Stumbling and Mumbling

Rules and incentives

When I read this from the usually excellent John Palmer, I thought it was just vindication of Isaiah Berlin's saying that the great goods cannot live together: Canadians are a great good, football is a great good, but the two together are a horrible mess.
Turns out I was too optimistic:

The Football League board is to consider a proposal to scrap draws and decide matches by penalty shoot-outs.

Apparently, the winner of the shoot-out will get two points and the loser one.
I hope April Fool's Day has come early, because this idea stinks. It would increase teams' incentives to play defensively. Now, a team that puts 10 men behind the ball - as visitors to the Home of Football often do - has, at best, a chance of one point. Under this system, they have a chance of two. So they'll defend even deeper and be even less adventurous.
The result will be less variety and less interesting football.
So, whatever crack-brained imbecile thought of this - and, unsurprisingly, it might be a member of the Stupid Party - shows not just an ignorance of football tradition, but of economics too. Changes in rules change incentives.

Fix!

101 Great Goals asks: Was the FA Cup draw fixed?
Certainly, it's nice for the FA that there's a chance of a Manyoo-Money Launderers final. But this could have happened by chance.
What's more suspicious is Chelsea's progress in the Cup, in two ways:
1. They've had four home ties. The chances of this happening by chance are 0.5 to the power 4 = 6.2% (1 in 16).
2. Their first three ties were against lower-league opposition. In the third round, they got Macclesfield from League 2, when there were only 12 teams of 63  from League 2 or lower in the draw. In the fourth round, they got Forest from League One, when only 8 of 31 other teams in the draw were League One or lower. And in the fifth round, they got Norwich, when there were only 6 of 15 teams from the Championship or lower.
Though the probabilities of such easy ties coming out of a fair draw were reasonable in each round, they multiply to yield a low probability over the three rounds: (12/63) x (8/31) x (6/15) = 1.96%.
The chances of three home ties against such lower opposition are just 0.2%  - 1.96% x 12.5% - or 1 in 500.
This is very low for a random process, so it  should ring alarm bells.
Or should it?
First, the FA Cup draw consists of loads of chance events. Some combinations of these will look unlikely. But because there are so many unlikely combinations, some are likely to turn up. If you test enough hypotheses,  some will look statistically significant. Had things turned out differently, I could be raising suspicions about Manyoo's or S***s' draws.
There's a parallel here with the Drake equation (not, alas, named after Ted, the former Chelsea manager). It says that the probability of life on any given planet are minuscule, but because there are so many planets, life elsewhere is almost inevitable.
Second, we shouldn't judge processes merely by outcomes. The fact is that to rig the draw would require buying the silence of lots of people, such as the ex-players drawing the balls, which is unlikely.
There's a message here about economic inequality. Even fair processes can occasionally yield outcomes that look suspiciously unfair.

Idiot alert

The prize for idiot of the day goes to....
Me.
The data I gave in this post were all wrong: Chris and Matthew in the comments are correct. There is a positive (if statistically insignificant) correlation between fouls and bookings.
I had divided cards by fouls, not by games played; just a typo in Excel, but I should have spotted it.
Apologies to all, and especial thanks to Chris and Matthew,
My exposure as bigger idiot than previously thought isn't the only Bayesian prior to be shaken. It turns out that Teddy Sheringham is a better bloke than previously thought.
My world's in tatters.

Fouls and bookings: a negative correlation

Are referees biased against Arsenal? Arsene Wenger (pbuh) suggested last week that they were, as Arsenal get more yellow cards than average, even though they commit fewer fouls than any other team, as this table shows.
Here, though, is a curious thing. Across all teams there's a negative, albeit insignificant, correlation (-0.25) between fouls and cards (counting a red card as two yellows).
I suspect this is partly because referees are reluctant to hand out cards, with the result that dirty games (and teams) get fewer cards than they should.
And here's another oddity. Correlations between cards and points won or attendances are positive, albeit insignificant: 0.13 and 0.16 respectively. Referees don't hand out more cards to smaller clubs or poorly playing ones - if anything the opposite.
These correlations, however, are driven by the negative correlation between fouls and cards; teams that play well and attract big crowds commit (slightly but statistically significantly) fewer fouls.
This matters. The Premiership's official fair play table (pdf) takes in to account red and yellow cards but not (explicitly) fouls committed. But if cards and fouls are negatively correlated, this means a quite dirty team could wrongly top this table and so qualify for the InterToto cup.

Beckham: an Adler superstar?

