Liverpool's not underachieving, they're just regressing to the Soccernomics mean

As delusional as Wall Street CEO's

I can't help but feel for Liverpool supporters these days. Their club, over a period of three years, has been run into the ground by negligent and uncommitted ownership. Reading more and more about their plans to exit Liverpool, I can't help but feel their ownership is as delusional as the Wall Street CEO's of 2008 about which I am reading. They have a team not going to the Champions League for the first time in many years, a squad saddled with £237M of debt, and Hicks and Gillett want to flip the club for at least three times what they paid only three years ago? That's the height of denial.

All is not lost at Anfield. What has been a rough season will see Liverpool likely finish sixth in the table. The reality is that this is not too far off from the Soccernomics prediction for that side's average payroll over the last 10+ years. The reality is that all of the Big Four - Arsenal, Chelsea, Liverpool, and Manchester United - outperform the Soccernomics regression equation. See Figure 1, where all four hover above the upper right of the regression line, indicating their actual achievement in the table is better than predicted. Liverpool is the dot in the lower left of the four - the one closest to the regression line.

Figure 1: Regression equation of table finish vs. wages with CI and PI

While the gap between the Liverpool data point and the regression line seems small, keep in mind that both attributes are plotted on logarithmic scales. A small change in wages leads to a large change in table position. Given that Liverpool has been outperforming the Soccernomics regression equation, where does the regression analysis predict they will actually finish on an average basis?

The answer depends on which aspect of the regression analysis you look at.

• If one only looks at regression equation itself, Liverpool's finish this year isn't too far off from what the equation predicts. The predicted value for the y-axis given Liverpool's wage multiplier of 2.68 is 2.0121. Translating this y-value leads to an average finishing position of 6.94, or 7th in the table.
• Another way to look at Liverpool's current situation is to look at the 95% confidence interval (CI) for the average finish position. This will communicate the likely extreme average one could expect given the variation in league finishing position. Using the same software package that generated the plot, the bottom end of the 95% confidence interval translates to a y-value of 1.7588, or an average finish position of 9.364. Rounding gives Liverpool an average finishing position of 9 in the worst case scenario.
• Finally, one can look at the 95th percentile prediction interval (PI), which predicts the worst case individual finish given Liverpool's expenditures. This provides a y-value of 1.0532, or a worst case finishing position of 24.10. This would mean Liverpool would be relegated from the Premier League to the Championship. This highly unlikely, even given Liverpool's struggles this year. Thus we begin to see the limits of regression analysis and the distributions it generates.

Figure 2 shows the data referenced in the second and third bullet points.

Figure 2: Statistical output for CI and PI analysis based upon Liverpool wage expenditures

Liverpool's difficult season is really just a regression towards the mean. What their challenges point to are the ones likely coming for at least Manchester United and possibly Chelsea. Namely, to soar so high above the Soccernomics regression for so long, these teams have had to make ridiculous payments to players and saddle their squads with suffocating debt. It's unsustainable, and will self correct itself if UEFA doesn't take action first.