As some of you probably noticed already, your coach rankings (CR) have just changed. This is due to a change in how CRs are calculated. In short, the change involves the addition of race as a parameter to the ranking system.
Together with this change, all CRs have been recalculated from the beginning of the site. This means that matches that predates the ranking reset(s) we've had in the past are now part of your coach ranking.
In addition to the formula change, I have also changed the recently added limit on when CR starts to be a factor. It is now updated if both involved teams have played 4 or more matches. This change was made due to the introduction of the [U]nranked division.
For those of you who are interested in the (mathematical) details, read on for more details.
Before this change, the ranking system treated all races as equals. Two coaches with the same ranking, playing eachother with teams of same Team Strength (TS), would be considered equally likely to win a match, having a win probability of 50%.
Now, this is all good if the teams being played are of the same race. However, consider the situation where these two coaches are playing a game between dwarves and goblins. The dwarf coach most definately has an advantage here, and therefore the ranking system benefits the dwarves.
In order to prevent this situation, I decided to introduce something I call the racial factor. This is another number which is meant to target this problem with the old ranking system.
This racial factor is a number which varies between 0 and 100%, giving the win probability of each side where both CR and TS of the playing coaches is equal. This figure is incorporated into the ranking system as follows:
r: racial factor
p: win probability according to the Ranking help page
P: Modified win probability.
P = p ^ [ 5 ^ ( 1 - 2*r ) ]
This modified win probability is used in place of the old win probability in the ranking formula.
Easy enough, right?
Ok, so what about the racial factor then? How is that calculated?
This is the part where it gets tricky...
The racial factor is based on a racial ranking. This system works much like the coach ranking, using the same formula.
For each match that is played, the system looks up the racial rankings for the two involved teams, and changes the ranking based on the outcome of the match. For this ranking change, the system ignores the TS values of the involved teams since the TS effect of a match is taken into account elsewhere in the CR. Remember that the racial factor is supposed to be the effect of the race on the win probability and nothing else.
So this results in a large number of rankings for each race (in fact, 441 different factors at this time) and updates two values (for example dwarf vs gobbo and gobbo vs dwarf) for each match that is reported.
So, now we have a large table of racial rankings. To get the racial factor we use in the ranking formula, we again use the functions we all know and love. We set up an imaginary match between these two races, "your side" using the racial ranking of your team and the opposing side using a static ranking of 150 (which is the starting point for racial rankings just like CR itself), and again assume equal TS. Using these numbers, we use the same win probability formula we've used before, and the result is the racial factor!
Oh my, I am very sure that I lost most of you long ago, but there you have it.
Note that the racial factors change over time, and I will be publishing the current matrix of factors on the site shortly. I hope that this change will make CR more accurate and believe that most of you understand why this was put in place.
** Edit: You can now find the current racial factors on the statistics page.