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May 14, 2004
Taking One for the Team
When Does it Make Sense to Sacrifice?, Part 3
Last time, we established several initial estimates for "thresholds" at which point sacrificing becomes a good idea, either increasing raw run scoring or increasing the probability of scoring at least one run. While these estimates are a much more accurate way to evaluate the strategy of sacrificing, they are lacking in several key areas.
First, BP's resident Royals nut, Rany Jazayerli, pointed out that I ignored one of Tony Pena's favorite sacrifice situations: runners on first and second and no outs. This situation is easily punched into the equations developed last time and, jumping straight ahead to the conclusions, this state--nicknamed Situation 4--falls somewhere in between Situations 2 (a runner on first and no outs) and Situation 3 (a runner on second and no outs). Here are the actual numbers:
Situation 4 - Runners on 1st & 2nd, 0 Out ----------- Metric Threshold R-Squared AVG .201 .5204 OBP .223 .7901 SLG .211 .7055 Situation 4 - Runners on 1st & 2nd, 0 Out, Playing for 1 Run ----------- Metric Threshold R-Squared AVG .277 .3875 OBP .351 .5685 SLG .452 .3712
As you can see, when playing for multiple runs, sacrificing in Situation 4 makes sense only for pitchers. The threshold is low enough that even the two more extreme hitters--one with terrible hitting statistics followed by one with a high propensity for singles and doubles--cannot make this situation favorable for sacrificing. Playing for one run, it rises to the levels of validity, but not nearly as much as Situation 3 (.351/.436/.619). On a macro level, we can broadly say that it makes sense to sacrifice in that spot a little more than half of the time. Of all the situations encountered so far, this is the one in which the conventional strategy is most in line with the equations presented here: The best players will not sacrifice, but the average player will be called upon by his manager when the game is close and one run is paramount.
The second major shortfall of the equations is found in the assumptions presented at the beginning of Part 1. Primarily, assuming a 100% success rate for sacrificing is not an accurate reflection of the events on the field, a fact pointed out by more than a few readers. Therefore, the next improvement involves trying to estimate the outcomes of a sacrifice based on empirical data.
Rather than look at the batter's results in various sacrifice situations, we'll look at the resultant base/out situation. The reason for this is because the sacrifice is a play that both gives the defense a choice and places it under a great deal of stress. Trying to cut down the lead runner on a sacrifice is a high-risk, high-reward strategy and results in a variety of scoring decisions (errors, fielder's choices, etc.) that don't map absolutely to the resultant base/out situation. Further, the results of a sacrifice can be thought of as falling into three categories: success, failure, and overachievement. Obviously, when sacrificing, the batter is attempting to concede himself for the advancement of the runner. In "success," the batter is out, but the runner advances. In "failure," the runner is out and the batter is safe at first. In "overachievement," the runner advances and the batter is safe. (There is also the possibility of "miserable failure"--a double play--and a few other rare ending states after errors, etc.) Looking at the data for 2003 in three baserunner situations, the data yield the following results:
Situation Success Failure Overachievement Runner on first 61.7 23.5 14.8 Runner on second 60.4 21.2 18.4 Runners on first and second 59.3 25.7 15.0
There are some more detailed breakdowns within those measurements that I will include in the equations, but we can see from the numbers above that sacrifices are successful about 60% of the time. The question now is whether the overachievement and failure cancel each other out when looking at run expectation--verifying the original threshold estimates--or if our conclusions have changed significantly based on these new estimations for success rates.
To incorporate this information into the existing equations, we will simply enhance our estimation of run expectation for sacrificing, much like when Batter One was upgraded from a singles hitter to a full hitter. These outcome estimations will be added uniformly over all hitters; there will be no adjustment for "good bunters" versus "bad bunters." The reasons for this are many, but the primary one is that there just isn't enough data out there to qualify each player's sacrificing abilities. How good of a bunter is Barry Bonds? I have no idea, and we have no data on which to base assumptions. Observed data would certainly lead us to believe that there are certain players more adept at succeeding in a sacrifice situation than others, but the impossibility of accurately gauging the differences combined with the likely marginal increase in accuracy makes including them in the equations foolhardy. (Most of us do our best not to be foolhardy around here, so we won't add them.)
