Two Poles in goal

Note: If you don't follow Arsenal FC, this post may not make much sense to you.

Wojciech Sczesny's father Maciej used to be a pretty successful goalkeeper himself back in the day. This means that whenever he feels like talking about his son's current situation at Arsenal, some Polish sports media outlet will print whatever he has to say, which means that soon enough it will be all over British sports tabloids. Here's what Wojciech had to say on his Facebook account about dad's latest outburst:

Really shouldn't be dealing with this one day before the cup final but my father leaves me no choice.
I have not spoken to him in more than 2 years and just like everybody else I have had enough of his idiotic comments about The Football Club and The Manager I owe so much to! Therefore please do not consider his comments as my shared view. Thank You for your understanding!

When I saw this I immediately thought, how incredibly Polish. How familiar. We're basically a nation of people who all have extremely dysfunctional relationships with their fathers. That's why we're all borderline. Borderline Personality Disorder was practically invented in Poland.

A nice way to start off a Sunday

Arsenal beat Liverpool 2-0 away from home. Also, Arsenal's new striker, Lukas Podolski, scored his first goal.

Being both Polish and a fanatic soccer fan, I can't believe I never wrote anything about Podolski all this time. For those unfamiliar with this player, here's some background: he was born in Poland, both his parents are Polish, but they left Poland and settled in Germany when he was two years old. He holds a double citizenship. According to FIFA rules, if a player with a double citizenship is wanted by two national soccer teams, he can choose which one he wants to play for; however, he only gets to make that choice once and cannot change his mind later. Podolski chose to represent Germany and not Poland, mainly because the Polish federation was very late to the party and did not call him for the Polish national squad until he was 21. Some Polish soccer fans are very angry because of this, either at Podolski himself (for being a "traitor") or at the German soccer federation (for "stealing" a Polish player).

What's interesting in all this is that Podolski plays for Germany even though he feels more Polish than German. He always speaks Polish to the Polish media. Whenever Germany plays Poland, he makes a point of singing both national anthems before the game; also, when he scored two goals against Poland in the opening game of Euro 2008, he chose not to celebrate as a show of respect for Polish fans. He is married to a Polish woman and says that he will move to Poland once his professional soccer career is over.

All in all though, one has to remember that even though he is Polish, he is not a Polish soccer player. He started playing soccer in Germany, was picked out by German scouts, developed by German youth coaches, gained his experience in German soccer league. Polish fans who think he's been stolen need to realize that had his parents never moved to Germany, he'd most likely not become a player of the quality that he now has.

Congratulations Kuba

I saw an entertaining soccer game today: one in which Poland, co-hosts of the Euro 2012 tournament, tied Russia 1-1 coming from behind. What this means is that the Polish team is one win away (in a game against Czech Republic this Saturday) from advancing to the quarterfinals of the European Championship for the very first time.

Despite the fact that Poland looked slightly the better team and could just as well have won, the tie feels good because before the game everyone was writing us off as easy pray, as Russia is theoretically a much stronger team than Poland. What also feels good to me is that the goalscorer for Poland was a player that I'm personally a big fan of--the team captain Jakub (Kuba) Błaszczykowski. Błaszczykowski, 27, is currently a right-winger for the Bundesliga champions Borussia Dortmund. I've been following his career ever since he was a wee lad of 18, playing for a small club in Poland, telling everyone who would listen that one day Kuba was going to be great. Ha! Told you so.

One thing that many fans do not know about this player is that he lives his life in the shadows of an unspeakable tragedy. When he was 10, his father stabbed his mother to death right in front of him. Since then he has been raised by his uncle and his grandmother. Traumatized by the event, little Kuba refused to leave his bed for a week, and didn't utter a single word for months. Already showing sings of tremendous soccer talent, he has lost the will not just to play but to live at all. Somehow, though, he has been able to reclaim that will. So congratulations, Kuba, for today's goal, I knew that one day you were going to do something like this.

Here is a compilation of clips showing Kuba's skills throughout his career:

Penalty kicks and the handicap principle

Few hours ago I caught the first half of a soccer game that my team won 3-0. Coincidentally, the first goal of the game, scored off of a penalty kick by the team captain, was a good example of the handicap principle in action. If all you're doing is trying to maximize the probability of scoring, this is a dumb way to take a penalty, because it's needlessly difficult. But if part of your utility function is showing off, this makes sense: by taking an unnecessary risk of looking really stupid if you fail, you're signaling supreme confidence in your skills.

