Friday, April 10, 2009

Physics of Socio-Economic Systems: Soccer

In old textbooks, physics is often described as the science of inanimate nature,” and according to a more recent definition, it is “the science that deals with the structure of matter and the interactions between the fundamental constituents of the observable universe.” So it sounds like an oxymoron to talk of the physics of socio-economic systems. (And oxymorons btw have nothing to do with morons. If you learn anything from this blog it's that Stefan likes Greek.)

However, during the last decades, methods developed in condensed matter physics and statistical mechanics have been applied successfully to financial, economic and social systems, from the analysis of financial data and nonlinear market dynamics to the emergence of traffic jams and the outbreak of cooperation among success-driven individuals (a phenomenon you can witness on every physics workshop. The disease is in many instances short-lived and victims recover quickly when back in their home office). Thus, at the Spring Meeting of the German Physical Society (DPG)  that we visited some weeks ago in Dresden was discussed, alongside more traditional topics such as semiconductor physics and vacuum science (pumps, is all I say, pumps!), the physics of socio-economic systems.

As the DPG spring meetings are traditionally well attended by young students, dominantly those carrying a Y-chromosome, the lecture hall was completely crowded when Andreas Heuer presented the results of a study on the “identification of the different ingredients governing the outcome of a soccer match.” 

Heuer et al's work* shows that during a whole season of the Bundesliga the quality of a team can be characterized by a single fitness value that can be estimated from the league table. They then examined the question how important fluctuations of the team fitness around its average value are. Surprisingly, the effect of fitness fluctuations is very small. Another question that comes to mind is given the average outcome of a match, what is the probability for a specific result? In contrast to a previously suggested interpretations, Heuer et al find the number of goals per team in a match can be extremely well described by a simple Poisson process (for up to 8 goals).  Altogether, soccer turns out to be a surprisingly simple match with respect to its statistical properties.

Entering the building in Dresden where the conference was held, it was impossible not to notice the lack of women. Men, men, men, everywhere - except behind the registration desk obviously. And while women are typically underrepresented at almost all conferences in physics, we had the impression condensed matter is a particularly severe case (data, anybody?). Maybe that explains the attendants' fascination with soccer. Anyway, Bee's talk was in the same session, so we profited from the audience the earlier talks had attracted. 

For a German report on this talk see Jan Lublinski's article Mythen und Zufälle.

* Andreas Heuer, Oliver Rubner: Fitness, chance, and myths: an objective view on soccer results (arXiv:0803.0614v4 []).


  1. Physics is a predictive and testable mathematical model of observation.

    A scalar value characterizes soccer? That was tried with investment banking to assay risk, WIRED 17.03 (March) 2009: "The Secret Formula That Destroyed Wall Street."

  2. Johannes Kepler wrote:
    "Die wohlfeile Tochter Astrologia muss ihre arme, aber ehrsame Mutter Astronomia ernähren"
    "The venal daughter Astrology has
    to feed
    her poor, but honorable mother Astronomy"
    because he had to to horoscopes
    to earn his life.

  3. Hi Stefan,

    A great post demonstrating how statistical approaches can be used as an analytical tool with some success. It would appear to me that such an approach could also be used equally as well to discover if certain leagues may not be entirely on the up and up as to how refereeing can effect outcome. It would be interesting for instance if you looked at the results of the Italian league a few years ago to see how much deflection from the norms would have showed up. Of course the other thing that can’t be seen so clearly with such modeling are the effects had by great players such as Pele, Di Stefano, Beckenbauer , Cruyff and Madonna when they bring their A game, yet what is forgotten that can spoil it all are the Black Swans of football, for only they can see the future:-)



  4. Can games with more statistical complexity become as popular?

  5. ...Beckenbauer , Cruyff and Madonna
    Hello Phil,
    that team might find great numbers
    of spectators... :=)
    It is remarkable, that soccer, in
    Germany long time disgusted as
    "Podoboötismus" has reached
    academic honors, without uproar
    of the saviours of occident :=)
    O tempora, O mores!

  6. Hi Phil,

    It would appear to me that such an approach could also be used equally as well to discover if certain leagues may not be entirely on the up and up as to how refereeing can effect outcome.

    Actually, the talk following Andreas Heuer's was by a guy from Poland, Andrzej Jarynowski, who just tried to address this issue. It seems (I didn't know nothing about this) that the Polish premier league has been ridden by a corruption scandal over the last years, and he attempted to find traces of this is the results of the matches.

    The talk was quite entertaining, but in the end it came out that he couldn't see signs of the scandal in his analysis of the scores. However, I wondered if the methods used by Andreas Heuer might not have been more successful.

    Cheers, Stefan

  7. Hi Arun,

    Can games with more statistical complexity become as popular?

    Heuer made some remarks about other sports in his talk as well. If I remember correctly, he said that his method didn't work very well for sports where there are typically much more goals per match, such as basketball and handball, which both have at least some popularity in Germany.

    But as soccer is the only really global team sport, you may be right ;-)

    Cheers, Stefan

  8. Hi Georg

    soccer ... has reached academic honors, without uproar of the saviours of occident :=) O tempora, O mores!

    What should we expect, now that even Pope Benedict is a fooball fan ;-)

    Cheers, Stefan

  9. Hello Stefan,
    here You can read all the truth
    concerning that contagious pestilence:,M1

  10. Hi Georg,

    “O tempora, O mores!”

    Yes it would have been much easier in Cicero’s “time” as the “custom’ would have been to have the conspirators be judged by lions. Oh how I long for simpler days:-)



  11. Hi Stefan,

    That’s interesting that this also was attempted, yet with Heuer’s method judging fitness such anomalies might become more obvious. I also took note that in Heurer’s analysis he dismissed the concept of a winning streak while confirming the real existence of losing ones although not being able to determine if they relate to physiological factors or injury. So Stefan if you are ever looking for a career change you could start up a sports book and set the betting lines. However I would advise avoid the use of the Gausssian copula function for analysis, as its been rumored that it may not be completely reliable :-)




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