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April 7, 2005

Crooked Numbers

On the Run

by James Click

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One of the major themes in performance analysis of batters is context independence, the idea that a batter hits just as well whether his team is tied in the bottom of the ninth or up by nine in the eighth. This idea is at the core of the clutch hitting argument and is borne out by statistics: while clutch hitting exists, there are no persistent clutch hitters. Great hitters are great clutch hitters; terrible hitters are terrible clutch hitters.

Context independence can also be applied to situations involving the interaction between baserunners and the batter at the plate. The idea that a runner on a particular base can consistently influence the batter's performance is contrary to the idea of context independence. But listen to a ballgame and you're almost guaranteed to hear discussion of baserunners disrupting a pitcher's timing, rhythm, focus...maybe even his hairdo.

While context independence governs a great deal of batting performance, the presence of runners does affect a noticeable change in the opposition. Pitchers typically go to a stretch delivery instead of the windup. Defensive players position themselves differently, preparing for a possible double play or playing deeper in the outfield to give up a single while preventing a double. The first baseman is assigned to cover the bag and keep the runner from stealing rather than playing back and off the line.

The immediate results of this can be seen in the performance of batters broken down by the baserunner situation in 2004:


YEAR    RUNNERS       PA    AVG   OBP   SLG   ISO   MLVR
2004   2nd & 3rd     4292  .275  .414  .451  .176   .179
2004      3rd        5644  .287  .384  .450  .163   .136
2004   1st & 3rd     6379  .291  .342  .454  .163   .074
2004      1st       38136  .280  .338  .440  .160   .039
2004      2nd       17210  .247  .367  .394  .147   .004
2004    Loaded       5041  .276  .314  .443  .167  -.002
2004    Empty      103422  .262  .325  .426  .164  -.018
2004   1st & 2nd    14083  .258  .327  .415  .157  -.032
The highest situations, as measured by MLVr, are those in which a runner is on third: second and third, third, and first and third. However, the isolated power in these situations is similar to those when the bases are loaded or empty, so much of the difference of MLVr may be a result of intentional walks, a decision element that should be removed in order to better maintain context independence. Removing intentional walks, the numbers for 2004 now look like this:

YEAR    RUNNERS      PA     AVG   OBP   SLG   ISO   MLVR
2004      3rd        5644  .287  .361  .450  .163   .097
2004   1st & 3rd     6379  .291  .337  .454  .163   .066
2004   2nd & 3rd     4292  .275  .347  .451  .176   .065
2004      1st       38136  .280  .337  .440  .160   .037
2004     Loaded      5041  .276  .314  .443  .167  -.002
2004     Empty     103422  .262  .325  .426  .164  -.018
2004   1st & 2nd    14083  .258  .327  .415  .157  -.032
2004      2nd       17210  .247  .340  .394  .147  -.045
While the OBP with runners on second and third dropped from .414 to .347 (and thus MLVr from .179 to .065), the three situations with a runner on third, excluding when the bases are loaded, remain at the top of the list. More importantly, batters perform better in general with runners on base than when the bases are empty. While this may not be as conclusive looking at the 2004 numbers, batters hit worse with the bases empty in 2003 than in any other situation, even when removing intentional walks. In 2002, only with runners on first and second were batters less adept than with the bases empty.

Batters do better when there are runners on base and the year-to-year consistency of offensive performance given a particular combination of baserunners is high. Thus, it can be said with confidence that baserunners do alter batter performance slightly.

However, the argument about baserunners disrupting pitcher timing and focus isn't applied smoothly to all runners. When David Ortiz or Mike Piazza is on first base, there's rarely any discussion about the runner disrupting the pitcher with the threat of a stolen base. Most sluggers are so comically slow on the basepaths that many pitchers rarely give them a second look, choosing instead to focus on getting the out at the plate. But when a Carl Crawford, Carlos Beltran, or Willie Mays Hayes is on first, boos can begin to rain down as the pickoff moves to first mount. These situations, opposed to those involving Ortiz or Piazza, are where the pitcher is purported to give up more hits as he's distracted by a hyperactive baserunner.

