When is a sacrifice bunt a statistically “good” option?

In the past several years the sacrifice bunt has come under fire as a "waste of an at bat" and "lowering your chance to score." No one denies that outs are very valuable in baseball, but is it ever a good idea to intentionally give up an out to advance a runner (or runners)?

I am more interested in cases where the pitcher is not at bat.

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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.

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