The practice of using the normal distribution basically for every task is totally outdated especially nowadays that you have everywhere software that implement a wide variety of statistic functions. It was necessary when you needed to solve problems with just pencil, paper and a set of tabulated values. Plus, the concept of "confidence interval" could be easily misunderstood. OP, what do you think it means?
For this problem you are trying to infer your win rate and it's a simple exercise of bayesian inference. Long story short, in R you could obtain your belief interval with the following code (there should be more to be said about the priors):
Code:
beliefInterval<-function(wins,losses)
cbind(lower=qbeta(0.025,wins+1,losses+1), upper=qbeta(0.975,wins+1,losses+1))
beliefInterval(21,39)
giving:
Code:
lower upper
[1,] 0.2416017 0.4769485
You can check the above function changing the values of the arguments and see that it never leads to absurd intervals as the sports betting one.
Last edited by nickthegeek; 07-26-2018 at 03:43 AM.
