paper: FRC Elo 2008-2016

[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.