You could rank by the lower bound of the X% confidence interval of the success rate for each person. For a fixed success rate, the confidence interval becomes narrower the larger N becomes. By ranking by the lower bound of the interval, you are ordering them by the value you are reasonably sure they are "at least as good as". This takes into account both the point of the estimate of the success rate, as well as how much data supports that estimate. For two individuals with identical success rates, the one with higher N will rank higher, and for two individuals with identical N, the one with higher success rate will rank higher.

You can play with the width of the CI you want to use as a means of adjusting how much you want to emphasize the point estimate versus the sample size. For a wide CI like the 95% CI, you're effectively using a very conservative estiamte of the true success rate, while for narrower CIs, you're putting more weight on the point estimate than the sample size.

As an example, this would rate a person with an 85% success rate with an N of 1000 (lower 95% CI win rate of 82.6%) higher than a person with a 90% success rate but with an N of only 100 (lower 95% CI win rate of 82.0%).