“FINE” (“the end”), howled the front page of La Gazzetta dello Sport, Italy’s most popular sporting newspaper. “Apocalisse, disastro” wailedCorriere dello Sport, one of its rivals. Muted supporters, some of them weeping, filed out of bars across the land. An impotent 0-0 draw against Sweden in Milan’s San Siro stadium on November 13th, following a 1-0 defeat in Stockholm three days before, meant that the impossible had happened. Italy’s four World Cup titles have only been surpassed by Brazil. Yet the Azzurri have failed to qualify for next summer’s tournament in Russia—their first absence in 60 years.

In a country which treats football like a religion, such a debacle is an occasion for national mourning. Gianluigi Buffon, the team’s beloved goalkeeper (pictured), tearfully apologised for having “failed at something which also means something on a social level”. For many fans, the disaster seemed emblematic of a broader national malaise. Italy’s economy has struggled to recover after two deep recessions in the past decade. The news on November 14th that GDP growth has risen to 1.8% annually, beating expectations and reaching the highest mark since 2011, was drowned out by claims that the failure to qualify would cost €100m ($118m) in foregone television and sponsorship revenue. The country’s swing towards populist, anti-immigration politics was also clear in the post-match bickering. “Too many foreigners in the field, from the youth to Serie A, and this is the result,” tweeted Matteo Salvini, the leader of the Northern League, a nationalist party, regarding the makeup of Italian club teams. The nation’s favourite game certainly has its problems, but they are hardly severe enough to warrant such hysteria. More concerning to football fans, both in Italy and around the world, should be FIFA’s gravely flawed ranking system, which played an unacknowledged role in pushing the Azzurri towards the World Cup abyss.

Mi ritrovai per una selva oscura

No team is immune from a bad streak at an inopportune time. Also watching the 2018 World Cup from their living rooms will be the Netherlands, who have reached the semi-finals of the last two editions; Chile, the reigning champions of South America; the United States, the reigning champions of North and Central America; and Cameroon, the reigning champions of Africa. However, inconsolable Italians say that the team’s failure to qualify cannot be dismissed as a mere hiccup. Instead, they argue, it is reflective of a trend towards terminal decline. Serie A, the country’s top club division, is unrecognisable from its glory days in the 1990s, they say, and domestic clubs are no longer capable of producing talented local players.

There is a grain of truth to both of these complaints, but not much more. Start with Serie A. Between 1988 and 1998 Italian clubs ruled the world: they appeared in nine out of ten finals in the Champions League, Europe’s premier knockout competition, and won four. That period of dominance ended abjectly at the start of the 21st century, as a number of poorly-run sides declared bankruptcy and several more were found guilty of match-fixing. The setbacks came just as football was reaching new audiences around the world, which allowed English, Spanish and German clubs to expand their revenues at a much faster pace. In the past decade Italian teams have graced just three Champions League finals, triumphing in one.

Yet Serie A fans have good reasons to be optimistic. Two of those Champions League final appearances have come in the past three seasons, thanks to a resurgent Juventus. The average strength of Italy’s top-division teams has now caught up with Germany’s according to ClubElo.com, a website that rates clubs by the Elo formula, a ranking algorithm used in many sports which awards points based on the strength of a team’s opponents and the importance of their matches. The same source estimates that Serie A includes four of the world’s top 20 teams, a figure bettered only by Spain’s La Liga and England’s Premier League, each with five. Though Juventus have lifted the Coppa Campioni d’Italia on the last six occasions, this season Italy’s league is the most open of the major European divisions. Napoli are the current favourites, according to FiveThirtyEight, which gives five sides at least a 5% chance of winning—three more than for any other “big-five” competition (those in England, Spain, Germany and France).

A related complaint is that Italian clubs fail to produce talented home-grown players, as Mr Salvini alleges. In the past decade only four Italians have been nominated for the Ballon d’Or, an annual award for the world’s best player which is voted for by journalists and typically includes a shortlist of 20 to 30 candidates. That puts Italy below seven other countries.

Though the award might seem spurious, it is a good benchmark for the distribution of world-class footballers around the globe and the strength of their home countries. For the 28 teams that had a Ballon d’Or nominee in the past ten years, the number of players nominated closely hugged their average Elo ratings, as measured by the World Football Elo Ratings website (see chart). Italy’s average Elo score was seventh, a similar position to its number of nominees. That suggests that the team’s performances have roughly reflected its players’ abilities. There have been some notable highs and lows, with results at major tournaments ranging from profoundly disappointing, such as departing the last two World Cups at the group stage, to laboriously effective, such as the streaky run to the European Championship final in 2012.

