Bunt it Like Barton

Daric Barton, first baseman for the Oakland Athletics, is currently tied for the Major League lead in sacrifice bunts. And a lot of people really do not like that.

Over at Athletics Nation, an A’s fan site, statistics-savvy contributors have been calling for manager Bob Geren’s head for months. Joe Posnanski agrees. He wrote a column the other day suggesting that, among other things, “[s]omebody tell that man to stop doing that immediately.” Matt Klassen at FanGraphs also agrees, arguing that every single one of Barton’s bunts has been a bad idea. How could the team that led baseball’s statistical revolution in the late-1990s and early-2000s be so stupid? How can Billy Beane sit back and let his manager throw away out after out by allowing Barton, a good on-base hitter, to sacrifice his plate appearances?

As Tom Tango explains, it is not so simple. Tango makes two points: 1) Barton may have a chance to reach base when he bunts; and 2) all the bunting may force infielders to play in, giving him more hitting room and making him more successful when he does choose to swing.

The latter point is difficult to measure, but Tango has provided help with the former. His run expectancy calculator is a wonderful tool that allows some analysis of Barton’s bunts. It is based on the idea that every combination of baserunners and outs has a certain average “run expectancy.” There can be zero, one, or two outs in the inning, and there are eight possible configurations of baserunners (empty, first, second, third, first and second, first and third, second and third, loaded). Multiply the three out states by eight baserunner states, and there are 24 different situations that can come up in an inning. For each of these states, a team can expect to score, on average, a certain number of runs to the end of the inning — the run expectancy. Input a batting line into the calculator, and you get a table that shows the run expectancy for all 24 states.

One more consideration before we plug in some numbers: the current A’s team is not good at hitting. Since they score fewer runs per game than most teams (in other words, fewer runs per 27 outs), each out is worth a little less than it would be for an average team. Their lack of offensive punch also magnifies the value of a runner moving 90 feet closer to home.

I plugged the A’s season batting line through Monday into the calculator, and all run expectancy numbers come from the resulting tables. Let’s first look at the numbers when Barton bunts with a runner on first and no outs. On average, the A’s should expect to score 0.873 runs between this situation and the end of the inning. If Barton successfully bunts the runner to second, the state changes to a runner on second and one out — a situation which yields an expectation of 0.648 runs. So by successfully bunting in this situation, it would appear that Barton has cost his team, on average, about a quarter of a run. However, a successful sacrifice bunt is not the only possibility. Barton could reach base, resulting in runners on first and second with no outs (run expectancy: 1.493). The bunt attempt could also fail, resulting in a runner on first and one out (run expectancy: 0.499). Barton is a good bunter and always bunts with the speedy leadoff batter on first, so his chance of failure is probably very low. For the sake of argument, let’s say he can expect to pop his bunt up or fail in some other way only about two percent of the time. What about reaching base? Using all of these numbers, a little algebra can tell us how much of a chance Barton needs to have to make this a good play.

P(Bunt Fails) * .499 + P(Bunt Succeeds) * .648 + P(Barton Reaches) * 1.493 = .873

I suggested that P(Bunt Fails) is perhaps .02, so we can set P(Barton Reaches) = X and P(Bunt Succeeds) = .98 – X to make the probabilities add up to one. Solving for X gives about .27, or 27 percent. This means that if Barton has a greater than 27 percent chance of reaching base when he bunts with a runner on first with no outs, then he is actually increasing the number of runs his team should expect to score. If he has a less than 27 percent chance of reaching base, he costs his team runs and would be better off simply swinging away.

Reaching base could include a bunt hit or a fielder error, but a 27 percent chance still seems like a stretch. How about when there is a runner on second and no outs, the situation in which Barton has most often been successful? Posnanski specifically blasted the decision to bunt in that situation, but the numbers are actually a bit better. Here is the equation:

P(Bunt Fails) * .648 + P(Bunt Succeeds) * .895 + P(Barton Reaches) * 1.715 = 1.044

With a runner on second and no outs, again assuming a two percent chance of total failure, the threshold is 19 percent — if Barton has better than a 19 percent chance of reaching, he is helping his team score more runs. The number still seems high, but, contradicting Posnanski, it appears that bunting in this situation is a better play than when there is a runner on first.

Barton has appeared to be bunting for a hit on many of his sacrifices, and though he has not succeeded, he must believe there is some chance he will get on base. And there are two other factors at work. First, the fielders must play further in if he is likely to bunt, making his non-bunt appearances in these situations far more valuable. Second, Tango’s tool also gives the chance of scoring at least one run for each state, and this value stays constant at about 41 percent when Barton successfully bunts a runner to second, and actually rises from 58 percent to 65 percent when he bunts a runner from second to third.

Indeed, Barton’s bunts are far more complicated than some commentators have made them out to be. As Mitchel Lichtman explained during the playoffs last year, when a few Yankees sacrifices left viewers baffled, we cannot simply analyze the before and after state of a “successful” sacrifice bunt. The range of possible outcomes includes the bunter reaching safely; the effect on the fielders should the batter choose to swing is also a factor. The A’s may actually know what they are doing here.

This post originally ran at Ball Your Base.