The clash of two anthems

In just over six months, my hometown will be hosting the national soccer teams of Italy and Spain as part of the 2012 UEFA European Football Championship. I'm always very excited when those two national teams play each other, not only because they're both chock-full of players who are legends of the trade, but also because those countries' national anthems are my favorite ones of them all (of those two I like the Italian one better). Both songs are energetic and melancholy at the same time. I'm looking forward to hearing them in close succession on June 10, 2012. Below the fold, you can take a quick listen yourself.

Because it's beautiful

This post is a propos absolutely nothing. It is about the artistry of the first touch in soccer. Below is a video with a compilation devoted to a very specific element of soccer technique: the "touch-fake," where a player receiving a pass uses just one touch to bring the ball under control and wrong-foot the player who marks him at the same time. Watch and admire. Note especially the very first goal, which I think is one of the most amazing ever scored.

Headbutting in soccer

Remember Zinedine Zidane headbutting Marco Materazzi in the 2006 FIFA World Cup final? Of course you do. Headbutting is actually quite widespread in the game (for anecdotal evidence, see here, here and here). I have trouble understanding why that is though. Why don't they punch instead? The penalty for headbutting someone is the same as for punching them: immediate expulsion from the game. If someone made you mad enough to headbutt them, they probably made you mad enough to punch them, and if you find yourself in a fight, your first instinct is to punch not headbutt anyway.

Shallow thinking

Today in the World Cup we've had another terrible and game-changing referee call. In a knock-out game between Germany and England, with the scoreline reading 2-1 to Germany, the referee called back a perfectly legitimate goal for England which, if allowed, would tie the game at twos. The Germans then went on to win the game 4-1.

I'm not going to write about FIFA and its ridiculous policies when it comes to botched referee calls; first, everyone can see the obvious themselves and second, it just makes me too mad. Instead I'll write about something a lot of fans and sports journalists have said after this game. Look, Germany won 4-1, they say, so you can't really claim that that one goal for England would have made any difference.

To put it mildly, it is a very unintelligent thing to say. What on Earth makes you think that, with the game tied 2-2, the rest of it would've gone the same way as it did with the score being 2-1? This is not a controlled experiment, this is life. You can't just change one variable and expect all the rest of them to stay fixed.

The structure of soccer is such that it provides a strong disincentive to playing an offensive game. If the other team commits most of its players to defense, scoring against them is very hard. Furthermore, the very act of trying to score against them is extremely risky: you have to commit seven or eight players to play on the other team's half. This means you're exposed at the back, which creates a constant danger that when the defending team manages to steal the ball from you they will get to have a quick breakaway with lots of space to play because your defenders are trying to attack. Such counter-attacking "sucker punch" goals happen all the time in soccer, and that is why teams always try to avoid committing too many players up front. They only do that when they absolutely have to--that is, when they fall behind in a must-win game. So if the English were given that goal they clearly deserved, the game would have been tied, and England could play a careful, defensive game. But because of the referee call, they had to chase, commit players to offense, which allowed Germany to score two easy counter-attacking goals. I'm not saying Germany would have lost if that goal was allowed. I don't know that. But I do know that it would have been a very different game.

Added: And the referees aren't quite done yet. Another unfair, game-changing call occurred in the very next match, Argentina-Mexico. Argentina scored their first goal from an obvious offside position. An early lead allowed Argentina to adopt the comfortable "defend and counter-attack" strategy.

Keep whining

Congratulations to the U.S. men's national soccer team for beating Algeria 1-0 and advancing to the round of sixteen as Group C winners. Congratulations especially to the U.S. No 10 Landon Donovan for keeping his cool under enormous pressure and converting what almost certainly was the very last scoring chance of the game.

The game with Algeria was an incredible thriller. A scoreless draw would have seen the U.S. eliminated while any kind of win would ensure their qualification, but despite the U.S.'s huge advantage in shots, possession etc. the goal did not come until three minutes before the final whistle, so the fans were kept on their toes for a long time.

