By Will Flanders, PhD

On Tuesday night, Milwaukee Brewers outfielder Christian Yelich attempted a bunt for a hit in extra innings, much to the consternation of much of the fan base. The typical complaints that “your best hitter shouldn’t bunt” and “Craig Counsell should be fired (though it is unlikely he called for the bunt)” were heard throughout social media. But what does the data actually show about the wisdom of this decision?

I put this question to the hardest possible test — using Yelich’s performance over the course of the first half of this season as the baseline for what could be expected if Yelich swung away. Combining this with data on how many runs the Brewers are likely to score in the inning under each scenario, we can decide definitively whether his choice was the worst decision in the history of the game or not.

The biggest assumption underlying this analysis is in determining the likelihood that Yelich’s bunt would be a successful hit. I based my percentage here on an article from Baseball Prospectus last year that determined slugger Joey Gallo would be likely to hit .470 bunting against the shift. Yelich was not facing a full shift in this situation, but he is also significantly faster than Gallo — currently second in the NL in Stolen Bases. Consequently, I use a 45% probability of a successful bunt here.

The chart below shows the number of runs expected in an inning (Run Expectancy) after each type of hit in the scenario at which Yelich’s at-bat took place (no outs, no one on). The probabilities column is based off how often Yelich has had each of these outcomes this year. The final column, Expected Value Runs, is simply the probability multiplied by the Run Expectancy. These are added up at the bottom in bold to estimate how many runs Yelich is worth per plate appearance.

One may wonder why a solo home run is worth more than a run in this scenario (1.48). This is because a solo home run restores the situation of no outs and no runner on, under which a team is expected to score .48 runs.

The first thing to notice in this chart is what an incredible season Yelich is having. Combining all of these probabilities, Yelich is worth nearly .40 runs to the Brewers every time he comes to the plate. But the Bunt Hit is worth very close to the same amount — .0125 less. If, instead, the probability of a bunt hit succeeding were to increase 47%, Yelich would have made the right decision, increasing the Brewers chance of scoring. Slight changes to any of the other probabilities would also make the bunt for a hit a reasonable choice. Given that Yelich was in a slight slump for the last week, it may have been even more reasonable.

The other point here is that even for a player like Yelich who has arguably put together one of the best first halves in baseball history, bunting for a hit is only very slightly a bad play. Of course, the probability of success would drop over time if bunting became something the defense expected. But for middle-tier players facing dramatic shifts, bunting for a single could be an even smarter decision. This is not inconsistent with the analytic approach to the game — the key contribution of analytics is in realizing that any means of getting on base increases the chance of scoring. This includes bunt singles just as much as walks.

Will Flanders is the Research Director for the Wisconsin Institute for Law & Liberty (WILL) and an avid Milwaukee Brewers fan.