A Shohei Ohtani 50/50 odds update

Last week, I modeled Shohei Ohtani's pursuit of 50 home runs and 50 steals to predict when he might reach that historic double milestone. But that prediction isn't static. Every time Ohtani plays a game, the odds of him reaching 50/50 change. But the good news is: updating the model is as easy as pressing a few keys and listening to my computer hum for a while.

This isn't going to be a long article. However, it is an updated set of probabilities, and that's what this exercise is about. Ohtani hit two home runs in his weekend series against the Guardians, leaving him just four home runs and four steals shy of a half century in every stat. His chances of reaching 50/50 are 61.3% in my simulations – before this series they were 55.6%.

As a quick refresher, I simulate the probability of him hitting 50 of each stat using a Monte Carlo simulation that takes into account his talent, his opponents, and the stadiums he plays in. I also introduce a random fluctuation in his home run talent: sometimes he's good, sometimes he's not, and sometimes he's somewhere in between. Then I simulate the season a million times and determine if he hits 50/50, and if so, in which game he does so.

The two home runs in the weekend series have pushed forward slightly the most likely date he will reach the 50/50 threshold. Before his series against Cleveland, my simulation suggested the Dodgers' Sept. 27 game in Colorado was the most likely game in which Ohtani either steals a base or hits the home run that puts him over the line. That's still the case — but now tied with the previous game on Sept. 26 in Los Angeles against the Padres. In addition, the Padres series has overtaken the last Rockies series as the three-game series in which he is most likely to set the mark.

Here is the complete set of probabilities for each game:

I think these projections do a good job of solving a tricky problem. But I'd like to make one point about their limitations: Steals aren't quite as easy to model as home runs. Pretty much every time Ohtani comes to bat, his ideal outcome is a home run. He swings to hit home runs, and pitchers do their best to prevent them. The past is very good at predicting the future here, because intent doesn't change from one at-bat to the next. Steals don't quite work that way. Sure, Ohtani's speed is a consistent and important factor; the same goes for his baserunning instincts, the opposing pitcher's ability to hold him down, the catcher's throwing arm, and so on. But how much he wants to steal is also crucial. He tries to steal more often in the second half of the season than in the first, and his urge to walk will presumably only increase when he sits on, say, 50 home runs and 49 steals. I'm modeling a world with real talent at steady state, but I think it would be reasonable to shift the distribution a little earlier if Ohtani hits the home run plateau before the stolen base plateau, which looks more likely today than last week.

Anyway, some takeaways: The final six games of the season are the most likely times history will be made. The series against the Padres is currently the best bet, despite San Diego's excellent pitching staff. The final series of the season, against a bad pitching team, is the next most likely. The odds of Ohtani hitting 50 in both series are higher now than they were on Thursday, and I may even be underestimating them, considering he may decide to attempt more steals as he nears the history-making line.