Actually, it was much worse than that. The Americans did score a goal much earlier, in the 25th minute, but the goal was disallowed on an offsides call. Video replay showed the call was obviously wrong and the goal should have stood; but in soccer the referee calls are final and they cannot be reversed by any type of review, video or otherwise. So until Donovan scored his goal, the U.S. fans were facing a possibility that their team will be cheated out of the next round rather than eliminated from it. Actually, it was even worse than that. The U.S. was going into the Algeria game having already been cheated out of a win by a bad referee call (they scored a goal against Slovenia which was mistakenly disallowed; had it been allowed, the U.S. would have won their game instead of tying it and the game with Algeria would not have been a must-win for them).

In a post-game interview, Donovan was asked what his feelings were when the U.S. goal against Algeria was called back. He said he felt that there was no point in "moaning about it," as he put it. In one sense, he's right: since referee calls are irreversible, the only thing a team can do in that situation is to try to forget about it as quickly as possible and keep pushing for another goal. But now that the game is over, I think it's time to start moaning. The curious thing, however, is that if the team started complaining, many (if not most) fans would react to it without much sympathy. They'd say something like "Quit whining, you've won the game, what more do you want!" But the outcome shouldn't matter. Unfair treatment doesn't stop being unfair just because the victim manages to prevail in spite of it. If a black person had to go through a racially biased job recruitment process, got the job, and then decided to sue his employer for discrimination, we would sympathize with him--and rightfully so. Most of us wouldn't say "You got the job, didn't you, so stop complaining!"

Learn your game theory

When you do, you won't be surprised by things that, after a moment's thought, aren't all that surprising.

Here's the situation: today in the last round of the World Cup Group A, Mexico played Uruguay while South Africa competed with France. These were last games of round one, and they were deciding which teams advance to the knock-off stage of the tournament (round of 16). Best two teams in the group advance, the other two are knocked out of the tournament. It pays to be the best team in the group, as it means that you will likely be paired up with a weaker team in the knock-off round (no. 1 team from group A plays with no. 2 team from group B and vice versa). The situation after previous two games was such that, in case of a tie between Uruguay and Mexico, both teams ensure that they qualify, regardless of the outcome of the South Africa-France game. Because of this, essentially all sports media have decreed that both teams will play for a scorless draw: they will both come out on the pitch with an unspoken understanding that, since a tie is good for both of them, and since not scoring is the safest and least suspicious-looking way of ensuring a tie, they will both avoid serious attempts at attacking the rival's goal.

The sports media couldn't be more wrong. If they they had any brains, they wouldn't be worried about this game being rigged. In fact, the only rational thing for both teams to do is to try to score and score early, because the situation that the teams are in is that of a classic Prisoner's Dilemma, and the only rational thing to do in a Prisoner's Dilemma is to not cooperate. Sure, it is good for either team to tie, but it's even better to win. If they win, they ensure a top spot in the group and thus raise their chances of avoiding Argentina in the next round; if they tie, they may be second (depending on what happens in the other game). Suppose you're Mexico's coach. It's the 88th minute of the game and the result is nil-nil because Uruguay has in fact "cooperated" by not trying to score on you. What do you do? Tell your team to score, of course; if you do, Uruguay will likely not have enough time to tie the game back, and so you will ensure yourself a win and the additional prize of avoiding Argentina. But the Uruguay coach knows that you face that incentive, so he will not cooperate in the first place. You know that the Uruguay coach will not cooperate, so you will not cooperate either. The only rational tactics ("equilibrium" in game theory lingo) is for both teams to try to score early to avoid being a "sucker" when it's too late in the game to retaliate. A tie is of course still a likely outcome of the game, but both teams will play for the win, not for the tie.

This is in fact what happened. Both teams were seriously trying to score. In the end, only one of them turned out to be successful (Uruguay won 1-0), but both tried to; neither team was faking their attacks. (Mexico still qualified because they lucked out in terms of the score in the other game.) Sports media call this result "surprising" and salute Uruguay for being "spontaneous" and "non-calculating." The truth is exactly the other way around. The result is not surprising, and Uruguay's tactics were calculated and rational.

Where does their soccer money come from?

To bore my readers completely, another post about soccer. In a recent paper about the sport, economist Jim O'Neill wrote that "Poland's economy has decoupled from the performance of the national football team in the past decade."

