Monday, March 26, 2012

Math in the Movies

I grabbed the following screenshot while watching Moneyball the other day:

If I understand it correctly (and feel free to jump in), the formula

$\frac{53!}{(41!)(12!)}(.520)^{41}(.480)^{12}$

is the probability that, say, a team with a track record of winning 52% of its games (during, say, a 51-47 season) will win exactly 41 of its next 53 games, without respect to the order in which they are won.

With the help of my trusty HP-15c (yes, I found it!), I calculated that probability as .0000906, which is (1) a pretty low probability and (2) pretty much what you will always get when you are trying to find one among a whole lot of possibilities.

What I don’t know is why you would want to know this, or from what book this page was taken.  (In context, my best guess is a Bill James book.)  Anybody?

Professor Hale said...

It also assumes that winning is a random chance and not in any way influenced by the skill of the teams or even if the opposing team shows up.

Jehu said...

Your equation looks fine. Your calculator probably has a button for the 1st term, 53 combined 12 at a time (or 53 combined 41 at a time, they're the same number).

Dr. Φ said...

Jehu: yes, but I didn't use it. I used the factorial button.

Prof Hale: Well, if it was random chance, I assume the probabilities would be .5 per game. I also assume the .52-.48 takes into account the relative skills and potential forfeits.

Steve Sailer said...

I got a $200 HP calculator for my high school graduation in 1976. It finally broke down in 1984 and I replaced it with the HP 12C that, last I checked, is still on sale (the profit margin must be immense). The 1976 one was better than the 12C because I could operate it one handed and hold a pencil in the other hand. The 12C needed two hands. Steve Sailer said... It looks like a Bill James book from the 1980s. Dr. Φ said... Steve: Maybe I just have small hands, but it is a small calculator that I can hold and operate one-handed. IIRC, the 12C was optimized for and marketed towards business/finance users, while the 15C was built for engineers. The 15C is no longer made, and now sells on ebay for twice what my father paid for mine in 1984 ($150). Interestingly, the people I know that have them really like its two-thumb operation.

Thanks for commenting, btw. This is like a super big deal for me.