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.