Determine rank by taking confidence in Elo estimation into account

[GoogleCodeExporter]

The ranking of players is currently decided directly based on their Elo score. 
This is probably not as great as it could be because the confidence of the 
score could be very bad. The Trueskill ranking algorithm addresses this by 
calculating a "rank" as a function of the score and the standard deviation of 
the estimate of the score. Because bayeselo is similar to Trueskill in that it 
estimates the score according to a normal distribution, we can apply the same 
principle here. The formula to determine Trueskill rank (R) is R = μ - 3σ, 
where μ is the mean of the estimate and σ is the standard deviation of the 
estimate. What this boils down to is that the rank is "conservative" in the 
sense that we are 99% sure that the player's actual score is actually higher 
than the displayed rank. Because σ will always become smaller over time, the 
result is that the bot will usually start low and gradually rise in the ranks 
as it plays more matches instead of jumping around the ranks wildly until the 
estimated μ settles down. It also means that once we have a nicer game 
scheduling algorithm in place that takes rank into account, bots will first 
play lower ranked bots and bots with less certain skills before moving up to 
the higher ranked bots, giving them greater variety in their opponents without 
seeming unfair.

This is filed as a separate issue from #88 intentionally because it's really 
asking for a different thing.

Original issue reported on code.google.com by Jake.McA...@gmail.com on 9 Sep 2010 at 10:56

[GoogleCodeExporter]

I would like to clarify that the + and - numbers reported by bayeselo are not 
the standard deviation. It's possible that the 3σ can be approximated closely 
enough by just using the - number in its place, but I'm not sure.

Original comment by Jake.McA...@gmail.com on 9 Sep 2010 at 11:08

[GoogleCodeExporter]

Dropping ownership

Original comment by Jake.McA...@gmail.com on 10 Sep 2010 at 12:33