How do I weight Win/Loss Percentage Based on Games Played? I have a spreadsheet I use for tracking my statistics in a game across a number of different factors such as Map, Group Size and Class. 
In each case, I use the win percentage to determine a rating out of 5 (rounded to the nearest $.01$). For example, when playing with a friend, I have a win percentage of $44\%$, this translates to an overall rating of $2.20$ in my current spreadsheet. Likewise, when playing alone, I have a win percentage of $49.64\%$ which translates to a rating of $2.48$. 
I have $50$ games played with 2 people and $137$ games played alone.
I would like to adjust the rating to reflect the number of games played, such that a win percentage of $50\%$ over $100$ games will be rated higher than $50\%$ over $50$ games.
I'm not quite sure how to approach this. Has anyone any suggestions or places I can turn to to help me solve this problem?
 A: Your current rating is proportional to an estimate of the winning probability. You appear to be interested in a pessimistic estimate, so as to favour more precise measurements.
This can be done by basing it on the lower end of a confidence interval. For instance, if we use the lower bound of the Wilson score interval with a confidence level of 90%, we get


*

*38.7% for 25/50 (rating of 1.93)

*41.9% for 50/100 (rating of 2.09)


Choose the interval and tune the confidence level to your taste. The greater the confidence level, the more skeptic the rating.
An alternative is to use a Bayesian approach. Starting with a pessimistic prior (lower values being more probable), update it and make your rating proportional to some average of the resulting distribution.
For example, if we start with Beta(1, 10) and rate on the expected value, we get


*

*$\frac{26}{61}$ for 25/50 (rating of 2.13)

*$\frac{51}{111}$ for 50/100 (rating of 2.30)


Similarly, tune $\beta$ to your preference. A larger $\beta$ means a more pessimistic prior.
In choosing, you might want to consider how you would like your rating to behave in extreme cases such as 0/1, 0/2, 0/20, 1/1, 2/2, 20/20.
