Bill James pointed this out a long time ago. If you don’t know Bill James, you should look him up. I consider him to be one of the most influential statisticians of all times. This post relates to one of his first conjectures: sacrificing outs for runs, referred to as small ball, is a bad strategy.
ESPN’s Gamecast, a webtool that gives you pitch-by-pitch updates of baseball games, also gives you a pitch-by-pitch “probability” of wining. Gamecast confirms the conjecure with data. How do they calculate this “probability”? I am pretty sure it is based only on historical data. No modeling. For example, if the away team is up 4-2 in the bottom of the 7th with no outs and runners on 1st and 2nd, they look at all the instances exactly like this one that have ever happened in the digitally recorded history of baseball and report the proportion of times the home team wins. Well in this situation this proportion is 45%. If the next batter successfully bunts, moving the runners over, this proportion drops to 41%. Furthermore, if after the successful bunt, the run from third scores on a sacrifice fly, the proportion drops again from 41% to 39%. The extra out hurts you more than the extra run helps you. That was Bill James’ intuition: you only have three outs so the last thing you want to do is give 33% away.