Game theory | Fifty years of hurt

England’s dry spell is nothing unusual, and unlikely to end soon

The Three Lions are far from the only international football team to have suffered a barren patch

By J.T.

IF, LIKE your correspondent, you are an Englishman who has drawn England in your office sweepstake before the European Championships, which kicked off in Paris on June 10th, you will have conflicting emotions. You might feel more fortunate than colleagues who have picked minnows Albania or Hungary out of the hat. A glance at the betting odds could raise your hopes, as England are fourth favourites to triumph in France, with only the hosts, Germany and Spain more fancied to win Europe’s quadrennial international tournament. But any hopes will be quickly dampened by a familiar, unshakeable certainty that the Three Lions will crash out ignominiously—again. This summer marks half a century since the nation that invented modern football last won an international trophy, and twenty years since they progressed past the quarterfinals at a major tournament. The odds suggest that the drought is 90% likely to continue this summer.

England’s failure to repeat the glory of 1966, when they won the World Cup on home soil, has tormented supporters. The national side is generally very good, but has performed poorly at major tournaments, thus raising expectations before dashing them. In fact, the current squad are not much weaker than the side that won the World Cup fifty years ago. One way of measuring this is with an Elo system, which transfers points between teams after they play each other, and awards more credit for victories against good sides, by big margins, and in crucial games: Costa Rica gained a lot of Italy’s points for beating them at the 2014 World Cup, while Germany pinched few of Gibraltar’s after thrashing them in a qualifier last year. Variations of this system are now standard in many American sports, while the Elo mechanism used to rank international football teams has more predictive power than FIFA’s own system.

By this gauge, England are the eighth-best side in the world, have had the fourth-highest average score since 1970, and would beat top-ranked Argentina 36% of the time in a knockout match at a neutral venue. They are just 90 points worse than the heroes of half a century ago (see chart), roughly the same gap as between Bayern Munich, the reigning German champions, and Paris Saint-Germain, their French equivalent. Intriguingly, England have been as strong in the last ten years as they were through the 1970s and 1980s. Though the influx of foreign talent into the Premier League has reduced the playing time for Englishmen, the national team hasn’t weakened.

Yet England’s strength outside of major competitions—they have lost just three of their last ten non-tournament games against Italy, the Netherlands, Spain, France, Portugal and Germany, and have historical winning records against the last four of those—has counted for little. The last decade has been particularly miserable. England failed to qualify for Euro 2008, struggled against Algeria and Slovenia before suffering a thumping to Germany at the 2010 World Cup, were outplayed by Italy at Euro 2012, and claimed a solitary draw against Costa Rica at World Cup 2014. The contrast of England’s obvious potential and inability to realise it in important games is at the heart of “Three Lions”, a nostalgic anthem written by comedians David Baddiel and Frank Skinner: “England’s gonna throw it away, gonna blow it away, but I know they can play”.

When “Three Lions” was released in 1996, with its promise that football was coming home, fans sung of “30 years of hurt”, not knowing that the next 20 would be worse. There is no doubt that England have underachieved in that time. Using odds from William Hill from 1990 to 2014, and accounting for the margin that bookmakers add to their odds to make a profit, we can see that England had an average 7.8% chance of winning the last six World Cups they have qualified for, and an average 10.2% chance of victory at their last five European Championships. By adding those probabilities together, we get an estimate for how many tournaments they were expected to win in that period, which is 0.98 (see chart). Odds for older tournaments were not available. But working from a rough assumption that England have had a 10% average chance of winning tournaments they appear at—since these used to have fewer entrants—their expected trophy haul would be around 2.4, from 24 attempts. A more generous estimate, of a 15% average chance of success, produces 3.6 expected trophies. These projections are hard to match if you have only played in one final, and if you have lost six of the seven penalty shootouts that you have participated in. (England’s players have a worse record when it comes to spot-kicks than any other major European side, and are most likely to exhibit signs of pressure, such as refusing to look at the goalkeeper.)

Yet for all the English moaning about a long winless run after failing in the last 17 tournaments they have appeared at, such streaks are not unusual. Spain endured 44 years of hurt (1964 to 2008) that were arguably more grim than England’s, reaching just one semifinal. France entered international competitions for 54 years (1930 to 1984) before winning one, as did the Netherlands (1934 to 1988). Portugal have never collected a major trophy. Since the odds of any particular team winning one of these events are small, the chances of a dry spell are high. In the 24 tournaments that England have appeared at, assuming an approximate 10% probability of victory at each, the chances of seeing a run of 17 failures were about one in three. (With a 15% average chance of success, it is closer to one in seven.) Take ten teams of similar strength, make them play 24 tournaments each, and the chances of seeing at least one stretch as bad as England’s rise to more than 90%. (Or 70%, if you are using the more optimistic estimate of each team having a 15% chance at any given tournament.)

That such barren periods are bound to happen to good teams won’t make England fans feel any better, or rid their team of a reputation for choking. Nor will supporters welcome the news that the hurt is unlikely to end soon. Even with the generous guess that England will continue to have a 10% chance at major tournaments—the current odds for the next World Cup are hovering around the 5% mark—and on the assumption that they will qualify for every single one, there is around a 40% probability that they won’t win anything in the next twenty years. The Three Lions are only ever a handful of games away from ending the rot, and a good run over the next few weeks is not impossible. But should Mr Baddiel and Mr Skinner live to be 100, they may well have to sing about 70 years of hurt.

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