I've done my best lately to highlight the bias of Phil Dowd when it has come to officiating Arsenal matches. Today he did the best to bust up my theory (at least statistically) by tossing my Gunners a wonderful opportunity to earn three points via some favorable officiating. Unfortunately, Arsenal did their best to not take the opportunity to keep pace with Manchester United. In fact, it was a massive missed opportunity. Let me explain...
In generating data for an upcoming post on Premier League officiating, I created binary logistic regression (BLR) analyses for each team over the 2005/06 through 2010 seasons. Similar factors were considered in these BLR's as in my last post on officiating, but significant factors were set at p-values <= 0.10. I know that may upset some stats geeks who would prefer p-values of <= 0.05, but the reduced sample size requires it or very few teams would have any significant terms. Creating a BLR for each team allows for the study of how sensitive a team's chances of winning are in regards to each match statistic. Thus, having a match's statistics allows us to retroactively examine the odds of either team winning the match.
Which terms are significant in each team's BLR provide some insight into how each team wins and loses.
For Arsenal, differentials in shots, corners, and fouls seem to not have a statistically significant effect on their odds of winning, while venue and differentials in shots-on-goal, yellow cards, and red cards do have a statistically significant impact. Each of the four statistically significant terms comports with expectations - playing at home and a greater number of shots on goal are positively correlated with odds of winning, while yellow and red cards are negatively correlated.
For Blackburn, shots and red cards are not statistically significant. Venue, shots-on-goal, corners, fouls, and yellow cards are statistically significant. The coefficient for the corners term is negative, which indicates that an increasing differential in corners lowers Rovers' chances of winning a match. There may be a rational reason for such a relationship - a greater number of corner kicks means more of Rovers' shots may be getting knocked out, indicating fewer shots on goal and fewer goal scoring opportunities. The rest of Rover's terms correlate to expectations.
Now that BLR's have been created and their rationality checked, it's time to apply them to the match statistics. The table below summarizes the match statistics according to ESPN.com. Differentials for each match statistic for each team were calculated, and then applied to each team's BLR model. This allowed the calculation of the likelihood of each team winning the match, shown in the far right of the table.
You're reading the table correctly - Arsenal led in every major category except fouls (dead even) and had a five-in-six chance of winning such a match. Arsenal's failure to win the match is a one-in-six occurrence, one that cost them two points and may end up costing them the title race in the Premier League. Notice that Blackburn's chances of winning were only 31%, but that's the odds of winning and not the odds of drawing. Somewhere between Arsenal's and Blackburn's odds of winning is the odds of a draw, something that a BLR can't quantify.
I still think Dowd is a bit biased against Arsenal - you'll all see why next week when I publish the second part of my study. It is clear, however, that biased officiating is not what is costing Arsenal this seasons' championship. It's an inability to score when given opportunities like those in the Blackburn match, or second half collapses due to defensive lapses like those seen against Tottenham, Newcastle, and Sunderland, that's costing them the championship.
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