J.D. Drew was faced with a decision two days ago.
In a 3-2 count with Matt Joyce up and Dan Johnson on deck, the Red Sox had a 1-0 lead in the 7th inning with Carlos Pena on third and 1 out. When Matt Joyce hit a fly ball deep into foul territory, J.D. Drew could've either let it drop and have Clay repeat the pitch, or he could've caught it and let the Rays tie the game. J.D. took the latter option and caught the ball, and surely enough, Carlos Pena tagged up and scored with no difficulty. Although JD later said that he meant to drop the ball, that's not how things ended up happening. Let's take a look at which was the right move, what J.D. meant to do, or what he actually did.
We all know how the game ended, and in hindsight obviously Drew would rather have not caught the ball, but at the time, which was the mathematically optimal decision? The win expectancy for the Rays before the catch was 47.6% and after moved to 52.2%. On the surface, this looks like an immediate win for a Tampa Bay offense that had been struggling horribly, but it's not quite so simple. With a little ignoring of certain contextual elements and crude approximations, we can take a closer look at this decision.
The Run Expectancy in that situation was .983. This isn't an accurate representation here, however, because Matt Joyce was up to bat. Matt Joyce is an above-average hitter, and so the Run Expectancy is actually slightly higher than what it appeared to be. Adjusting his .398 wOBA against right-handed pitchers to a run expectancy scale suggests that in this situation, he's .061 runs above average. Suddenly the run expectancy becomes 1.044.
Another consideration that needs to be factored in here is that Clay Buchholz is pitching in front of the Boston defense. His xFIP is actually slightly worse than league average right now despite his shiny ERA, and given his career 10.2 HR/FB%, it's fair to regress his projected ERA going forward to league average. Fortuitously, the Red Sox defense also grades out as roughly league average according to UZR, so the effect of Buchholz and the Red Sox on the run expectancy is nearly negligible then.
The final consideration is the count. The count in that situation was a hitter friendly 3-2 full count. The Run Expectancy in full counts has been found to be .035 runs above average. We can now adjust the run expectancy of the situation before the fly ball goes to JD to be 1.079.
So was JD's decision justified? The adjusted run expectancy before the catch was 1.079, and after the catch it was 1.117. It looks like JD Drew's decision to catch the ball cost his team approximately .038 runs. An impact like that is marginal, and in the split seconds JD Drew had to decide whether or not to catch the ball, he didn't exactly have a chance to consult the run expectancy tables. Still, it appears that JD's accidental catching of the ball was not the right move.