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A quick and dirty way to use your idea is to multiply the accuracy measure by (1-0.5^n), where n is the total number of picks used to calculate the accuracy ratio. This will always order people with the same accuracy ratio from most picks to least picks, but it prevents people with lower ratios from being considered more accurate that people with higher ratios unless they have a lot more picks.

7/7 correct gives an accuracy of 1.0*(1-0.5^7) = 0.9922
9/9 correct gives an accuracy of 1.0*(1-0.5^9) = 0.9980

6/8 correct gives an accuracy of 0.75*(1-0.5^8) = 0.7471
12/16 correct gives an accuracy of 0.75*(1-0.5^16) = 0.7500

7/7 correct = 1.0*(1-0.5^7) = 0.9922
24/25 correct = (24/25)*(1-0.5^25) = 0.9600
149/150 correct = (149/150)*(1-0.5^150) = 0.9933

As you can see the factor (1-0.5^n) heads towards 1 very quickly with increasing n, and nothing blows up on you in this way.

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