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I grabbed the following screenshot while watching Moneyball the other day:
If I understand it correctly (and feel free to jump in), the formula
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?
6 comments:
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.
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).
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.
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.
It looks like a Bill James book from the 1980s.
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.
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