Joe Mauer finishes the night four for four, raising his batting average to .429. It was a big night in Joe’s quest to hit .400 for the season, as he cut the odds of his reaching that goal in half. Based on a 162 game season, the probability of Mauer hitting .400 went from .01 to .02 (double the probability, halve the odds). Based on a 140 game season (Joe came back from injury with 140 games left), the probability went from .0016 after Sundays’ game to .0032 after tonight’s game. The following graph is updated through tonight’s game showing how the probability of Mauer hitting .400 progressed through the season. Click for a larger image.
Just curious: how are the odds higher in a longer season? It seems intuitively like the fewer games you play, the better chance you have of achieving an outlier outcome. And the more games you play, the more likely you’ll regress to the mean, or toward a normal batting average. So I would think the shorter season would help Joe: less chance of regressing below .400. Can you explain?
Thanks for doing this though. I was googling for odds of him hitting .400 and was having a surprisingly hard time. You’re the first site I found!
The other odds question I had was, what’s the over-under on Mauer’s BA, that is, what batting average does he have a fifty-fifty chance of ending up either above or below?
The calculation I do tries to predict his remaining at bats. I assume the rate of accumulation of at bats will be the same as up until now. So for the 162 game season model, I divide his at bats by the Twins games played. In the 140 games model, I do the same, minus the first 22 games. If you will, the 162 game model assumes he’ll get hurt again, and bring the number of expected at bats for the season up very slowly. The 140 game model assumes the season just started late. So the 140 game model is projecting more at bats for Mauer than the 162 game model. That’s why the odds are lower in that one. My guess is that the 140 game model is more accurate at this point, but Joe does have a history of injury, which is why I include both.
I’ll try to work on the over/under later today.
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