Midfield General

It’s All Fun and Games Until Someone Loses a Vertebra

Neymar’s injury shows what happens when soccer enters a bad equilibrium.

It has not been the best week at the World Cup, especially for American fans. Striker Jozy Altidore failed to take the field for the United States, which lacked a spearpoint to its attack in its heartbreaking loss to Belgium. Meanwhile, after a goal glut in the group stage, the scoring taps have almost run dry. And worst of all, the tournament's poster boy has been knocked out by injury. All of these unfortunate events can be explained using game theory -- and at least one of them could have been avoided. Here's how.

First, consider Altidore, who'd strained a hamstring during his team's opening game against Ghana. Coach Jürgen Klinsmann had him in uniform for the clash with Belgium, but the big center forward didn't play. You could forgive American fans for their disappointment; chatter from the United States camp suggested throughout the run-up to the game that Altidore would be ready. In the end, though, it was a bluff. Altidore's injure was too severe for him to recover in time, and Klinsmann admitted as much after the game.

In game theory, this is called signaling. Talking up Altidore was an attempt to make Belgium waste time preparing for an opponent that they wouldn't even face. As long as there was a non-zero probability that Altidore would play, the Belgians' best strategy was to spend a non-zero amount of time considering how they would defend him.

The United States ended up losing to Belgium 2-1, which was a big score for the Round of 16 and the quarterfinals. Earlier, the tournament had offered 2.8 goals per game in the group stage, but the next 12 matches averaged only 1.9 even with several periods of extra time. Again, this was partly the result of strategy.

In the group stage, the rules of the tournament give teams an incentive to play offensive soccer and run up the score; after all, the United States only advanced because of goal difference. But in the knockout rounds, when teams are more evenly matched, the most important thing is not to concede. Once a team scores, it has little incentive to send players forward looking for more goals; the preferred way to finish the game is by bunkering the defense. Indeed, three of the 12 games in the Round of 16 and quarterfinals finished 1-0, compared with eight of the previous 48.

The events above can be explained by game theory, but they couldn't necessarily have been avoided. That's not the case with Neymar's injury. Towards the end of a rough-and-tumble match, the Brazilian star was kneed in the back by Colombia's Juan Zúñiga and had to leave the field on a stretcher. At the hospital, he was diagnosed with a broken back. Yet his World Cup did not have to end this way.

To understand why, imagine that Brazil and Colombia were playing without a referee. In this hypothetical situation, each team would have a choice of whether to play dirty or clean. If both play dirty, neither will have a clear advantage and both will leave the field with injuries. If both teams play clean, then they'll both avoid injuries as well. But if one team plays dirty and the other doesn't, the dirty team will have a clear advantage.

This is a classic Prisoner's Dilemma. With no cooperation between the teams, both will play dirty, as it's the best strategy regardless of how the other team plays. Clearly, it would be better if they could both commit to playing clean. On their own, however, they can't credibly make this commitment. That's where the referee comes in.

The referee's job is to impose the good equilibrium so that the teams avoid the bad equilibrium. By laying down the law early in the game, usually by calling fouls for any illegal contact and issuing cards for particularly dirty ones, he can give the teams a strong incentive to stick to the high road.

Unfortunately for Neymar, Spain's Carlos Velasco Carballo did not perform this vital function in Brazil's match against Colombia. As former World Cup referee Graham Poll put it, "Carballo wore the referee's kit, but he wasn't in charge." He let foul after foul go unpunished, sometimes not even stopping the play, until he finally pulled out a yellow card against James Rodríguez -- himself the victim of numerous fouls -- after 67 minutes. When Neymar went down with only a few minutes left to play, Carballo did nothing.

Game theory can be a tool to beat an opponent, but it can also make an entire tournament safer and more enjoyable. Hopefully FIFA will convey that message to its referees before the next round of the World Cup begins.

Eitan Abramovich / AFP / Getty Images

Midfield General

Blame the Foreigner

In soccer, as in politics, plenty of Russians think the root of all evil lies in the West.

MOSCOW — Russia may be having a great year for territorial expansion, but its national teams are having a stinker. After the hockey squad flamed out at the Olympics despite playing on home ice, the soccer team crashed out of the World Cup without a win. Yet there is a silver lining to this sporting cloud: though their teams' failures were disheartening, Russians can still find comfort in the overarching notion that Mother Russia knows best.

Russia's two tepid draws and one loss in the group stage have led to soul-searching and finger-pointing in Russia soccer circles. Fortunately for Russian self-esteem, most of those fingers have pointed at the team's head coach, Fabio Capello. The 68-year-old Italian, who in 2010 coached England's World Cup team, was reportedly the highest paid coach at the World Cup, earning $11,235,210 -- an annual salary 763 times greater than the average Russian's, according to Forbes.

