well, if you know something about pro basketball players, and since I said “pro” basketball players, it would be reasonable take as a “prior” the average hit rate for pros, which is about .75.

http://www.nytimes.com/2009/03/04/sports/basketball/04freethrow.html

]]>i disagree with your specific difference you called out. with a pro basketball player… if given know other information the free through is .5. it will go in or not. this is not really different than taking two random baseball teams you have no information on. The bball players free throw percentage is perhaps slightly more informative than a baseball teams winning percentage to predict likelihood of hitting any shot or winning a game.

am i wrong?

]]>When a pro-player makes, say, a free throw, they do so with a probability p, which is greater than .5 (depending on the pro player). Since the player is experienced at free throws, there’s no good reason to believe that his or her probability of getting the next basket should go up or down based on one observation.

However, in this problem, with two randomly chosen ball teams, and without any other information, the chance that one will beat the other is .5. After one team wins, the estimated chance of it winning again against the same team should be updated to greater than .5. So everyone was correct in assuming that p would go up beyond .5, but it just turns out to be the case that one win, while informative, isn’t that informative.

BTW, I’m doing the same analysis in basketball and hockey next.

]]>I’m sure this is related…

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