David Beckham's mega-bucks move to LA Galaxy sheds light upon the economics of superstars.
Maybe the Galaxy are right to believe that his salary will pay for itself, as Beckham's celebrity attracts Americans to "soccer."
The interesting question is: where does Beckham's celebrity come from?
In Sherwin Rosen's view of superstars, it comes from the fact that small differences in ability can efficiently translate into massive differences in income. A great-looking model cannot be replaced by two lesser-looking ones, nor a top film star by two lesser ones, nor a great footballer by two good ones. The upshot is that people at the top of their professions can earn massively more than those slightly below them.
But is this really true of Beckham? There are loads of players with more looks and ability than him - Cesc, Thierry, and perhaps some who don't play for Arsenal. But Beckham will earn far more than these. Indeed, he's comparable in looks and ability to Freddie Ljungberg, who's been struggling to avoid a move to West Ham.
Why should two similar men have such contrasting fates?
This is where Moshe Adler comes in. People, he said, like to consume the same art that others do, or to talk about the same people that others do (pdf). They want, therefore, to focus disproportionate attention upon one or two people. And these people get greater fame or wealth than other similarly talented persons. Beckham, then, is profiting not from his superior talent, but from being a focal point - though, of course, he and his missus have strived for this.
There's good empirical evidence that Adler's theory can explain the emergence of superstars. Here's evidence from German football (pdf). And here's some from Pokemon cards (pdf).   
This, of course, matters. If Adler's right, inequality is not necessarily efficient.

Iain Dowie and Bayesianism

Charlton Athletic's decision to sack Iain Dowie reveals, I suspect, two ways in which management decision-making can go wrong.
1. Over-reaction. In judging whether Iain Dowie is a good  coach, we should compare his reasonable success at Oldham and Palace against his poor performance in the first 12 games of this season. In theory, we can use Bayes' formula to weight these competing considerations.   But why should we weight the last 12 games more heavily than three years of success?
It could be that Charlton chairman Richard Murray is just over-reacting to a small sample of evidence, which is contaminated by bad luck. There's some evidence that stock market investors can do this too.
2. Over-confidence. Just three months ago, Murray thought Dowie was such a good boss that he offered him £11.2m to spend on players. Now, he thinks it's worth spending £2.5m to be shot of him. In both cases, he seems to have been remarkably sure of his judgment.
These aren't the only biases of which Murray might be guilty. Maybe there's also: neglect of probability, the failure to see there was a good chance of Charlton doing badly in 12 games anyway;  the pseudocertainty effect, the tendency to make risky choices when faced with a possible bad outcome (relegation); and the fundamental attribution error, the tendency to over-rate the importance of individual agency.
The message here is that apparently simple judgments - to sack a man or not - can be prone to numerous errors, when the evidence is uncertain.
* No mention of Charlton would be complete without reminding everyone of the famous fight between Derek Hales and Mike Flanagan, recalled here. When Hales says the fight "was a bit more than that", he's referring to the fact that Flanagan called him a one-bollocked bastard.
** My main reason for posting this is to show that I can illustrate my posts with something other than pictures of beautiful women.

Foolish Fifa

Isn't this a really stupid idea?:

Fifa and the international players' union...have proposed the implementation of a six plus five system, whereby six members of a side must be eligible to play for the club's national association.

Just consider the winners and losers from this. Winners:
1. Mediocre players in countries with the richest leagues, who'd see demand for their services rise.
2. The richest clubs, who can afford to pay high prices for domestic players. The premium teams pay for English players, which is already huge - Michael Carrick cost £8m more than Xabi Alonso - would rise even further.
Losers:
1. Good players from countries with poorer leagues, who'd have less opportunity to play in richer countries. You might object that the best players will still find a place in top teams. But how will they get the chance to develop their talents if they can't play in the strongest leagues when they are young? Would Arsene Wenger really have been able to buy and develop Toure or Eboue (say) under Fifa's proposed rule?
2. The fans. We'll have to watch Harry Hoofalot chasing his first touch in an even more uncompetitive league, in which the money-launderers and Manyoo have bought up the best English players.
Luckily, Fifa's rule almost certainly contravenes European law, so there's little chance of it being implemented. I hope...

Dirty football pays

Don Revie was right - playing dirty football is the key to success. This paper by Christos Papahristodoulou shows that in last year's Champions League, there was a strong correlation between the number of fouls a team committed and the number of points won (0.877) or goals scored (0.762).
The correlation between fouls and yellow cards is only 0.688.
Indeed, the correlation between points won and fouls is greater than the correlation between points won and goals scored, corners or shots wide. Dirty football, it seems, works better than attacking football; Arsenal and Barcelona might have been outliers last year.
What's more, there's a statistically significant positive correlation between goals scored and both fouls committed and being caught offside.
Chelsea's performance on Wednesday could suggest that Jose Mourinho and Didier Drogba know all this.

