According to the calculations done in this James Click article titled "Taking One for the Team: When Does it Make Sense to Sacrifice? Part 1", he concludes:
Thus, we can conclude that, in this simple case, no matter who is
coming up next, any batter hitting below .075 should always sacrifice,
while any batter hitting better than .243 should never sacrifice. If
nothing else, this conclusion lends further credibility to the idea
that pitchers should almost always sacrifice if given the opportunity.
In the second part of his series, he notes:
Finally, we need to consider that sacrificing is a strategy often
employed when getting one run is more important to winning than
scoring many.
and
The values in Situation 3 immediately stand out. Virtually every major
leaguer is under those numbers; so, according to this model, it is
almost ALWAYS a good idea to sacrifice in that situation if only one
run is needed. This conclusion flies in the face of many of the
conventions usually espoused by performance analysts, but it is
supported by the raw numbers from the run probability table. Notice
that the probability of scoring at least one run increases from .635
to .693 when sacrificing in Situation 3.
Note: Situation 3 is a man on 2nd with no outs.
He concludes in part 3 of the series:
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.
So the final conclusion that he draws is that a sacrifice bunt makes sense only in one situation: man on second, no one out, and a single run is the goal.
