An Update on Aaron Judge’s Historic Home Run Pursuit

I regret to inform you that there won’t be many more of these articles about Aaron Judge’s chase for 60, 61, and 62 home runs. It’s not because they aren’t fun to write (they are), or because they aren’t well-received (I think they are). Judge is just hitting home runs too dang fast. What game should you go to if you want to see his 60th home run? It was Tuesday. You missed it. The way he’s hitting, 61 and 62 don’t seem far behind.

Here, for example, are the game-by-game probabilities of Judge hitting his 61st homer:

If you’re a Yankees fan, the next four games in the Bronx are a double dip of fun. If you attend all four, you have a 75% chance of seeing him tie Roger Maris for the franchise (and American League) home run record. It would be against the arch-rival Red Sox, who have been eliminated from postseason contention. And of course, the first day is the best day to see number 61, because there’s no chance he will have hit it before then.

What about number 62? You probably won’t see that tonight, though you never know:

Judge’s torrid pace in recent weeks has moved up the probabilistic timeline. When this counter started, the series against the Blue Jays in Toronto was the most likely time to see something historic, but he’s sped things up by clubbing five homers in his last seven games. Forget 62; could we be see 65 homers, or even 70?

To that end, I’ve added a few more bells and whistles to my home run modeling. Last time, I added a stochastic Aaron Boone who rarely and randomly gave Judge a rest day. This time, I’ve taken a cue from my colleague Dan Szymborski and added a little wrinkle to the model.

Previously, I estimated a true-talent home run rate and used that for every simulation. That works pretty well for the center of the probability distribution, but if you’re looking for outliers (like 70 homers), it falls short. As Dan noted in his piece on triple crown odds, picking an underlying player talent level from a distribution does a better job of reflecting reality than using a static number.

In plain English, Aaron Judge might be 7% likely to hit a home run on any given plate appearance over the medium and long run, but that’s not necessarily the case week to week. Sometimes, he might be feeling good and briefly have an 8% true-talent likelihood. Sometimes he might be feeling off, and only have a 6% likelihood. There’s no way of knowing in advance which of the two he’ll be, but players don’t produce at a monotonic level forever. They get hot and cold.

If Judge is going to hit 70 homers, it stands to reason that he’ll probably do it when he’s the best version of himself, on a personal home run tear. In each simulation, I picked an underlying home run rate talent from a distribution of possible Judge home run rates rather than just using the average. I think this model does a better job of accounting for the odds of something remarkable happening.

Here, for example, are the days when Judge might hit his 66th homer, tying Sammy Sosa on the single-season home run list:

That works out to a 32.4% chance, and if you’re going to witness that home run in person, you’ll want tickets to the last series of the season, naturally enough. To hit six homers in 14 games, Judge both needs to be in good form and likely needs almost all of those 14 games.

With this method, I feel more confident in saying that 70 is a long shot, even with the way Judge is playing. With the changes in my approach, he gets there in roughly 2.4% of simulations. That’s not very likely. On the other hand, it’s a phenomenal achievement anyway. If I told you Judge had a 1-in-40 shot of hitting 70 homers before the year, you’d laugh at me. Of course he didn’t! And the dead ball should only have lowered those odds. Even if 2.4% isn’t a huge amount in the abstract, it’s enormous in the context of the sheer difficulty.

Likewise, Judge almost certainly won’t hit 73 homers. But he might! It’s not outside the realm of possibility anymore. It happened in 1,500 simulations out of a million, or 0.15%. That’s twice as likely as something we’ve probably all seen in Monopoly at one point or another: two consecutive dice rolls that both produce snake eyes.

Really though, what Judge is doing can’t be reduced to probabilities. He’s on one of the great offensive tears of all time. Even last night when he didn’t hit a homer, he smashed two doubles and added a walk. Every batter has an off night – but not Judge. He’s produced a wRC+ above 100 in 15 of his last 16 games, with an aggregate OBP above .500 and SLG above 1.000. The home run chase is fun, and fun to write about, but let’s not lose sight of the fact that regardless of if or when Judge hits a given milestone home run, he’s doing something we’ll probably never see again.