paper: Miscellaneous Statistics Projects

In this post, Citrus Dad asked for a comparison of my Elo and OPR match predictions for the 2017 season. I have attached a file named “Elo and OPR comparison” that does this. Every qual match from 2017 is listed. Elo projections, OPR projections, and the average of the two, are also shown for each match. The square errors for all projections are shown, and these square errors are averaged together to get Brier scores for the three models.

Here are the Brier score summaries of the results.

Total Brier scores		
OPR	Elo	Average
0.212	0.217	0.209
		
Champs only Brier scores		
OPR	Elo	Average
0.208	0.210	0.204

The OPR and Elo models have similar Brier scores, with OPR taking a slight edge. This is directly in line with results from other years. However, predictions this year were much less predictive than any year since at least 2009. This is likely due to a combination of the non-linear and step-function-esque aspects of scoring for the 2017 game. My primary prediction method last season actually used a raw average of the Elo predictions and the OPR predictions, which provided more predictive power than either method alone.