Boy, did it ever. It decoupled in the sense that both national and club team soccer perform abysmally. What's interesting is that in at least four post-communist countries that are poorer than Poland (Bulgaria, Romania, Russia and Ukraine), soccer is doing great. In all those countries, fans care about the sport about the same. Of those five countries, Poland is the richest on per capita basis (PPP GDP's per capita are as follows: Poland $17,900; Russia $15,100; Bulgaria $12,600; Romania $11,500; Ukraine $6,400). And yet, there is huge disparity in how much money is being invested in the sport in Poland versus four other countries. The richest team in Polish soccer top-tier league has an annual budget of about $15 million. The richest teams of Romania, Russia, or Ukraine operate on budgets that are eight to ten times larger. The same magnitude of disparities can be seen when comparing entire leagues. In case of Russia this can be sort of explained: First, they're not that much poorer, and second, in aggregate terms they're actually richer (their GDP is more than three times larger). But Bulgaria, Romania and Ukraine are poorer both in aggregate and per capita terms. Their fans do not care about the sport any more than Polish fans do. And yet they spend more than ten times as much on soccer as Poland does (and it's mostly private spending, too; there's very little government money in it). I don't understand why this happens.

Studying games without game theory

Journal of Sport & Exercise Psychology has an experimental paper on soccer penalty-taking. The design is supposed to measure differences in perception and performance in penalty-takers under under stress and no-stress conditions. A bunch of players were asked to take a bunch of penalty kicks each; the control group were told that nothing depends on how often they score, whereas the treatment group were rewarded for performance in various ways, monetary or otherwise. Three things were then measured for penalty-takers in both groups: what they were looking at before taking the shot, how long they were looking at it, and how well they did (i.e. frequency with which they scored). The experiment finds that members of the treatment group were more likely to concentrate their eyesight on the keeper before the shooting more, and performed worse than members of the control group.

This is a flawed research design.

The flaw is to take into account only the psychological aspect of the penalty shooting game while completely ignoring the game-theoretic aspect. A penalty kick is a simultaneous-move game between the taker and the goalkeeper: the taker decides where to place the ball, and the keeper decides which way to dive, both at the same time. Moreover, it is a game in which neither the taker nor the keeper can afford to stick to one choice all the time: if the taker only shoots near the left post, for example, the keeper will figure it out and start diving left all the time; similarly, if the keeper dives only to the right, the taker will start shooting left. (In game theory lingo, the game has no pure strategy equilibrium.) However, it does have an equilibrium in randomized strategies (mixed strategies). What this means is that each player picks a certain frequency with which he plays each strategy; for example, assuming for simplicity that you can only shoot left or right, the taker chooses to shoot left with some probability p and right with some probability 1-p, whereas the keeper chooses to dive left with some probability q and right with some probability 1-q, where p and q are both strictly between 0 and 1. In other words, both players realize there is no single strategy that works all the time, but that there can be a certain mix of strategies that can work some percentage of the time, just like poker players realize that there is no strategy to play any given hand that's always correct, just a strategy that's correct on average. What's more, once you choose to play equilibrium frequencies, you score with a certain fixed rate no matter where the keeper dives (if you're the taker), or save with a certain rate no matter where the taker shoots (if you're the keeper).

The sports psychology paper is missing all this. As a result, we have no idea whether players that perform better do so because they have been placed under "no-stress conditions" or because they are closer to equilibrium frequencies than their counterparts. The correct design would be as follows. First, you calculate equilibrium shooting frequencies (here's one attempt at this). Then you proceed with the treatment/control design and let your players shoot enough times to be able to tell if they're converging on the equilibrium frequency or not. Those who do not will unfortunately have to have their datapoints thrown out: you won't be able to tell if they're doing well/badly due to control/treatment or due to deviating from the equilibrium. However, if you see the difference in performance between treatment and control groups among players that do follow the equilibrium strategy, you can be sure that that difference is really due to treatment.

I have a suspicion that if the equilibrium variable were accounted for, the significance of results from this paper would disappear.

On soccer, comic books, bread, and uninteresting questions

Dan Drezner wonders out loud in Foreign Policy why great world powers aren't dominating soccer. Right now, the seven largest GDP's in the world are (in descending order): the United States, China, Germany, Japan, Russia, India and Brazil. According to FIFA, the seven best men's national soccer teams in the world are Brazil, Spain, Portugal, Netherlands, Italy, Germany, and Argentina. Drezner's question is: why are only two countries from the first list represented on the second? Why aren't the U.S., China, and India dominating the soccer pitch? After all, they have way more money available to invest in soccer than, say, the Netherlands, Portugal, Italy, Argentina or Spain.

