paper: FRC Elo 2008-2016

[Caleb Sykes]

Originally Posted by Michael Hill

A couple things, it appears you are just using the raw elo differences in calculating red win likelihood. that is (red1+red2+red3) - (blue1 + blue2 + blue3).

I'm thinking if you're going to calculate win chance, you want to average out the elo on each side. However, it seems FRC Elo win percentages don't quite follow chess win percentages based on Elo. I went ahead and generated a cumulative distribution plot based on 2016 match data (and given elo ratings from the spreadsheet). I got what is shown in the plot below. The blue line is the "standard" chess Elo win probability CDF (a logistic distribution CDF), while the orange is from match data. I fit both a logistic CDF (gray) and Gaussian CDF (yellow).
The modded Logistic Dist had a mean of 0 and st. dev of 55 while the Gaussian dist had a mean of 0 and st. dev of 93.



What does this mean? Well, potentially, difference in Elo rating could potentially be a better predictor of winning FRC matches than chess matches. That is, a small difference in average alliance Elo rating has a larger effect on Win % in FRC (2016) than chess.

Looking at Elo averages instead of sums should be equivalent to changing the x-scale on the cdf by a factor of 3, and that looks like what you have posted. It doesn't really change anything, because all you are doing is changing the scale. I used the sums in my calculations, which should provide a cdf similar to those found in things like chess.