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Decius comments on Alternative to Bayesian Score - Less Wrong
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But that doesn't output 1 for estimates of 100%, 0 for estimates of 50%, and -inf (or even -1) to estimates of 0%, or even something that can be normalized to either of those triples.
Here's the "normalized" version: f(x)=1+log2(x), g(x)=1+log2(1-x) (i.e. scale f and g by 1/log(2) and add 1).
Now f(1)=1, f(.5)=0, f(0)=-Inf ; g(1)=-Inf, g(.5)=0, g(0)=1.
Ok?
Huh. I thought that wasn't a Bayesian score (not maximized by estimating correctly), but doing the math the maximum is at the right point for 1/4, 1/100, 3/4, and 99/100, and 1/2.