Estimating related metrics using Maximum A Posteriori

English is not my mother tongue; please excuse any errors on my part.

I've recently faced a problem for which I haven't found any solutions after investing a lot of time. Here is the summarized problem statement:

Imagine our dataset being the history of matches of a football team, and each point in our dataset is either zero (lost) or one (won). Here we define four metrics that we want to estimate;

• winning ratio (# of wins / # total matches)
• the index of the first win in the dataset
• the average distance of win indices in the dataset
• has the team won any of the first three matches?

I already know that the first metric is estimated using MLE or MAP, but I don't know how to estimate the other ones.