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May 14, 2004

Taking One for the Team

When Does it Make Sense to Sacrifice?, Part 3

by James Click

Part 1
Part 2

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
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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
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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