This is a really uninteresting question if I ever saw one. It's uninteresting because the answer is so obvious: cultural preferences. The U.S., India and China simply don't care as much about soccer. (Why? I don't know; that question is actually somewhat interesting.) Thinking that richer economies should, all else equal, be better at soccer than poorer ones stems from a very basic mistake: forgetting that what people (and whole economies) spend money on is a function of not just their resources, but preferences as well. Asking why China isn't one of the top three soccer powers in the world is a bit like asking why Bill Gates is not one of the largest comic book buyers in the world--after all, he has more money to spend on comic books than almost anyone else.

Back in the dark days of communism in Poland, the supply of bread and its prices were regulated by the government. When the system fell, those regulations were lifted. I remember the opponents of this arguing that regulating the supply of bread cannot be left to the market because if it is, the rich will buy up all the bread and there will not be enough left for the poor. The same mistake is at work in this objection.

An amusing case of hindsight bias

Hindsight bias is a propensity to see events that happened as much more predictable that they could possibly have been before they had actually happened. Here's an example from ancient history: team Romania during 1998 soccer world cup in France. After winning their group in the first round stage of the competition, and before their first knock-out game with Croatia, the entire Romanian team dyed their hair yellow (see picture below).

The team then proceeded to lose the game 0-1 which ended the tournament for them. I remember reading tons of articles in sports press at that time saying that everyone should have seen Romania's loss coming because, since Romanians were paying so much attention to unimportant things such as dying their hair yellow it was obvious that they weren't focused enough on soccer.

Does anyone have any doubt that, if Romania happened to win that game and advance, those very same journalists would afterwards be writing about how everyone should have seen Romania's win coming because a vivid display of unity such as everyone dying their hair yellow was a strong indicator of how focused and dedicated their team really was?

Mixing it up

Recently I watched a soccer game in which a goal was scored similarly to the one in the video below:

When an attacker has only the goalkeeper in front of him but is approaching the goal form an angle, he has two choices. He can try and place the ball either between the keeper and the "near post" or between the keeper and the "far post." Shooting towards the near post is the less risky option; the striker is less likely to miss the target altogether than when he aims for the far post. However, a near post shot is easier for the keeper to save (provided that he dives in the right direction). In the game I was watching the striker shot towards the near post and scored, just like in the video. The announcer then said: "In situations like this one, when the striker scores on a near post shot it's always the keeper's fault." I hear that line quite often actually. It's wrong, and a little game theory can show why.

A one-on-one when the striker is charging the goal at an angle is a 2x2 simultaneous move game. The striker has two options: "shoot near" or "shoot far," and the keeper can either "dive near" or "dive far". The important thing here is that the keeper as well as the striker make their decisions simultaneously, i.e. each picks his strategy not knowing what the other will do. (If the keeper waits to see which way the striker shoots before deciding where to dive, it will be too late to stop the shot. If the striker takes too long to shoot, the keeper will simply scoop the ball from under his feet.) Now saying that a near post goal is always the keeper's fault is equivalent to saying that keepers should always dive towards the near post; since near post shots are easy to save if you dive in the same direction, this would ensure that no goals (or almost no goals) would be scored on those kind of shots. But it wouldn't be a reasonable thing for a goalkeeper to do. If the keeper always dives near, then the striker could always shoot far towards the unprotected corner of the goal, and score with a very high rate. What the keeper needs to do instead is to play a mixed strategy: randomize between diving near and diving far. This will force the striker to randomize between shooting near and shooting far, and reduce the rate at which goals are scored in these situation to a minimum. Now since near shots are easier, the keeper should protect the near post more than the far post; i.e., he should dive near with probability higher than diving far. But, in equilibrium, he can't dive near every single time, and thus every once in a while a striker will score shooting towards the near post. And it won't be the keepers fault at all.

We like ladders better than trees

Sports fans are usually obsessed with rankings (be they player or team rankings); soccer fans are no different. FIFA (the international soccer organization) has its own rankings of national teams, but given how flawed those are, many soccer statisticians are trying to come up with their own. The best ones seem to be Voros McCracken's (his soccer blog is also very interesting) and Nate Silver's (the political scientist that runs the famous FiveThirtyEeight.com website).