One statistical indicator should indeed keep Italian fans up at night: only one Azzurri member nominated since 2007—the mercurial Mario Balotelli, who has not represented his country since 2014—is under the age of 30. The defensive core of the current national side is made up of veterans from the victorious 2006 World Cup campaign. Mr Buffon, centre-backs Giorgio Chiellini and Andrea Barzagli, and holding midfielder Daniele De Rossi have 463 caps between them. Three of them announced their retirement after the embarrassment against Sweden; Mr Chiellini is expected to follow soon.

But here too there are reasons to peer through the gloom. Italy’s under-20 team reached the semi-finals at this year’s junior World Cup. The under-21 squad progressed to the same stage of the summer’s European Championship. According to the 21st Club, a football consultancy, players under the age of 23 account for a sixth of minutes in Serie A, which is about average for a big-five league. Among the beneficiaries has been Gianluigi Donnarumma, who became AC Milan’s first-choice goalkeeper two years ago at the age of 16, and now stands as the heir apparent to Mr Buffon.

Lasciate ogni speranza, voi ch’entrate!

The more realistic causes for the Azzurri’s early World Cup exit are bad luck and poor management—though the biggest culprit on the latter charge is probably not the most obvious one. Italians have lumped most of the blame on Gian Piero Ventura, the team’s coach, whose 16-month tenure came to an end on November 15th when he was sacked by the Italian Football Federation (FIGC). From the start Mr Ventura, a dour 69-year-old whose only silverware has come in the third and fourth divisions, struggled to convince his countrymen that he was worthy of the top job. Italy has no shortage of decorated coaches, and among the pantheon that might be interested in leading the national side is Carlo Ancelotti, the only living manager to have won the Champions League three times (with two as a player for good measure).

Mr Ventura’s command came under greater scrutiny as it became clear that the Azzurri might struggle to qualify. There was nationwide scorn when he dropped the team’s most potent threat, 26-year-old winger Lorenzo Insigne, for Monday’s crucial game in Milan. So clear was the dissent among the troops that when the coach asked Mr De Rossi, a defensive substitute, to come on with his team in desperate need of a goal, the veteran player pointed at Mr Insigne and refused to leave the bench.

Yet a growing body of research suggests that managers have surprisingly little impact on how well a team plays. In a study of English professional clubs between 1973 and 2010, Stefan Szymanski, an economist at the University of Michigan, found that 90% of a side’s performance was determined by its wage bill, and that only a handful of managers consistently performed above their team’s expected level. Though the Azzurri were never brilliant during Mr Ventura’s reign, they were far from terrible. Of the 54 European teams in the group stage they ranked eighth for shot differential, creating 8.1 more chances per game than they conceded, and ninth for goal difference. Their final tally of 23 points would have led to automatic qualification in three of the other eight groups. They were mocked for drawing in a home match with lowly Macedonia, who were ranked 92nd by Elo. But France suffered the same fate against Luxembourg, ranked 143rd, and also ended up with 23 points, which was enough to finish first in their pool and book a place in Russia.

The biggest problem that Mr Ventura faced was being pitted in the same group as mighty Spain, knowing that only the top team could qualify automatically, whereas the runner-up would face a tricky two-legged playoff. It was an unfortunate name to pull from the hat, but also one that could have been avoided, if not for the incompetence of the FIGC. At the time of the draw, which was conducted in July 2015, Italy were 17th in the official rankings maintained by FIFA, football’s global governing body. That put them in the basket of second seeds, while the likes of Spain, Germany, Portugal and England loomed in the first basket, along with a few surprising names, like Romania and Wales. The latter two countries had swindled their way into a favourable draw by exploiting the ridiculousness of FIFA’s ranking methodology.

The FIFA formula awards more points for games in important competitions and against stronger opposition, both of which are sensible rules built into the Elo calculation. But Elo does not penalise teams for playing uncompetitive fixtures or unfancied sides: winning such games simply makes a very small difference to a team’s existing rating. FIFA, on the other hand, measures a country’s strength by taking a simple average of points earned in the matches that they have contested—which punishes those that have played more “friendly” games outside of major tournaments, since they are far less valuable. Unsuprisingly, the Elo method is a significantly better predictor of match outcomes.

