Miguel Cabrera went one for four with a walk Thursday afternoon. His competition for the batting title, Mike Trout, went 0 for 4, so Cabrera leads the batting race .333 to .324. Josh Hamilton is his competition for the home run title and the RBI title. Hamilton did not play, and now leads Cabrera in home runs 42-41. Cabrera leads in RBIs 130 to 123.
Cabrera now has the following probabilities of at least tying for the three major categories against the player in direct competition:
- Batting Average .875
- Home Runs .435
- RBI .938
Multiply those together, and his probability of winning the triple crown is up to .36, or 36%. That’s up from 32% yesterday. He’s advanced a bit every day. Trout is now just a point ahead of Derek Jeter in the race for the batting title. If Jeter passes Mike tonight, I’ll switch Derek into the calculation.
The spreadsheet for figuring the Batting Average and Home Run probabilities is here. The RBI probability is calculated by running 10,000 simulations of the end of the season based on the players’ performance in and frequency of various on base situations this season.
You can’t just multiply those numbers, since they obviously aren’t at all independent events. A homer raises Miguel’s average, gives him an rbi, and so on. That means his chance of winning the triple crown is higher than .36 — I think it’s probably a lot higher.
James » I’m okay with underestimating the probability. I should probably expand the simulation to take account of all three races.
There is also a chance that Encarnacion passes Cabrerra in HRs. Maybe that chance is .435. Encarnacion has 40. Let’s say that Cabrrera will win the RBI and AVG titles for sure. That just leaves HRs. Let’s give him a 1 in 3 chance (it is him, Encarnacion or Hamilton). Then multiplying we would get a 33% chance (maybe a little higher due to ties). I think we don’t have to worry about James’ issue if we make AVG and RBIs a sure thing. But Dunn and Granderson could also lead the league in HRs (they each have 39). What are the odds makers in Vegas or places like that saying?
Cyril Morong » I tried to find a Vegas line online and couldn’t. If you find one let me know.
No, you don’t have to worry about independence if you set the probabilities of his having the most RBI and highest AVG to 1!
And sorry, I don’t know what I was thinking before, since obviously his chance of winning the triple crown can’t be higher than his chance of having the most HR, no matter how dependent the events are. Oy.
But one last thing: Cabrera beating Encarnacion is definitely not (probabilistically) independent of his beating Hamilton. To beat Hamilton he’ll probably have to go on a tear, in which case he’d almost certainly beat Encarnacion too.
James » Also, since I’m basing this on career home run rates, Cabrera’s probability of beating Edwin should be pretty high.
Hamilton has missed the last 3 games. If he is not 100%, that will affect the odds. And if the Rangers can clinch the best record, they could rest him even more.