Instead of just looking at whether or not batters perform better with baserunners on base or on certain bases, we must instead distinguish between a Cecil Fielder and a Vince Coleman. To do so, I've compiled the batter performance for each baserunner in 2004 when the baserunner was at first and no one was on second. For example, Scott Podsednik was on first with no one on second for 175 plate appearances in 2004. In those plate appearances, the batters behind him hit .242/.304/.319.

Next, each player is assigned a "threat" score that is quite simple: his total SB and CS, divided by the number of times he was at first with no one on second. While this is very basic and fails to consider situations in which the baserunner may choose to steal third or home, those situations are rare enough that the numbers still divine what we'd expect, namely that players like Jose Reyes, Podsednik, and Crawford are near the top while nearly every catcher in the big leagues is at the bottom.

Then each player is assigned to one of three groups: major threat, mild threat, and slow as evolution. These three groups are of roughly equal numbers of plate appearances. Players in the major threat group attempted a steal at least 8.0% of the time they were on first. The second group was between 2.8% and 8.0% while the slow group was 2.8% or lower.

To complete things, the weighted composite batter performance was calculated for each of the three groups and yielded the following results:


 MIN   MAX   AVG   OBP   SLG
8.0%  100%  .295  .348  .463
2.8%  8.0%  .274  .334  .439
0.0%  2.8%  .274  .331  .424
Interestingly, there may be something to the old argument that a threat to steal distracts the pitcher enough to positively influence the batter's results. But before we draw any conclusions, there's one more adjustment that could be made: the normal performance of the batters behind the base stealers. Typically, base stealers are placed at the top of the batting order, followed closely behind by the big sluggers to drive them in. It's possible that the performance of the batters behind the "major threat" group above is the result of better batters being up behind those runners.

To solve that problem, for each runner on first a composite average batter is generated by weighting each actual batter's performance on the season by the number of plate appearances he made with the runner on first. Thus hitters batting towards the top of the order in front of the top hitters in the third and fourth spots won't be unduly credited with improving batter performance when compared to those runners on base while the pitcher is at the plate. Running the numbers one more time:


 MIN   MAX   AVG   OBP   SLG
8.0%  100%  .270  .337  .437
2.8%  8.0%  .264  .333  .434
0.0%  2.8%  .263  .327  .422
These numbers reveal that the suspicions about the batters behind the faster runners were correct to a point. However, while the batters behind the "major threat" runners were better than those batting behind the lesser threats, they do not account for the full difference in batter performance between the three groups. Instead of the .270/.337/.437 batting line we could expect from that group, the batters behind the "major threats" posted the .295/.348/.463 line from the previous table. Looking at the overall differences:

 MIN   MAX   AVG   OBP   SLG
8.0%  100%  .025  .011  .026
2.8%  8.0%  .010  .001  .005
0.0%  2.8%  .011  .004  .002
The "major threat" baserunners do appear to increase the following batter's performance by .025 batting average points. While OBP and SLG increase also, keep in mind that both of those metrics contain an element of batting average, so from this data it appears that walks actually decrease and power remains the same. The second and third groups of baserunners also increase the performance of the following batters, but much less significantly than the "major threat" group. Averaging those two out, we can say that the "major threat" group increases the following batter's expected performance by .015/.009/.023 over other baserunners.

So the next time you're listening to a ballgame and the announcer claims a hit is the result of a pitcher focusing too much on a basestealer instead of the batter, it's not entirely untrue. Context independence is still largely in control, but the subtle influences of the presence of a base stealer do reveal themselves to be slightly positive over the long haul.

---

If you're heading to the Giants-Dodgers game tomorrow night, be sure to stop by the Borders at 200 King St, right across from PacBell/SBC. Heck, even if you're not going to the game, I'll be signing books and talking baseball from 6pm as long as people are willing to go.

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