# Drilling Down into a Bunt Situation

Mitch Moreland led off the bottom of the sixth inning Monday night with a single and stood at first with the score knotted at zero. Elvis Andrus was at the plate with Michael Young and Josh Hamilton due next. Given the pitching duel seen so far and expectation for the remainder of the game, an Andrus bunt would not have shocked many people.

Followers of win expectancy rightfully agree with that call not being made. Sacrifice bunts rarely increase a team’s chances to win. It is, however, a bit more complicated to apply the tenets of win probability to an exact situation than it is to speak in broad concepts.

For one, win expectancy is blind to the specific players involved which can play an important part in skewing the numbers. But there are more subtle assumptions present as well that are worth delving into. A pertinent one in this case is that the markov chains inside win expectancy are calibrated around a run environment. Typically, we use the average run environment for the park in play, but on an individual game basis the environment can vary quite wildly due to the two pitchers in the game.

Examining whether a bunt call might have been proper involves figuring out the expected run environment of the game going forward. Based on the pitch counts of Cliff Lee and Tim Lincecum, the strength of the bullpens behind them and the venue, the number I roughly calculated pegged it at 3.4 runs per team per nine innings. Ignoring the chances of a failed attempt and a fielding error and making the simplistic assumption that a sac bunt would move Moreland to second 100% of the time, that presents a bunt play as being worth -1.4% of a win to the Rangers.

So even with the lower run environment, the call is still overall a bad one, but how low would the run environment need to be before a bunt would result in a positive change in win expectancy?

The break even point is around 1.1 runs per team per nine innings, which should give you an idea of how far off the bunt was from being profitable due to the run environment. One point one runs is not a realistic assumption under almost any condition.

How about the timing though? If the same situation presented itself later in the game, with fewer innings left to play, would that make it profitable? It certainly increases the benefit of the bunt play, but it turns out that it still never gets it past the 0% barrier.

There are times that sacrifice bunts are called for probabilistically. Nearly all of those,however, have to do with moving a runner from second to third. To justify moving a runner from first to second, a manager would need it to be late in the game and the run environment to be abnormally low.

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Matthew Carruth is a software engineer who has been fascinated with baseball statistics since age five. When not dissecting baseball, he is watching hockey or playing soccer.