Having taken these adjustments into account, the updated threshold estimates when attempting to maximize run scoring are:
Situation 1 - Runner on 1st, 1 Out Metric Threshold R-Squared AVG .195 .5788 OBP .221 .7913 SLG .178 .8893 Situation 2 - Runner on 1st, 0 Out Metric Threshold R-Squared AVG .191 .5916 OBP .206 .9086 SLG .182 .7891 Situation 3 - Runner on 2nd, 0 Out Metric Threshold R-Squared AVG .249 .7195 OBP .305 .8511 SLG .363 .8074 Situation 4 - Runners on 1st & 2nd, 0 Out Metric Threshold R-Squared AVG .218 .5810 OBP .253 .8786 SLG .266 .7870
And the data when the primary objective is one run:
Situation 1 - Runner on 1st, 1 Out Metric Threshold R-Squared AVG .199 .4532 OBP .224 .6506 SLG .174 .7928 Situation 2 - Runner on 1st, 0 Out Metric Threshold R-Squared AVG .233 .6333 OBP .282 .8688 SLG .322 .7677 Situation 3 - Runner on 2nd, 0 Out Metric Threshold R-Squared AVG .364 .7390 OBP .450 .5197 SLG .646 .4976 Situation 4 - Runners on 1st & 2nd, 0 Out Metric Threshold R-Squared AVG .268 .5323 OBP .338 .7738 SLG .430 .5070
The first thing to note is that most of the numbers have moved in from the extremes. On the lower end of the spectrum, the threshold in Situations 1 and 2 have come up from the extremely low levels, sometimes under .100, to numbers slightly under and around .200. While this doesn't really change the conclusion about these situations, it does add a small degree of validity to the idea of pitchers bunting in these situations. Additionally, across the board, adding the probabilities for actual sacrifice outcomes--instead of using an assumption of 100% success rate--actually increased run expectation for sacrificing. While sacrifices "overachieve" less often than they "fail"--as noted above--the cost of the failure is much less than the gains of the overachievement. These calculations had a greater difference on Situations 1 and 2 than they did on Situations 3 and 4.
For a final update, we'll use the opportunity to take the opposing strategy into account to some extent. As reader J.P. pointed out, the opposing manager would likely intentionally walk the next batter or two after a successful sacrifice in a late-game situation where one run is paramount. To take this into account, the equations that compute the percentages for scoring at least one run now assume the same double play rates even after a successful sacrifice. This update will obviously not affect Situation 1 (a runner on first and one out) since after a sacrifice there are already two outs, but the other three situations are updated.
Playing for One Run (IBB) Situation 1 - Runner on 1st, 1 Out Metric Threshold R-Squared AVG .199 .4532 OBP .224 .6506 SLG .174 .7928 Situation 2 - Runner on 1st, 0 Out Metric Threshold R-Squared AVG .177 .6314 OBP .192 .8686 SLG .153 .7636 Situation 3 - Runner on 2nd, 0 Out Metric Threshold R-Squared AVG .277 .7823 OBP .350 .5505 SLG .451 .5240 Situation 4 - Runners on 1st & 2nd, 0 Out Metric Threshold R-Squared AVG .206 .5521 OBP .235 .8028 SLG .263 .5234
Thus, having eliminated some of the key inefficiencies of the equations from their initial iteration, the following conclusions can be drawn about the data.
When run maximization is paramount (early in the game, in high run-scoring environments, etc):
When the probability of scoring at least one run is paramount (late in a close game, in a low run-scoring environment, or facing a dominating pitcher, etc):
Therefore, in the broadest conclusion possible, we can say that sacrificing is a good idea when pitchers are batting and, for most of the hitters in the league, when there is a man on second, no one out, and a single run is the goal. Even then, there is a set of the league's best hitters who should never lay down a bunt; which is too bad, because it would be fun to see Bonds square around, just once.