Re: Baseball Question
It doesn't work that way. For example, suppose you watched ten hands of heads-up Poker and saw one player win seven of the pots. Would you then be 70% confident he was the better player?
Your formula overestimates the confidence we have in a small number of observations. If we see one person win one hand, we're certainly not 100% confident he's better. On the other hand, it underestimates the confidence we have in a large number. If one player wins 51,000 of 100,000 hands, we're a lot more than 51% confident that he's the better player.
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