Sunday, 19 October 2014

So the Ball Doesn’t Go In by Chance. But Do We also Know Why?

Football leaders who come from a business background generally are met with great scepticism by the wider public and everyday evidence shows this is often deservedly so. The take of Ferran Soriano, CEO of Manchester City FC and former Vice President of FC Barcelona, is an interesting one, though: he warns against readily translating business ideas into a football context and instead extracts from his business background rather the conviction that a thorough understanding of the logic behind a phenomenon – let it be business or football – will allow for improving upon its management. Moreover, to better understand the logic of football, he embraces authoritative research findings in this arena.

As a notable example, in the first chapter of Goal: The Ball Doesn’t Go In by Chance, the now CEO of the Citizens points to findings by researchers Szymanski and Kuypers of a club’s success being strongly positively correlated with how much the club spends on players' wages, but not transfer budgets – a key take-away featured also in Soccernomics, the bestseller co-authored by Szymanski. Two things are striking about Soriano’s account. First, that he seems to get the interpretation of the findings more right than the researchers in question. Secondly, that it appears to be the “common sense” Soriano refers to that helped him get the interpretation more right, but that a true logic for doing so remains hidden. In this post, I will explicate the logic behind a plausible interpretation of these findings. This will also provide a handy checklist for when interpreting research findings more generally.

In Soccernomics, the authors mention that, based on analysis of historical data from the English Premier League, they are able to conclude that, “the correlation [of a team’s league position] with players’ pay [over a long period is] about 90 percent. In short, the more you pay your players in wages, the higher you will finish”. Even more than the content of this claim, what is interesting here, from a scientific perspective, is the leap from one step to the next: the strong positive correlation is suggested to imply a causal relationship of the type “A leads to B” (with "A" being players’ pay and "B" league position). The A->B causal interpretation, however, is only one of at least six possible explanations for the strong positive correlation. I will argue that it is most probably not the applicable one here and that Soriano intuitively rather seems to have gotten the most plausible one. 

Possible explanations for the strong positive correlation include the following:

1.     There is correlation, but no causation. In fact, correlation does not automatically imply causation: some things just happen at the same time, but without one causing the other. For instance, following the Dutch Armada’s recent surprisingly disappointing performances in the Euro 2016 “qualifiers” – let’s more accurately call them “friendlies”, as everyone is to qualify anyway – journalists started speculating, rather jokingly, that the Dutch may be encountering the “curse of the third”. Apparently, since 1980, no country other than Germany that ended third in the preceding World Cup has been able to qualify for the subsequent Euro Championships. People of common sense readily understand that this is just a “funny coincidence”, e.g. similar to England on average being more successful when playing in red than white jerseys. Moreover, the number of data points would be too small to make any rigorous claim to the contrary. Szymanski et al.'s analysis appears to be based on ample data so that this explanation of mere coincidence can comfortably be ruled out.

2.     The strong positive correlation is not due to coincidence and thus indeed points to a causal relationship. In this case, the causal relationship can still be one of at least four types:
  • A leads to B. In our example, higher wages directly lead to a better league position, i.e. the explanation proposed by Szymanski et al.
  • B leads to A. In our example, a better league position leads to higher wages. Winning a league naturally implies winning prize money, of which the players are to get a significant share. Not all that implausible as an alternative explanation then, perhaps. But note that the proportion of prize money in a typical footballer’s wage tends to be rather small.
  • A and B are positively correlated, not because one causes the other, but because they have a common cause (“C”). A typical example would be the one of the use of sunglasses and temperature being strongly positively correlated. Neither one causes the other. Rather, they both have a common cause, viz. intensity of sunlight. In our case, A and B would seem more closely connected than merely through a possible common cause, though.
  • What is also possible is that A does lead to B, but only indirectly, i.e. through another variable, viz. a mediator ("D"). In our case, it seems most plausible that paying higher wages (A) leads to a better league position (B), but primarily if not only to the extent that these wages are used to employ better players (D).

So, which one will it be?

