Using the Probability of Winning to Evaluate Sacrifice Bunting

As I mentioned in my last post, I developed a computer program to estimate the probability of winning a game for every combination of score, inning, outs, and men on base.  This was an implementation of the Markov Chain methodology as described in The Book: Playing the Percentages in Baseball .

On pages 35 to 43 of The Book, there are tables of the probability of winning the game for all the possible situations based on Major League Baseball statistics.

For example, the probability of winning the game with a man on first base and none out in the bottom of the ninth inning when one run down is 0.353.

Let's assume that the home team lays down a successful sacrifice bunt in this situation.  Then, there would be a runner on second base and one out.  The calculated probablility of the home team winning the game at this point (in The Book) is now 0.296.

Thus, a successful bunt in this situation actuallly reduces the probability of winning the Major League Baseball game according to these calculations.

I collected data from the International Softball Congress World Tournament in 2011.  Then I used my computer program to do the same calculations.

I found the probability of winning the game in the bottom of the seventh inning when the home team is down by a run and they have a man on first base with none out.  It is calculated to be 0.344.

If the home team lays down a successful bunt, they will have a runner on second base with one out.  In this situation, the probability of winning the game is calculated to be 0.278.

So similar to the values found in The Book, a successful bunt, in this situation based on ISC data, actually reduces the probability of winning the game.

There are only a few situations in which a sacrifice bunt increases the probability of winning the game.  One is when the score is tied in the bottom of the ninth inning in the MLB or in the bottom of the seventh in the ISC with a runner on second and none out.

In this case, the probability of winning the game before the sacrifice bunt, in a MLB game, is 0.817 and the probability after a successful bunt that moves the runner to third with one out is 0.835.

The equivalent values for an ISC game are 0.803 before the bunt and 0.825 after a successful bunt.