Money and Football: Big Spenders Take All?

It’s Transfer Deadline: D-Day for many managers and club Presidents across Europe to scramble together their winning team for the months to come. One of the main insights stemming from a “soccernomics” approach is that transfer-fee spending does not lead to positive results on the pitch, but that wage spending does. This relationship was proposed some years ago by sports economist Stefan Szymanski and sports journalist Simon Kuper in their bestseller Soccernomics and, meanwhile, has influenced some of the most powerful people on the business side of sports, such as Ferran Soriano, CEO of the highest-spending sports club worldwide, Manchester City, as evidenced in his book Goal: The Ball Doesn’t Go In by Chance. In an earlier post, I pointed out that a causal relationship going from wage spending to success is very unlikely to exist. Interestingly, in his new book Money and Football: A Soccernomics Guide, Professor Szymanski formally reiterates his stands on the matter, although he actually gives away that it is wrong... I’ll explain very succinctly.

Prof. Szymanski states that there is a very high correlation between wage spending of football clubs and their league position. He now acknowledges that correlation (i.e. two things occurring at the same time) does not automatically imply causation (i.e. one causing the other). However, he points out that, “now there are some statistical tests that one can implement in order to get a better idea about whether a relationship is causal. Some (but) not all of these studies support the view that causation runs from wage spending to league success” – without any indication of what “some (but) not all” concretely means (e.g. two out of ten?, nine out of ten?; which ones yes and which ones no?) He further mentions – and here I certainly do follow – that, “it’s also important to have a theoretical model in mind" and he goes on by suggesting that, "it’s very hard to develop an argument to explain the data that does not entail causality from wages to performance.” Don’t mind if I at least gave it a try:

Wage and talent, or quality, of a player tend to be very highly correlated – including for reasons mentioned by Prof. Szymanski, i.e. that players are operating in a competitive market, with lots of information being available on players and their performance. As a result, a team made up of highly-paid players often reaps success. But the causal driver is the talent, not the wage. In other words, if a same quality player would earn less (within reasonable bounds), performance would be very likely to be the same. For example, do we really expect Kevin De Bruyne to start playing so much better even now than last season just because his wage just nearly doubled? Ridiculous. The driver of – player and team – performance is the quality of the player(s). The wage a player earns is an indicator of that quality, but it does not drive that quality.

Source: mcfc.co.uk

Prof. Szymanski actually confirms exactly that with his “revised formulation” of the pay–performance relationship in his new book. He mentions that money is the key to success, not because by paying donkeys very high wages you will become successful, but because a big checkbook gives you access to superstars (i.e. very high-quality players). It doesn't take a PhD to realize that, if you put two and two together, what this in fact means is that quality, or talent, not wage, drives success. And that quality or talent tends to be highly correlated with wages, due to supply and demand dynamics of the market for players. Prof. Szymanski actually concludes that his "pay-performance line works because there is a market–...the market prices the relationship...between talent and success"! (emphasis added)

For those who love statistics, my conjecture corresponds to a strong suspicion that Prof. Szymanski's results demonstrate what is known in the jargon as omitted-variable bias. According to Wikipedia, "in statistics, omitted-variable bias occurs when a model is created which incorrectly leaves out one or more important causal factors. The "bias" is created when the model compensates for the missing factor by over- or underestimating the effect of one of the other factors." Leaving out an actual variable for talent, or quality, while including a variable that is highly correlated with quality (such as wage) may thus lead to showing a very strong direct relationship between wage and success - but only because talent as such has erroneously been omitted. A look at the original 2002 Journal of Sports Economics paper by Hall, Szymanski and Zimbalist confirms omission of a talent variable in both the regressions and the causality tests.

The main lesson for sports managers out there? Look out for talent, not just to spend your money! Something the likes of Swansea’s Garry Monk realized quite some time ago – partly out of necessity – and something Louis van Gaal still doesn’t – partly for lack thereof. Fortunately for mad King Louis, he seems blessed with Maecenases who don’t seem to either.

Source: BBC's Match of the Day (30/08/15)