In a comment to the Joe Mauer post, Bill writes:
The last thing I’d want to do is take any attention away from my favorite active player, but what do you suppose the odds are of Pujols passing H-Ram for the NL batting title (and thus having a shot at the triple crown)? Obviously there are multiple moving parts there (Mauer’s only competing against a number, not another player), so I don’t suppose you can just come up with this kind of “1 in X” analysis.
What we need to figure out is the probability that if Albert hits X, what is the probability of Ramirez hitting less than X, and then multiply those two probabilities together for every X. We then sum those products to get the final result.
I made the following assumptions:
- The players will continue to accumulate at bats at the same rate. That means another 146 AB for Pujols, 159 for Ramirez.
- I used their current career batting averages for the probability of their getting a hit. For Pujols that’s .334, for Ramirez .317.
Then for every hit value from 0 to 84 (it’s unlikely Albert gets more than 84 hits), I calculated the probability of Pujols getting exactly that many hits in his remaining at bats, and the cumulative probability of Ramirez getting that many hits. I also calculated the batting resulting batting average for the two at those hit levels.
Then for each hit level for Albert, I found the highest hit level for Hanley that would still give Albert the batting title. I took those probabilities and multiplied them together. For example, if Albert were to get just ten hits the rest of the way, he would bat .258. If Hanley gets 0 hits the rest of the way, his batting average would be .259, so the probability of Albert winning in that situation would be 0. A more realistic example has Pujols collecting 49 hits for a .3274 BA. He then finishes ahead of Ramirez if Hanley knocks out 39 hits or less. That’s the combination with the highest probability, 0.0227.
Summing all the individual probabilities results in an overall probablility of .3259 for Albert finishing ahead of Ramirez in the batting race. That doesn’t mean he wins the batting title. Pablo Sandoval is still in the mix, and Bruan and Helton are more than capable of putting on a push of their own. One in three aren’t bad odds, however.
Something that I think is difficult to quantify in this projection is the “new” approach Albert can take at the plate, with Matt Holliday behind him now.
While I wouldn’t go so far as to suggest that Albert would radically change how he hits or views each at bat, he’s almost certain to see fewer walks, which may actually result in more outs.
Without Holliday, he had to just take his walks and let someone do the damage behind him, in most clutch situations. With Holliday there, he’s not getting as many walks, but he’s also not afraid to be a bit more aggressive because he knows Holliday is up next and has just as good a chance to knock in the run if he doesn’t.
I could be completely wrong, but his average may suffer a bit while improving his slugging numbers and HR and RBI total.
Maybe not. Definitely fun to watch though.
I was thinking Albert Pujols may have an outside chance of passing Hanley Ramirez if he got hot and Ramirez started cooling off and they would meet in the middle giving Pujols a chance to win.
With Ramirez hitting in the 350’s there is less chance of that happening because averages don’t fluctuate that much this late in the season.
The way Mark Reynolds is hitting homers and Prince Fielder is driving in runs Pujols may not win any of the Triple Crown categories.
Wow, thanks for looking at this. That’s MUCH more likely than I expected.