Quantifying the Bias of Arsenal’s Referees vs the Rest of the League’s Clubs « Untold Arsenal: Arsenal News. Supporting the Lord Wenger; coach of the decade
Quantifying the Bias of Arsenal’s Referees vs. The Rest of the League’s Clubs
By Zach Slaton and DogFace
This post can also be found at http://numbersgameblog.blogspot.com/
Author’s Note: Special thanks to DogFace for his co-authorship on this post. His voluminous data set, unending patience, invaluable insight and contribution, and constant editorial feedback throughout the creation of this article was invaluable. He’s a wonderful blogging partner with whom any Gunner or statistician would be lucky to work.
In my first post in this series on Numbers Game blog I used DogFace’s match data to explain how Phil Dowd is the least desirable referee for Arsenal as he not only shows the most biased officiating in terms of fouls, yellow cards, and red cards, but he also shows the largest effect on Arsenal’s likelihood of winning a match. That analysis focused on the effects of all of Arsenal’s referees, but did not quantify how those referees officiated other teams’ matches. This post contains such an analysis, and the results are very interesting.
To aid in such an analysis, a binary logistic regression (BLR) model was created for each team’s likelihood of winning a match based upon a number of factors. Each BLR model includes terms that capture the effects of venue (home/away) and differentials of shots, shots-on-goal, corners, fouls, and fantasy points for yellow and red cards. Not every term was significant for each team – terms that had a p-value of 0.10 or less were eliminated from the team’s BLR and their coefficient for that term is set to zero.
I know that may upset some stats geeks who would prefer p-values of