Where does this equation come from?? Does anybody know the wikipedia link (or similar) that explains it?
(posterior_mean) = lambda * (prior_mean) + (1-lambda) * (max_likelihood_estimate)
Where:
$$0 \lt lambda < 1$$
and max likelihood estimate is just the mean:
$$\mu_{ML} = \frac{\#success}{\#total}$$
Also, What is Lambda?