Wednesday, February 18, 2009

Mr. February

Conditional probability can sometimes be useful in genetics, so I came up with a problem for my students to solve. In you're itching to see how much you remember from stats in college, here's your shot:

You go to Fenway Park for a Red Sox - Yankees game. 80% of the fans there are Red Sox fans, while 20% are Yankees fans. Further, 10% of Red Sox fans are obnoxious, while 100% of Yankees fan are obnoxious. An obnoxious person is sitting behind you. What are the chances he is a Red Sox fan? Answer below.

But what I'm really interested in is the 'battle' for Red Sox SS -- as in, who will combine with Varitek to form the worst bottom-of-the-order combo in baseball this year? I mentioned earlier that apparently Lugo had committed himself this offseason to getting his tape worm removed, and it looks the Dominican witch doctor who was treating him came up with the correct blend of herbs, spices, and vodoo chants, as Mr. Lugo is looking much less emaciated this year.

Couple this data point with recent statements by Francona, and I'm pretty sure that Lugo will trot out there on Opening Day, while Lowrie serves as Mr. Super Sub, bouncing around between 3B, SS, and 2B to give time off to the regulars. Since Lowrie is white, I assume that he will also take over pinch-bunting duties, which the Red Sox never do, but Tim McCarver will call for during all nationally televised games.

If things break right for the Sox -- meaning Saito is healthy, Penny is effective, and Ramon Ramirez can handle the KC-to-Boston transition (he's the guy they got for Coco) -- the Sox could have the best pitching staff in all of baseball, with a solid rotation and a shut-down pen. But this is not a team that is going to score a ton of runs, certainly not to the level of days of yore, when Mark Bellhorn was leading the offense to ~950 runs a year. Their offense is by no means anemic, but especially if Ellsbury doesn't improve his game, it is an offense that has several easy outs.

So to solve the problem, we use Bayes Theorum:

We want to know P(A:B), the probability of a Red Sox fan given it is an obnoxious fan.

P(A) = probability of a Red Sox fan = 0.80
P(A') = probability of not a Red Sox fan = 0.20
P(B:A) = probability of an obnoxious fan given it is a Red Sox fan = 0.10
P(B:A') = probability of an obnoxious fan given it is not a Red Sox fan = 1.00

P(A:B) = P(B:A)*P(A) / [P(B:A)*P(A) + P(B:A')*P(A')] = 28.6%

I like those odds. You should throw your beer in his face and pop him in the nose before even getting a glimpse at his ball cap.