Superstars and talent

Superstar salaries aren't just a big reward to talent. That's the message of this paper (pdf) by Egon Franck and Stephan Nuesch.
They studied the influences upon the market value of players in the Bundesliga. They found that whether a player had a personal webpage was more than three times more important for his value than whether he played for his national team. What's more, goals and assists are insignificant influences upon market value, whereas the number of page returns from Google, and the number of press mentions, are significant.
This corroborates Olivier Gergaud and Vincenzo Verardi's study (pdf) of the prices of Pokemon trading cards, which found that prices are not related to observable characteristics. Both vindicate Moshe Adler's view of the emergence of superstars, against Sherwin Rosen:

There are many artists who possess stardom-quality talent. What produces superstars...is the need on the part of consumers to consume the same art that other consumers do. This need arises from the fact that the consumption of a piece of art is not a momentary experience but a dynamic process in which “the more you know, the more you enjoy.” Consumers build “consumption capital” in art, and the larger the capital the greater is the enjoyment from each encounter with the art and the artist...
The star emerges from among several artists who are all equally talented. Obviously, talent cannot be the determining factor in this process. Instead, consumers select an artist at random when they add a new artist to their consumption basket. It is simply by pure chance that one of these artists ends up with more patrons than the rest.This initial advantage makes the lucky artist the most popular, and since consumers prefer popular artists, other consumers will switch to her as well. An initial advantage can thus snowball into superstardom. 

All this suggests that mega-salaries might not be economically efficient. More importantly, it suggests the money launderers paid well over the odds for Michael Ballack. 

Who should own footballers?

Who should own footballers? This is the question raised by West Ham's purchase of Javier Mascherano and Carlos Tevez.
The odd thing is that the Irons have not bought the pair. Their registrations are owned by a couple of media companies. West Ham have only bought a lease on the two.
Is this efficient?
Start with the basic economic principle - that assets should be owned by the person most able to maximize their value.
Ordinarily, this argues for an individual to own his own human capital, as this maximizes his incentive to develop his talents. However, three things argue for football clubs to partially own players, by holding their registration and thus limiting their ability to move:
1. The value of a player is maximized by a team playing to his strengths. Thierry Henry's abilities, for example, are maximized if Arsenal play through balls to his feet and have players running off him, rather than if they hoof it long to his head a l'Anglais. There are asset complementarities between team and player. And where assets are complements, they should be jointly owned*.
2. The value of a team - and hence its players - is maximized if the players play together for a long time, and so can gel. For example, the success of the Manyoo team of the late 90s was based in large part upon the fact that many of its players had been together since the youth team. And the fact that the England team has for years been worse than the sum of its parts is partly due to the fact that they don't play together long enough.
Allowing teams to own players' registrations helps them hold onto players and so grow together to be a better team.
3. If clubs can get a transfer fee for a player, it increases their incentive to discover and develop talent. That raises the attractiveness of the game, and so increases players' earnings.
Now, the question raised by the Hammers Two is: why (if at all) are these arguments fading? Here are three possibilities.
1. Clubs' control over top players is weakening. When Ashley Cole wanted to leave Arsenal, there was little the club could do to keep him. Arsenal's ownership "right" had little practical value**.
2. Short-term time horizons. West Ham believe the benefits of a few months of uncertain  ownership of the players - maybe the possibility of getting into Europe next season - outweigh the costs, of being less able to build a team for the long-run. It's common for managers to complain that they don't get the time to build a team in the modern game. Alan Pardew seems to be acting on this principle.
3. The value of top players depends more and more upon their image rights. These are better maximized by media companies, which have expertise in the field, than by football clubs. Maybe the rise of celebrity culture means that football teams are more and more regarded as collections of individuals than as collective units.
In cultural terms, I deeply lament point 3. But is it sufficiently powerful to make it efficient for media companies rather than clubs to own players? I'm not sure, especially in this case: Tevez in particular is so ugly he could be mistaken for a West Ham fan***.
* This raises the question of why players don't own clubs. I guess it's partly because they don't want the risk.
** If you believe Chelsea, a similar thing happened with William Gallas. But no-one believes the word of money-launderers.
*** Yes. I did write 600 words solely to mention this.