The Zen Master who keeps Arsenal outperforming the model
Several weeks ago my fiance asked me the question below.
In a paragraph or less, why did you determine you like Arsenal?
You see, this is my first season being a supporter of Arsenal. I had followed soccer off-and-on earlier in my life, but I truly fell in love with the beautiful game during our local team's, the Seattle Sounders FC, inaugural season in Major League Soccer. The season was winding down, I wanted to continue my growth in following the game, and I had several friends that were Liverpool supporters. Naturally, I could follow their lead in watching the EPL but I had to find my own club to support. After some intense research and a few initial matches, I decided to become an Arsenal supporter. Hence, the question from my fiance as my first season as a supporter came to an end. My response is below, with the bold section referenced later.
First, I wanted a reasonably successful club to follow, but not a Yankees-style juggernaut. Arsenal also had a reputation of "beautiful, ball-control passing" soccer rather than a single superstar approach, which was of interest to me. Third, Arsene Wenger is a classically trained economist prior to being a soccer manager and is at the forefront of using detailed, obscure statistics to identify talent early and then develop them - that's cool to me. Finally, they are one of the few clubs in the Premier League to run a profitable business year in and year out through intelligent expenditures and resisting huge transfer fees.
A lot of this was based upon anecdotal or non-statistical analyses. It turns out that there is a statistical way to prove the bold sections above.
In my recreation of the Soccernomics regression there were a few additional results I did not publish in my original post. In addition to basic regression analysis, most statistical packages also highlight any "unusual observations" within the data set. Unusual observations are identified via three methods:
- Standardized residuals (unusual responses)
- Leverages (unusual predictors)
- Cook's Distance (influential observations)
The statistics package I used for the analysis utilizes standardized residuals to highlight unusual observations. Any standardized residual greater than 2 indicates a data point of interest. The full regression statistics for the Soccernomics analysis is presented in Figure 1 below.
Figure 1: Regression analysis for Soccernomics data
The first entry under "Unusual Observations", Obs 2, corresponds to Arsenal's statistics. In this case, the model predicts a response (Fit) of 1.9841 based upon the measured value of 0.97 for the input of ln(wage multiplier). However, the observed value for -ln[p/(45-p)] is 3.0681. This provides a residual 2.44 times the standard deviation of the sample of residuals.
How significant is this gap? Translating the fit predicted by the regression, I get a value of 7.137. This translates to an average finishing position of 7th in the Premier League table. Instead of averaging 7th, Arsene Wenger's squad has average 2nd in the league over ten years on a relatively shoe string budget compared to Chelsea and Manchester United. Liverpool, who spends about the same amount of money as Arsenal, averages a 4th place position.
As I pointed out in my last post, all of the top four teams in the Soccernomics analysis outperform the predicted response of the regression analysis. Arsenal is the only one that statistically outperforms the other three in terms of getting a better bang for the buck. This is the statistical proof of what we Gooners have known all along - Wenger is one of the few managers to outperform the marketplace.
Note: As always, if you have any analyses you would like to see performed or friendly wagers settled, leave a comment on the open thread.
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