Friday, December 17, 2010

Some Light Statistical Reading: Why I Use Relative Measures Instead of Absolute Measures

One of the cool experiences I have had since my post showing the undeniable correlation between squad transfer cost and table position went live last Thursday was being contacted by none other than Stefan Szymanski, one of the co-authors of Soccernomics.  Stefan was quite complementary in his email to me, with much of the content in the email falling along the lines of his column in the Evening Standard.  He also attached four of his academic papers he's written over the last two decades, which was a treasure trove of data and analysis that was behind many of the chapters of Soccernomics.  I have linked to each of them at the end of this post, but being academic papers each of them has a fee associated with them.

Of the four, the most enlightening to an American sports fan would be the paper he co-authored with Stephen Hall and Andrew Zimbalist in the Journal of Sports Economics entitled "Testing Causality Between Team Performance and Payroll: The Cases of Major League Baseball and English Soccer."  This paper does a great job comparing the ability to "buy trophies" in US baseball and English soccer, with far more in-depth analysis than I ever could perform.  Their main goal was to determine causality - does pay build better teams, or do better teams beget high salaries?  What's great about this piece is that it clearly explains the authors' approach to which measurements they use in their analyses and why.  I am often challenged as to why I use multiples of an average and relative finish position, rather than absolute pay and points, and Szymanski, Hall, and Zimbalist summarize better than I ever could why these metrics are key.
"In particular, [in studying Major League Baseball] we focus on winning percentages in the regular season and payroll spending by each team relative to the average payroll spending of all teams for the season.  If wealthy teams can buy success, we conjecture, then the most precise measure of their spending is the ratio rather than the rank.  For example, given that luck still plays a part, then the team that spends the most is more likely to achieve the highest ranking if it spends 10 time the average rather than 5 times the average."
Essentially, outspending your rivals to greater degrees ensures a greater possibility of minimizing the effects of the noise generated by random events like injury, freak plays, etc.  The added benefit is that using this approach helps linearize the payroll data, and compensates for the natural diminishing returns as payrolls escalate to place in the top few league table positions.  The authors then continue later in the piece to explain why they look at long-term averages rather than point data from each season.
"However, given that there are numerous factors that may influence a team's performance in a particular season, many of them purely random, a more reliable test of the effect of spending might be to consider those teams that overspend during the long term to see if they outperform the rest."
This is exactly what the authors do in this article and what Szymanski and Kuper do in Soccernomics, with both approaches yielding regression equations that explain much of the variation between performance and team payroll.  It was with this approach in mind that I studied the Transfer Price Index and utilized MSq£ for my unit of measure when studying the effect of squad transfer cost on table position.

While I have chosen to highlight this paper due to the applicability of the excerpts above, I would recommend the four papers below to anyone interested in soccer econometrics.

Key Stefan Szymanski Papers

Hall, Szymaski, and Zimbalist. "Testing Causality Between Team Performance and Payroll: The Cases of Major League Baseball and English Soccer."  Journal of Sports Economics. Vol 3 No 2.  May 2002.

Szymanski and Smith. "The English Football Industry: profit, performance and industrial structure." International Review of Applied Economics. Vol 11 No 1. 1997.

Szymanski. "A Market Test for Discrimination in the English Professional Soccer Leagues." Journal of Political Economy. Vol 108 No 3. 2000.

Garcia-del-Barrio and Szymanski. "Goal! Profit Maximization Versus Win Maximization in Soccer." Review of Industrial Organization. Vol 34 No 1. February 2009.

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