The problem with rankings is that they imply a linear order that sometimes just doesn't exist in reality. For example, the usefulness of ranking soccer teams is presumably that if we see that, say, Spain is ranked no. 2 in the world whereas Denmark is ranked no. 12, then Spain is the more likely winner in a Spain vs. Denmark game. The problem is that linear rankings require transitivity (i.e., transitivity is a necessary condition for a relation to be a linear order.) The transitive property is easy to explain. Suppose Spain is a better soccer team than Denmark, and Denmark is better than Venezuela. Then it seems common sense that Spain is also better than Venezuela. If this is indeed the case and if, in fact, this property is true for any three teams we choose, then the relation "better soccer team than" is transitive. If there's no transitivity, we cannot rank soccer teams from best to worst. And in reality it isn't there. For example, all major soccer rankings put Mexico ahead of the U.S. But, at least in the recent eight years, the U.S. has a better head-to-head record against Mexico. It seems as though Mexico's record is superior to that of the U.S.--except when those two teams play each other. But this means there's no transitivity: Denmark is ahead of the U.S., Mexico is ahead of Denmark, and the U.S. is ahead of Mexico. The linearity of the order breaks down.

This is not to say that statistical methods of measuring team strength are useless. Far from it. Both Silver's and McCracken's systems, for example, are capable of producing the odds for essentially any given game. That's extremely useful--but very different than providing a consistent linear ordering of all teams in the world. The latter just does not exist in reality.

Coincidentally, there are many more examples of us trying to impose a linear order where there is none. It's often the case that we see a total order in situations where the true order is partial--i.e. we're trying to put things on a ladder where the true underlying structure is that of a branching tree. (Note: unlike the soccer rankings situation, a partial order is still transitive. It's just not linear.) For example, you sometimes hear the question: "If humans evolved from chimps, why are there still chimps?" The confusion from which this question arises is that of treating the relation "evolved from" as a linear order, whereas in reality it's a partial one (evolution is not a ladder but a tree; chimps are not our "parents" but "cousins:" our "parents" and chimps' "parents" were "siblings"). For another example, the way we teach grammar in middle schools is based on an implicit assumption that grammatically correct sentences can be derived from rules if sentences are treated as strings of words. This assumption is incorrect: as shown by Noam Chomsky, in order for us to be able to provide algorithmic rules for generating syntactically correct sentences of any human language, those sentences necessarily have to be treated as trees, not strings, of words and phrases.

Does soccer reward cheating?

French striker Thiery Henry's recent dribbling the ball with his hand instead of his foot has lots of soccer fans asking this question. British economist Tim Harford thinks it does not; here's his reasoning:

Henry has been selfless. The rewards of his cheating go largely to his team-mates, who get to go to the World Cup with their names unblemished, and to fans of French football, once they get over the embarrassment – which they will. Henry himself faced all the risks. He might have been cautioned or sent off, but surely the far greater risk was what happened: only the TV cameras noticed the handball and a great striker’s reputation was tarnished. His subsequent pronouncements of guilt, shame and remorse have hardly put matters right. So, what would an economist have done? The answer is absolutely clear: economists would never cheat in front of the camera.

In other words, Harford thinks that when soccer players cheat it's because of an uncontrolled impulse rather than a deliberate response to incentives. From a single player's perspective, it doesn't pay to cheat, but sometimes the hand is just quicker than the head (or foot).

When it comes to Thiery Henry, Harford is probably right. There's no way the French striker could have though his blatant handball wouldn't be exposed on cameras, so it was probably just a reflex (that went unnoticed by the referee). But in general I think this is wrong; you don't always get caught on camera when you cheat. If your cheating is subtle enough, you'll have some room for plausible deniability despite the fact that the cameras will register what you did. Some blatantly dishonest plays don't look all that bad in replays.

A great employee with a bad hobby

If you are, like me, a fan of Arsenal F.C., you probably hate national team soccer. Things of the sort that has just happened to Arsenal's brilliant Dutch striker Robin van Persie happen to soccer clubs all over the world, and make their managers furious. In mid November, van Persie got called for national duty to play for the Netherlands in a friendly (i.e. sparring) game against Italy. In that game, he suffered an injury that rendered him unable to play for the rest of the 2009/2010 season. And this in effect means that Arsenal is no longer able to mount a serious campaign to win the English Premier League.

