algorithm - Predicting Probability of Winning Free-Throw % in Basketball? -

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my actual problem bit more general this, here specific example. in basketball, calculate free throw percentage as:

free-throw percentage (ft%) = free-throws made (ftm) / free-throws attempted (fta)

i have 2 teams, , each team have mean , variance of team's ftm , fta, can model each random normal variable (obviously ftm , fta correlated). can compute probability 1 team make more free throws other, example.

my question is... how can find probability 1 team shoot higher free-throw percentage other? why hard compute? ideas?

thanks in advance! :-)

it turns out ratio of distributed variable (such fta , ftm in model), distributed in way rather complicated describe! simplest (or perhaps least intractable!) case when both means 0, in case ratio follows cauchy distribution. distribution tough work with, because integrals representing mean , variance not defined. fta , ftm have nonzero means, oversimplification. don't think you're going find simple expression probability you're trying calculate.

another way @ might be: cares if math intractable...just simulate it! perform n trials, generating distributed values each team's ftm , fta, keep track of how many times team 1 has better ft% team 2. n might not need large, depending on how accurate estimate needs be...it can shown error in estimated proportion varies 1/sqrt(n).

i'd suggest modeling ftm other normal distribution. binomial distribution, parameters n=mean(fta) , p=mean(ftm)/mean(fta), seems better fit. 2 normal distributions, there's nonzero probability ftm > fta, doesn't make sense.


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