Q:

Algorithm for best Reputation League

I always wondered on what algorihm the best league of mine is chosen.

I am in the 0.16% of this quarter. That is rank 171 this quarter. But I am also ranked 113th this month.
Why is the stat for the quarter displayed when I have a better ranking in the month?

A:

You are 
quarter: 171th of 108499 ==> 0.1576%
month:   113th of 39822  ==> 0.2837%

And the reputation league shows the best one. So in this case, you have a better classification percentage in the quarter league although in the absolute classification you are higher in the list.
Update: as you show in comments, note that users with less than 200 reputation are not tracked in the leagues. So that is one of the reasons of having different amount of users ranked for every league.

