The initial discussion of my methods posted Friday night. J.D. Martinez fell back in the race for the batting title as Mookie Betts collected three hits to raise his BA to .339. Martinez stayed at .335 with a one for three night. The probability of Martinez besting Betts in batting drops to 0.37.
Neither Martinez nor Khris Davis homered Friday night. Martinez’s probability of at least sharing the home run title remains at 0.33.
Martinez drove in two runs Friday and Davis drove in none. Martinez’s probability of at least sharing the RBI title rises to 0.975.
Multiply those three probabilities together and the overall probability of Martinez achieving a triple crown stands at about 0.12.
Well, it’s higher than .12, because the categories are not independent!
We can pretty much ignore the RBI category since Martinez is so far ahead — to simplify let’s just give him that one.
Now, you said in reply to me earlier that Martinez could tie for the home run title “with one more home run, and still win the RBI title easily.” That is true but not really on point! It doesn’t matter much what *could* happen; what matters is what’s *likely* to happen, and the chance that Martinez finishes tied atop the home run AL board hitting only one more homer is small.
So the point now is that in most scenarios in which Martinez wins the home run title, he gets a bunch of homers; and in most scenarios in which Martinez gets a bunch of homers, his average rises.
Exactly how much dependence there is between the categories would be hard to calculate (and even tricky intuitively, since sometimes a batter increases his homers by increasing his fly ball rate which typically *decreases* his batting average!). But I think we can safely say that Martinez has a significantly better than 12% chance of winning the triple crown.
James » I rewrote the simulator to include home runs. It gives me a .50 probability that Martinez wins or ties both the RBI and HR titles. It was based on 2018, not their careers. I was surprised it was that high.
James » I was surprised it was high because I had a bug in my code. I fixed the bug, and the probability was about .429. However, the HR calculation I used was based on career HR/PA for both players, and the simulator was based on 2018. Using the 2018 values in the spreadsheet, I get .422, which times .975 is .411. So at least for home runs and RBI, independence isn’t that far off.
Given what Betts and Martinez did today, I suspect his odds of winning the batting title are way down.