I am in the process of building a very large post that lays out how Arsenal is treated by officials versus other teams in the league. To build such a case, I need to be able to show the impact of various match elements on the likelihood of a team winning the match. The tool I am using to build such a case is a binary logistic regression (BLR) that looks at venue and differential of shots, shots-on-goal, corners, fouls, and fantasy points based upon yellow and red cards.
I am still working on the final analysis, but in the meantime I have analyzed the impact of red and yellow card differentials on each of the Big Six's chances of winning a match. The plots below show the changing odds of winning a match as a function of red and yellow card fantasy point differential based upon data from the 2005/06 though 2009/10 seasons. The first graph shows a plot of the changing odds at home, while the second graph shows a plot of the changing odds for away matches. Both plots use the teams' average value for shots, shots-on-goal, corners, and fouls (broken out as home and away averages) as inputs to the model. Click on either of the graphs to enlarge them.
- Manchester United clearly is the least sensitive to card differentials at home. When playing to their average form, they win at least 75% of their matches.
- Chelsea is the most sensitive of the home teams in the Big Six. They drop from nearly 90% odds of winning to 30% over the range of fantasy point differentials they see.
- Chelsea maintains the best form of the six teams when playing away from home. This is due to the fact that the coefficient for the venue term of Chelsea's BLR was not statistically significant.
- Liverpool is the most sensitive of the Big Six when they are away from home. They go from a 90% odds of winning with their most favorable fantasy point differential to a 10% chance of winning a match when at the opposite end of the fantasy point differential.
- Arsenal runs middle of the pack both home and away, and have a relatively linear relationship compared to the other teams. This is due to Arsenal having the lowest magnitude coefficient in their fantasy point BLR term.
- Tottenham Hotspur and Manchester City maintain the worst overall form of the Big Six across the range of fantasy point differentials.