Think about this from a club manager's perspective. You buy players for your team, pay their wages, as well as invest money in coaching necessary to make sure their skills improve. In exchange, those players do their best to help your team win trophies. Of course, every once in a while during your trophy-winning campaign, some of your players will get injured. Soccer is very physical, sometimes downright brutal, so this is unavoidable. If this happens to one of your players important enough that their absence significantly diminishes team value, you'll probably whine a lot and curse your bad luck. You will not think it's unfair, however; after all, every player in every team faces a positive risk of injury in about every game they play. But then there are national teams, whose managers can call your players and use their services in their own competitions, thus exposing them to an additional risk of injury and, what's worse, when they do call them you cannot refuse (clubs that won't release their players for national duty face severe sanctions from soccer governing authorities such as FIFA or UEFA, ranging from fines to suspending a player or even revoking his license altogether).

To me, this situation is blatantly unfair to the clubs. What's also interesting is that most soccer fans I talk to do not see this fundamental unfairness, and tend to just dismiss club managers' complaints without even trying to provide an argument. In fact, there is only one rational argument in favor of the status quo that I've ever heard; it comes from a sports statistician Voros McCracken, and goes something like this. The very best soccer players are also more likely to want to play for their national teams (for reasons of prestige or whatever); therefore if you, as a club manager, wanted to be able to forbid them from doing so, you'd face a situation in which those very best wouldn't want to play for your club so you'd have to settle for choosing your employees from a weaker pool. You can think of the best soccer players as of great potential employees that have a dangerous hobby (namely, playing in national team competitions); since players that don't have that hobby tend to be weaker, you can't really complain about how unfair it is when one of your best employees gets hurt while exercising his dangerous hobby.

Rational as it may be, this argument is still wrong; here's why. The relevant question is not whether or not better soccer players are more likely to want to play for their national teams than weaker players do. The relevant question is: how important is the best players' desire to play for their national team as compared to the commitment to the club that currently employs them, in a situation when those two goals are in conflict? The problem is that, given the current set up, we can't know the answer, because whenever a player gets called for national team duty, it's not just his club that can't refuse; he himself can't, either. The price of such refusal is long suspension or perhaps even the end of career, and that's just prohibitive. In a perfect world, clubs would be free to draw contracts that could either let players partake in their national teams or forbid them to do so, and then players would be free to choose which type of contract they'd want to sign. If Voros were right, we'd see forbidding contracts paying out higher wages than the non-forbidding ones (holding player quality constant); if he were wrong, there'd be no such difference; and if he were really right, the monetary price that clubs would have to pay to make a player get rid of his hobby would be just too high, so there'd be no forbidding contracts at all. The thing is, as of now, neither the clubs nor the players have such freedom, so Voros' claim is perfectly unfalsifiable.

Interestingly, Voros' "dangerous hobby" analogy helps defeat his own argument. Great soccer players also are, on average, more likely to have personalities that make them seek thrills in dangerous activities such as motorcycle racing, mountain climbing, sky diving, bar fighting etc. Some clubs do draw contracts that actually contain clauses explicitly forbidding players to, say, ride bikes or climb mountains, on pain of being fined or even fired, and some players do choose to sign such contracts. Until players are allowed to exercise the same amount of choice over national team duty versus club duty, we can't claim to know which is more important to them.

Collective action problems in team sports

Below the fold is a video that could be used in a classroom, as it contains an extremely vivid example of a collective action problem. It's a clip from an international soccer game, a qualifier for World Cup 2010 between Slovenia (team in white) and Poland (team in red). Slovenia won the game 3:0, and the clip shows the second goal.

It's a counter-attacking goal, but a very unusual one in that the defending team actually has an advantage in numbers (usually it's the other way around). What this means is that as counter-attacks go, this one is fairly easy to defend against. But the defenders somehow just never get around to it. Even someone who doesn't watch a lot of soccer probably gets the impression that the defenders didn't really do all they could to prevent the goal. One of the announcers is saying that they're just too slow, not athletic enough. It's true that Polish defenders aren't exactly demons of speed, but this is way off. No one actually runs this slow. What happened was that they got stuck in a four-player Prisoner's Dilemma. Each of them was thinking: "I'm not going to run faster because if I did, I might actually catch up to the attackers, and then I'll be forced to make a defensive play, and if I screw that up, everyone will think the goal was my fault. There are three of my teammates close by, why doesn't one of them run faster and try to do something." As a result, no one did anything.

Team sports seem like a setting in which collective action problems just run rampant. I wonder what techniques coaches use to deal with them.