Not only do Szymanski et al. seem to incorrectly suggest that correlation automatically implies causation, but also that if there is causation, it must then be of an “A leads to B” nature. To appreciate how unlikely this explanation for the on-hand correlation would be, consider what it actually implies: that if you are to pay more (to whomever), you will obtain a better league position. So if you merely start paying your team’s current players as if they were Messi or Cristiano Ronaldo, your team would soon get the results of Barça or Real Madrid. Szymanski et al. seem at least to acknowledge this inescapable implication of their attribution of their findings and – more puzzlingly – seem to go with it: “The question, then, is...[with] this knowledge of the relative importance of wages and unimportance of transfers, how can you win more matches? ...In general, it may be better to raise the pay of your leading players”. Agreed, paying peanuts is likely to hire you monkeys. But is rewarding your monkeys as if they were stars going to turn them into a dream team, really?

What about Soriano? He, as readily, neglects coincidence, thus equating correlation and causation – though he seems to be ruling out coincidence already in the very title of his book. His interpretation of the findings: “So, if you want…a team with a chance of regularly winning championships, then you need to work consistently to have a big club that generates enough revenues to be able to sign the best football talent available.” So the finding that transfer expenditure does not seem to be strongly positively correlated with sportive success does not fool Soriano into believing that it is your current squad that you should simply start paying more. Interestingly, while he gives the impression he is merely reiterating Szymanski et al.’s conclusion, in fact Soriano is rather endorsing the alternative explanation of a favourable position in the league pre-requiring that high wages are used for attracting top talent.

Where Soriano does err, is in stating that per the analysis and findings by Szymanski et al., common sense has been “corroborated by mathematics”. A subtle, yet meaningful, distinction is to be made here. Szymanski and Kuypers were not using mathematics, but rather statistics and, more specifically, regression analysis. Why is this distinction important? Because mathematics is the only way by which general truths can actually be proven. For instance, that (a + b)2 = a2 + b2 + 2a.b can easily by proven by simple application of algebraic rules. Unless someone is able to spot an error in the mathematical proof, a general rule has thus been proven. Additionally, in the natural sciences, there are several general laws that are derived from observation. An apple falling from a tree, for instance, points to the existence of gravity, which will always apply on the earth’s surface.

It is very different in the social sciences, however, where human will and behavioural traits make that not all priors will necessarily lead to the same outcomes. Regression analysis is here typically used to discern meaningful patterns. Very importantly, though, such analysis cannot prove something to hold generally; it can only show for something to occur, with a certain level of probability (cf. confidence intervals) under certain conditions and controlling for certain factors. (One can prove for something not to hold generally, by means of an empirical counterexample, e.g. if a team of 8 beats a team of 11, it has been proved that this is not impossible. However, the general rule can never be proven (empirically): the fact that so far every time a team of 11 came to beat a team of 7 does not show – let alone prove – that that is what will always happen under such conditions.)

Consequently, in the case of regression analysis, and unlike with mathematics, it is not uncommon for different researchers to be able to show quite contradictory findings, based on similar data, e.g. by accurately vs. not controlling for mediation or a common cause.

In short, when there is strong positive correlation, several things can be going on, including nothing at all (i.e. coincidence); A leading to B; B leading to A; C leading to both A and B; mediation; or strong correlation may disappear when accounting for adequate controls. The "noisy neighbours'" CEO appears intuitively right in his interpretation of the potentially important football findings proposed by Szymanski et al. I would expect him to be first to acknowledge that it is helpful to have made visible the hidden logic of why that is so.

Thursday, 2 October 2014

Major League Beckham: Mindless Football Star or Hollywood Robber Baron?

“Football is an industry” and “football is entertainment” are two oft heard statements that true (European) football fans tend to have an allergic reaction to. Previously, because both were missing the point. Nowadays, perhaps more because of saudades to a long lost past. Authoritative sports news site sporza.be could not go past the presence of Beyoncé during Tuesday’s Qatari derby, PSG vs. FC Barcelona. So even those who did not see the CL game could rest assured they were abreast of its essentials.

