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# Need a formula to compare percentages based on different amounts (weighted?)

Posted on 2008-10-27

Okay, I probably knew how to do this at one point, but I haven't cracked a math book open in quite some time. How can I fairly compare averages based on different amounts?

Say a runner runs 100 races and wins 25 of them. He has a winning percent of 25%. But if another runner runs just 10 races and wins 5, he has a winning percent of 50%. Now, the second racer has a higher winning percentage, but the first runner has won more races and could be construed as a "better runner".

I know I could extrapolate and assume that if the second racer runs 100 races, he will win 50 of them, but I'm looking for a more accurate comparison of what they've actually done and not what they may do.

Is there some formula or theory I can use?

Thanks in advance