These friendly fixtures have historically been a good source of match practice and revenue in a sparse international calendar. But Wales and Romania decided that they were not worth the hassle. Between them the two countries organised just one friendly in the 12 months before the draw. They rose respectively to 8th and 10th in FIFA’s rankings, when the Elo ratings had them 24th and 41st respectively. Italy were ranked 14th by Elo at this point, after a bad showing at the 2014 World Cup. But the four needless friendlies that they played in the ensuing year, winning just two, harmed them further. Had they been 14th in FIFA’s table, instead of 17th, they would have been sorted into the first basket of seeds.

The footballing fates punished the FIGC’s mistake by grouping them with Spain and then twisted the knife again by pairing Italy in the playoff with Sweden, the strongest possible opponent, ranked 22nd by Elo. Still, the Azzurri had nearly 70% of possession across two nervy games, and 37 shots to Sweden’s 12, metrics that are strongly correlated with winning games. But a long-range volley in the first leg, which flicked into Mr Buffon’s net via the leg of Mr De Rossi, was enough to condemn Italy to an embarrassing 1-0 aggregate defeat.

Che sarà, sarà

Italian fans—and indeed their miserable Dutch, American, Chilean and Cameroonian peers—might take some consolation from the belief that international football is simply becoming more competitive. They would be wrong. The standard deviation of Elo ratings for the top 50 teams, a measure of how spread out they are, has been pretty consistent for the past three decades. Rather, their shattered World Cup dreams are a reminder that even a regional powerhouse has no guarantee of safe passage.

A more truthful comfort is that failing to qualify for the tournament in Russia next year has little bearing on how these teams will fare in Qatar in 2022. Across the last 60 years, we found that a country’s Elo ranking immediately after a World Cup was a decent predictor of its odds of winning the next one, but that knowing how it actually performed in the recent tournament made no improvement to our forecast. In other words, the position that the Azzurri hold at the end of next summer will be our best guide for their prospect of a comeback championship in Qatar, regardless of what happens in Russia. Their failure in this campaign does not suddenly mean that they are a terrible team with no hope of future success. Their two draws and two losses have nudged them down to tenth in the Elo rankings, just three places lower than when Mr Ventura started his tenure. If they keep that spot, their projected chance of victory in Qatar will be approximately 4%. It might not sound like much, but only the top three sides would have more than a one-in-ten shot, since the World Cup is essentially a roulette among a handful of top teams.

Such a prospect will feel like a very small glimmer of light at the end of long, dark tunnel. But despairing Italian fans should look to an example across the Alps. The last of the “big-five” countries to miss a World Cup was France. Having failed to reach the 1990 World Cup, Les Bleus endured perhaps the worst qualification meltdown in history four years later. Ranked fourth in the world and needing just a single draw from two remaining home games, France lost first to 51st-ranked Israel and then to 24th-placed Bulgaria, thanks to two last-minute winners. That too seemed like an apocalypse: “Inqualifiable!” (“Unspeakable!”) yelped L'Équipe. “Rocked by scandals and cowardice, undermined by crooks and buried under mounds of money, football is being dragged into disgrace,” warned France-Soir about the state of the domestic game. Les Bleus hosted the next tournament in 1998, showing up with a squad of young, attack-minded players. (Many of them, Mr Salvini might note, were the sons of immigrants: the team was known as the “génération black, blanc, beur”.) They won the championship, thrashing Brazil 3-0 in the final.

If there is a lesson in the Azzurri’s failure for other countries, it is that they ignore the biases of FIFA’s ratings at their peril. FIFA has admitted that it is currently reviewing the methodology, and might make some long-overdue changes, but for many countries it is already too late. The seedings for next year’s World Cup have been fixed using the rankings from October, with predictably bizarre results. Poland, placed 18th by Elo, are ranked 6th by FIFA and are therefore in the top basket of seeds for the tournament, thanks to their decision to limit themselves to only one friendly during the year to October. That has pushed Spain, whose four friendlies in the same period kept them in third position on the Elo table but 12th on FIFA’s, into the basket of second seeds. They face a possible draw with Brazil or Germany. In total, 12 of the 32 teams would be in different baskets if the Elo formula, rather than FIFA’s, had been used to assign them. African countries benefit from having played their regional championship in January, which has given them an extra dose of higher-weighted matches to boost their ratings. Asian countries suffer from deflated rankings due to especially weak opponents in World Cup qualifying. An inadequate formula is not just Italy’s problem, but the world’s.