A more noteworthy appearance in the Parc des Princes’ stands was David Beckham, who had concluded a most successful playing career in that very stadium with a heart-warming standing ovation only last year. What struck me most about Beckham’s close-up on Tuesday was how genuinely happy he seemed. According to the 'football as an industry' philosophy, it may have been an unpleasant day for him, though, as it was announced Kaká would soon be taking over from the former England captain as highest paid foreign player in the history of the MLS: Kaká will be netting US$ 7.1m p.a. at Orlando City, whereas Beckham reportedly earned US$ 6.5m p.a. when at LA Galaxy.

Source: futbolpulse.com

Even if he cared much about the money – and in case he doesn’t, surely his wife will – I would expect this comparison merely made Beckham smile. Abstracting from any sponsorship-related revenue, when signing his contract at LA Galaxy, Beckham's entourage ensured the inclusion of a clause that had been negotiated with the MLS. It concerned an option to enter a franchise team in the MLS (i.e. the US Premier League) in the future at an exercise price of US$ 25m – a fraction of what recent expansion teams were ordered to pay to the league (US$ 100m in the case of NYCFC and US$ 70m for both Atlanta and Orlando City). Furthermore, it is not just about coughing up the money; ask even the legendary NY Cosmos of Pelé and Beckenbauer how hard it is to even be considered for an MLS franchise these days. It should not be all that surprising, then, that already in early 2014, less than a year after his retirement, Beckham informed the MLS he intended to exercise his option.

Beckham’s expansion-team idea is a worthy textbook example of how to create and negotiate an outside-the-box option, one that is very easy for the other party to grant – it effectively cost the MLS zero at the time of negotiating Beckham’s LA Galaxy contract – and extremely valuable to oneself – a future monetary value of roughly US $70m to Beckham. Additionally, it was not the first time Becks and his entourage pulled off a trick like that. Beckham's signing for Real Madrid, in 2003, was facilitated by what became known as the 'Beckham law', a tax regime taxing qualified foreign workers in Spain at the lowest tax rate, regardless of their earnings. And when he then moved to the MLS, they there enacted...the 'Beckham rule', allowing for teams to designate a high earner to be exempt from the team's salary cap. Curiously also, in each of these cases, the major concession was beyond the prerogative of the club and was granted by a higher authority they somehow had been able to interest, viz. the league or the state.

And almost all of the credit goes to David Beckham. Did he come up with the expansion-option idea all by himself? More likely, he did not even have a clue about the stipulation as he signed his LA Galaxy agreement. Beckham is very much aware of the fact that he was not born the world’s smartest guy. It takes a humble person to acknowledge this and act upon it: Beckham thus surrounds himself with some of the canniest to take care of his business for him, rather than agents looking to sell him. So many averagely smart people refuse to acknowledge any need to do so and they tend to see their fortunes mysteriously vanish before their eyes as soon as they hang up their boots. The Greek philosophers can be proud of Beckham. Few if any in contemporary showbiz embody the adage that self-knowledge is the basis of all wisdom as well as this simple, working-class-born billionaire.

Source: foxsports.com

Regardless of the mostly irrelevant discussion about whether Kaká will actually become the highest-earning foreign player in MLS history, observers of the premier US soccer league may actually have something to get excited about. Next to Kaká, also Frank Lampard and David Villa are moving to the Land of the Free. And who would be surprised if Ronaldinho were to jump the Mexican border and pass through the MLS before playing his final trick?

Other than European leagues – at least traditionally – the MLS, by origin, is indeed an uncovered industry and so is David Beckham himself. In addition to having gotten the most out of his career and his image, Beckham is also getting the best of both worlds – idolatry in Europe and big business in the USA. One year after his retirement, he has all reasons to look happy. There is not a cloud in the sky for David. Whereas many of the stars of his generation must fear the uncertainty of whether they are found fit for a coaching career, Becks can soon preside over his own Miami-based club – and with a huge discount. It remains to be seen whether we will again witness someone who can bend it like Beckham.