The Defensive Runs Saved by Chris Taylor’s Hat

My father’s an avid tennis player, and there’s this thing he says anytime — or, because he’s a dad, precisely every time — he mis-hits a ball for an accidental winner. “Welp, I paid for the whole racquet,” is what he says. It’s a goofy way of acknowledging some good fortune, of apologizing for having benefited from something other than one’s actual skill.

The Los Angeles Dodgers pay Chris Taylor mostly for what he does with his bat and his glove and legs. But they employ the whole Chris Taylor. And while there was no reason to care about it before last night, one is compelled to acknowledge today that the whole Chris Taylor includes Chris Taylor’s ball cap.

Here’s why that’s relevant. With one out, runners on first and third, and the scored tied at 0-0, Houston’s Alex Bregman hit a liner to center field. What happened next actually kinda did shock everyone.

For those who haven’t fully pivoted to video, the footage above depicts center fielder Chris Taylor diving for Bregman’s liner, missing Bregman’s liner, and then somehow deflecting Bregman’s liner to left fielder Joc Pederson by means of his hat. While the base hit allowed Josh Reddick to score from third, the ricochet to Pederson forced George Springer to stop at second, limiting Bregman to a single. Rich Hill would strike out the next two batters. No further runs would score.

It’s safe to say that this wasn’t the most likely outcome on this particular play. In a thousand alternate realities, Bregman’s batted ball doesn’t strike the brim of Taylor’s ball cap, but rather rolls all the way to the wall, allowing Springer and Bregman to advance. In our present reality, however, Chris Taylor’s hat saved some portion of a run or runs. How many, though?

Because I’m more invested in the idea of this question than the particulars, I have no intention of answering it with any rigor. I will not, for example, estimate the time it would have taken for left fielder Joc Pederson to retrieve the ball and throw it in. I will not, for example, calculate precisely how far George Springer and Alex Bregman could have run during that same time period. Those are the concerns of people with a greater reservoir of internal resources than I possess.

What I will do — as someone who’s watched baseball for a few decades — is just guess that Springer would have scored and Bregman would have reached third. The liner was hit to the left-field side of Taylor. Pederson wasn’t actually all that far away. While Bregman is pretty quick, he likely wouldn’t have made it home. Plus, with just one out and Jose Altuve en route to the plate, there wouldn’t have been as much urgency for Bregman to score. So, a runner on third with an additional runner scoring: that’s the state of things in a world that hasn’t been visited by pilleus ex machina.

Establishing the base-out state of this hypothetical world allows us to estimate the runs saved by Taylor’s hat in the real one. We’ve estimated that, without the intervention of Taylor’s hat, an additional run would have scored and Bregman would have ended up at third with one out. We know that, with the intervention of the hat, Springer and Bregman were forced to remain at second and first, respectively.

The differences in those base-out states are depicted here, by way of Sean Dolinar’s run-expectancy tool:

A couple notes, quickly. Dolinar’s tool allows one to input both the true-talent wOBA of the batter and also the run environment. I selected a .350 wOBA for Altuve against Hill. Hill is an excellent pitcher; Altuve’s an even better hitter. The league-average wOBA for non-pitchers this year was .326. Facing Hill over and over and over, Altuve would produce something better than that, probably, but also nothing like the .405 wOBA he recorded against the league this year. So, .350 it is.

As for run environment, I’ve included another haphazard estimate. Teams scored roughly 4.65 runs per game this year; Dodgers Stadium played like a modest pitcher’s park, though. In light of that, a run environment of about 4.5 runs seems acceptable.

Those points having been sufficiently belabored, we can now perform the relevant calculus. In the hypothetical scenario discussed above, where Bregman’s liner reaches the wall, I guessed that Springer would have scored and Bregman would have reached third. Springer’s run is worth 1.0 runs, of course. The presence of Bregman on third with one out, according to Dolinar’s run-expectancy tool, is worth 0.946 runs. That’s a total of 1.946 runs.

In reality, that didn’t happen. In reality, Taylor’s hat deflected the ball to Pederson. Springer and Bregman had to stop at second and first, respectively, without an additional run scoring. According to the RE matrix here, a runner on first and second with one out is worth 1.071 runs.

Subtracting the second number from the first produces the runs-saved figure. Here’s the equation: 1.946 – 1.071 = 0.875 runs. That’s nearly a full run! In a game that the Dodgers led by just a run heading into the ninth! And while that same Dodgers club ultimately lost, it’s possible they would have lost even earlier had it not been for part of their center fielder’s baseball costume.