.72   -1.15  -1.24%
Kiko Calero              R            101   88.61   87.44   88.34   -1.18  -1.33%
Zack Greinke             R             63   95.50   94.22    N/A    -1.27  -1.33%
Kyle Davies              R            158   93.39   92.13   95.10   -1.25  -1.34%
Renyel Pinto             L             51   90.02   88.33    N/A    -1.69  -1.88%
Kenny Rogers             L            152   85.89   84.21   84.70   -1.69  -1.96%
Matt Lindstrom           R             56   98.60   96.56   95.73   -2.04  -2.07%
Jon Papelbon             R             53   95.90   93.79   93.58   -2.11  -2.20%
Manuel Delcarmen         R             84   95.26   92.18   91.83   -3.08  -3.24%

It's probably not surprising that we see Tom Glavine appear sixth on the list of pitchers who reached back for something extra with men on. To some extent, those who lose the most velocity may also be those who have more difficulty getting force on the ball from the stretch because of their mechanics, or who attempt not to overthrow with runners on base--note the hard throwers at the bottom of the list. I'll leave additional comments to readers, but I find this really interesting.

Snapping One Off

Just as with fastballs, there's little reason to suspect that the effort externality does not also apply to curves. After all, with runners on base, pitchers would be just as tempted to try and snap off a good curve as they are to load up on a fastball. To determine if this is the case we can look at the roughly 8,000 curveballs we have. These are defined as pitches below the pitcher's average velocity, that sink more than a non-spinning ball (indicating it has over-spin), and that break into batters of the opposite hand. Although this may occasionally include a good slider or sinker, the vast majority of pitches within this sample will be curveballs. We can then produce the same table as the one we started off with above:

Starting Velocity on Curveballs
Hand      Empty   RunnersOn   1 Runner   2 Runners   Loaded
Left      74.34     74.63        74.73      74.32     74.67
Right     77.13     77.45        77.39      77.08     77.95

We see roughly the same results. Both left- and right-handed pitchers throw a little harder with runners on base, and do so especially when the bases are loaded. Once again, the differences look slight, but when tests of significance are done for pitchers with 50 or more pitches recorded, the difference for right-handers is statistically significant at .01, and for left-handers at .10. The difference is that with curveballs it's important to look more closely at movement, so the following table breaks down left- and right-handed pitchers and their vertical and horizontal movement:


Hand/Value      Empty   RunnersOn   Loaded
Left/Vert       -5.14     -4.95      -4.31
Left/Horiz      -4.92     -5.03      -5.39
Right/Vert      -4.22     -4.13      -4.02
Right/Horiz      5.07      4.98       4.84

This is not quite what we might expect, because in three of the four cases pitchers were able to impart less movement on the ball with runners on base than with the bases empty. Only left-handers saw a little more horizontal movement, and even then the result was not statistically significant. However, once we realize that throwing a curveball harder does not necessarily give it more movement, and consider the fact that pitchers are also trying to avoid burying the ball in the dirt, it makes sense that we'd see a little less movement with runners on. The following table lists the top and bottom 20 pitchers in terms of gaining and losing velocity on their curves with runners on base:


Name                   Throws     Pitches   Empty Runners  Loaded    Diff Pct Diff
Jake Peavy               R             50   77.41   79.52   84.63    2.11   2.73%
Justin Verlander         R            130   79.05   81.14   81.81    2.09   2.64%
Matt Cain                R             60   78.62   80.30   83.60    1.68   2.14%
Brad Penny               R             69   76.65   78.20   76.80    1.55   2.03%
Brett Tomko              R             69   77.16   78.68   77.60    1.53   1.98%
Josh Beckett             R            120   76.27   77.59   76.61    1.32   1.73%
Ted Lilly                L             80   69.85   70.99   72.00    1.14   1.63%
Barry Zito               L             55   70.40   71.53   77.30    1.14   1.61%
Kameron Loe              R             68   75.88   77.06   77.72    1.18   1.55%
Felix Hernandez          R             91   83.81   85.05   87.13    1.24   1.48%
Wandy Rodriguez          L            124   75.40   76.50   76.77    1.10   1.46%
Mark Buehrle             L             75   71.54   72.49   73.02    0.95   1.33%
David Wells              L            127   69.67   70.59   69.80    0.92   1.32%
Anthony Reyes            R             51   76.31   77.31    N/A     1.01   1.32%
Woody Williams           R             69   75.13   76.03   77.24    0.90   1.20%
Royce Ring               L             62   72.33   73.19   73.20    0.87   1.20%
Danny Haren              R            114   80.78   81.75   81.98    0.97   1.20%
Brandon Webb             R             60   75.87   76.78   77.10    0.91   1.20%
Roy Halladay             R             55   77.44   78.27   76.90    0.83   1.08%
Doug Davis               L             94   67.08   67.77   68.37    0.69   1.03%
---------------------------------------------------------------------------------
Mark Hendrickson         L             59   72.96   73.15   74.02    0.19   0.26%
Gil Meche                R             74   77.15   77.32   78.40    0.17   0.22%
Bobby Seay               L             51   76.70   76.85   75.20    0.15   0.20%
Jeff Weaver              R             55   75.10   75.24   75.76    0.14   0.19%
Brandon Mccarthy         R             50   75.90   76.01   76.08    0.11   0.14%
Jeremy Guthrie           R             50   80.80   80.87   86.80    0.07   0.09%
Boof Bonser              R             66   79.98   80.02   77.50    0.04   0.05%
David Bush               R             82   71.31   71.21   71.75   -0.10  -0.14%
Adam Wainwright          R             65   74.36   74.24   74.02   -0.13  -0.17%
Javier Vazquez           R             87   75.39   75.25   78.20   -0.13  -0.18%
Richard Hill             L            120   73.81   73.66   73.47   -0.15  -0.20%
Heath Bell               R             86   84.91   84.67   83.80   -0.24  -0.28%
Gavin Floyd              R             63   78.44   78.12    N/A    -0.33  -0.42%
Matt Morris              R            128   71.39   71.06   72.13   -0.33  -0.46%
Yovani Gallardo          R             71   77.47   76.92   77.30   -0.55  -0.71%
Andrew Brown             R             64   83.83   82.92   83.00   -0.91  -1.08%
Francisco Rodriguez      R             51   81.99   81.09   82.13   -0.90  -1.10%
Roy Oswalt               R             79   74.06   73.06   72.09   -1.00  -1.35%
Sean Marshall            L             66   73.91   72.83   72.04   -1.08  -1.46%
Erik Bedard              L            153   77.62   76.44   76.03   -1.18  -1.53%

Pushing On

What can we conclude about the reality of the "effort externality"? At the very least we can say with near certainty that pitchers in general do indeed try and put a little extra on the ball when faced with trying to extricate themselves or their teammates from situations where runners are on base. Overall, that difference amounts to at most a couple miles per hour, but in a pinch, every little bit helps.

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