Another (statistical) way to look at World Cup performance

The best player in World Cup group play as of June 24th.

I am always on the lookout for good statistical measures of individual soccer players' contributions to overall team success. This has been elusive for a number of years, whether it's due to the pace of the game or the desire of many to not sterilize the beautiful game with a (largely American) obsession with statistics. One of the more popular methods for looking at individual players' overall performance is the Castrol Index, but this metric is a much better measure of individual, and not team, performance.

Over the last several weeks I have read tweets that proclaim "New Statistical Method Quantifies Soccer Player's Performance" that often linked to a summary of the study from a news organization (like Forbes). Very few of the tweets link to the original study, likely due to its relatively deep mathematical and statistical theory. I've read several of the articles and the original study, and can tell you the news articles leave out much of the very powerful details of the study that can provide us some great insight into World Cup 2010.

Before I go into explaining the power of the study, I must comment on its methodology and approach to provide proper background. The study is completed from the standpoint of asking, "What do individuals do to make teams succeed?" Soccer offers a good method for evaluating such theories because it provides a quantifiable outcome (goal differential), yet many of the player's contributions are hidden by the few traditional stats available and the few goals made in a match. This forced the authors to examine players' contributions in ways other than scoring - namely successful passing and assists given the choices each player was presented with. This allows every player, except for goal keepers, to be evaluated for their effectiveness in contributing to the team's success. By creating their own scoring system for such passes and shots on goal the authors have developed a way to evaluate each player's contribution to the team's success or failure, as well as a correlated method for translating the average of the player's scores to a positive or negative goal differential. A more detailed reading, for those interested in the statistical theory, is available here.

The statistical method manifests itself in the graphical representation in Figure 1. The thickness of the lines defines the frequency with which such passes are made, the color the score of the pass or shot path, and the size of the player circles the overall player score. One can see in each of the 2008 Euro knockout matches that not only do Spain's players provide more accurate passing, but they also have a greater proportion of their players executing accurate passing.

Figure 1: Graphical representation of Spain's Performance in Euro 2008 knockout matches.

The studies findings are fascinating, as the authors demonstrate their new test statistic correlates well with actual match results. Those findings include:

• The test statistic is defined as the difference between two team average scores in the study's new player score method. The authors are able to prove a statistically significant mean player score differential between teams where a win occurs versus a loss.
• When testing for sensitivity of the test statistic in predicting match outcome, the authors find a statistically significant difference between win and not win or lose outcomes. This proves that the test statistic, as conceived, accurately predicts the team's likelihood of having won the match based upon the observed behavior.
• In looking at the sensitivity of the test statistic, the authors found that Euro 2008 team performance could be accurately predicted by using the two highest scoring players on a team for the team average. This greatly simplifies any quick calculations one wants to make, and proves that most teams are only as good as their two best players.
• The sensitivity analysis also showed that when the test statistic is greater than 0.75, the odds that the higher performing team wins the match are 3:1.

It remains to be seen if such a model is as accurate at quantifying World Cup performance as Euro 2008. The authors of this study are working to assess this attribute, and their real time scoring can be found here. Assuming that it does, there are a couple of interesting conclusions to be drawn from World Cup play so far.

• Argentina, Spain, and Chile have been the best teams in group play so far as ranked by average rating difference. This is important, because the model showed that teams that played the best in group play tended to also play the best soccer in the knockout rounds of Euro 2008.
• Lionel Messi tops the list of highest scoring players, but Brazil has five of the top ten spots.
• As a preview of this coming Saturday's knockout round play, Ghana averaged a 0.7 team differential score vs. 0.3 average differential score for the US.
• Portugal's 7-0 drubbing of North Korea only yielded a 1.4 average score differential.
• The England/US match showed a 1.0 average score differential for England, which indicates the US was lucky to get out of the match with a goal.
• Conversely, the US had a 1.2 average score differential benefit vs. Slovenia. Remember, the odds say that the US should have won that match three times out of four. Further rationale for why the outcome didn't truly represent the team's effort.
• The US turned in their best performance of group play with an average player score of 2 for a differential of 0.6 vs. Algeria.
• Finally, Clint Dempsey is the US player with the highest average player score.

If you're interested in further statistics, the Amaral Lab's Footballer-Rating.Com website allows anyone to look at team, player, or match statistics. I recommend you check it out, if for no other reason than to see how your favorite team might stack up against their first knockout round opponent based upon group play scores. It will certainly be interesting to see how this model works within the data generated at the World Cup, the findings of which will be published at a later date by the study's authors.