The foul-mouthed leader of Russia's Liberal Democratic Party, Vladimir Zhirinovsky, called Capello a "thief" and said he should be summoned to the Duma to explain Russia's mediocre performance. Russian media outlets also have reported that Capello will, in fact, be called into the Duma in October to outline his plan to ensure there no is repeat in 2018, when Russia hosts the tournament for the first time. Other lawmakers have said Capello should forfeit his salary.

Such is life for imported talent in Russia. When speed skater Viktor Ahn, who used to represent South Korea, won gold for Russia in Sochi, the home crowd applauded more loudly than they had for the country's homegrown figure skaters. Russians also hailed Guus Hiddink, a Dutchman, as a hero after he led their soccer team into the 2008 European Championships, where it reached the semifinals. And Capello, who stars in a Coke commercial on Russian television and is arguably more recognizable than any of his players, became Mother Russia's favorite son for leading the team into the 2014 World Cup.

Indeed, Ahn, Hiddink, and Capello -- who blamed his team's elimination on a laser pointer directed into the eyes of goalkeeper Igor Akinfeyev just before Algeria scored an equalizing goal -- are just a few of Russia's many foreign commodities. Much like imported stainless steel appliances or one of Moscow's thousands of Audis, Capello is a coveted European good considered to be better than any homegrown equivalent. Indeed, since the collapse of the Soviet Union in 1991, Russia has looked abroad for its industrial technology, high-quality consumer goods, and even soccer coaching talent at the expense of developing its own.

But Russia's ties to its Western imports often resemble a love-hate relationship. In the wake of elimination, Russian players have received significantly less criticism than their Italian coach. Akinfeyev fumbled the ball on a benign shot during his team's opener against South Korea that ended 1-1, but Russian media exonerated the goalkeeper after he publicly apologized to the country for the blunder. None of the other players, all of whom are based in Russia's domestic league, has received much reproach. Yet Capello, who speaks to his players through an interpreter, has not yet been forgiven. The unspoken reason is his passport. The consensus is a Russian could have done a better job -- and for less money.

This mix of chauvinism and protectionism, fomented by Kremlin-friendly state-owned media outlets, has reinforced a prejudice that has grown stronger in Russia since the outbreak of the conflict in Ukraine: In Russia, the Westerner is to blame.

In soccer, still regarded as somewhat foreign despite the sport's long history in the country, this is an easily applied prejudice. Russia's inhospitable climate clashes with the image of a lush soccer pitch, making it more acceptable, in theory, to call upon foreign expertise -- and then reject it if things go badly.

But while foreigners have comprised the national soccer team's coaching staff for nearly a decade, Russia has never had a foreign hockey coach. Even after coach Zinetula Bilyaletdinov was fired following the home ice embarrassment at the Sochi Olympics in February, there was no outcry for Russia to look for a Canadian replacement. Yet even in hockey, Russia's de facto national sport, the country has still managed to make Westerners the scapegoats for its own misfortunes.

Indignant Russian parliamentarians and social media users blamed American referee Brad Meier, who officiated Russia's game against the United States in Sochi, for the team's failure. Because the net was off its mooring, officials disallowed a goal that would have given Russia a 3-2 lead with fewer than five minutes left in a round-robin game. The United States went on to win in an eight-round shootout. Because of the loss, Russia had to play a quarterfinal game against the gritty Finns, who eliminated the hosts under the reproachful eyes of their compatriots. Meier, who was viewed as a biased, Russophobic referee, was an easier target than a poorly constructed team of puck-hogging stars.

Amid Russia's annexation of Crimea and ongoing clashes in eastern Ukraine, the Sochi Games already seem like a distant memory. And Russia's gold medal at the World Hockey Championship in Minsk in May has healed Russia's bruised hockey ego.

The bruises may not heal so easily in soccer, as Capello is contracted through 2018. Sports Minister Vitaly Mutko -- a former head of the Russian Football Union (RFU) -- defended his imported coach, saying Capello's role in getting the team into the World Cup was a victory in itself. But the reality is that Capello's contract specifies a stiff financial penalty against the RFU if he is fired before the 2018 World Cup.

Committed to its foreign coach for another four years, Russia will be looking to strengthen the development of its young players at home rather than relying on the academies and training programs of prestigious clubs abroad. If things go well in 2018, there will be plenty of Russians ready to take the credit. If they don't, there will still be one Italian left to take the blame.

Yasuyoshi Chiba / AFP / Getty Images