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May 14, 2004

Taking One for the Team

When Does it Make Sense to Sacrifice?, Part 3

by James Click

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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
-----------
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):

  • Only pitchers should sacrifice a man from first to second in any circumstances. Even then, certain pitchers who are decent hitters should swing away.

  • With a runner on second and no one out, sacrificing makes sense when some of the league's worst hitters are due up, with a hitter with a high propensity for singles and doubles following. The most likely instance of this is as a lineup in the AL turns over from the ninth spot to the first spot. Even then, instances where sacrificing increases run expectation are rare.

  • Sacrificing with men on first and second is only a good idea when pitchers are due up. While the thresholds here are higher than in Situations 1 and 2, they still remain far too low for even the worst regular position players.

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):

  • Similar to the run maximization situation, only pitchers should sacrifice a man from first. Given that a pitcher would likely rarely be batting in this situation where runs are at a premium, this situation is likely to never occur.

  • Most of the league should sacrifice a man from second with no one out. While a line of .277/.350/.451 is slightly above average, recall that the skill set of the second batter due up should also be taken into account. On the whole, this finding is in the greatest agreement with conventional strategy.

  • When runners are on first and second, sacrificing is, again, not a good idea, a finding that is due almost entirely to the opposing manager's propensity to intentionally walk the next batter to keep the double play in order. This 10% decrease (approximately) in the scoring probability of the situation is enough to reduce the threshold across a great deal of current hitters.

  • If a manager is certain that the opposition will not intentionally walk Batter Two, the validity of the sacrifice is increased in these situations.

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.

Related Content:  Run Scoring,  Run-scoring,  OBP,  SLG

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