Santos da casa não fazem milagres. At home, saints do not perform miracles. —Brazilian proverb

What is the opposite of "miracle"? Perhaps "the usual" is a good antonym, but that doesn't really capture the anti-wonder, the anti-revelation that the victim of an "antimiracle" feels. Perhaps the best word to describe the opposite of miracle is one that Brazilian soccer fans know all too well—Maracanazo. As the World Cup returns to Brazil for the first time in 64 years, that word, that anti-miracle of 1950 when Uruguay upset the favored hosts 2-1 on a late goal in Maracanã stadium, might be the most fixed, most tangible ghost around.

The world has changed: In 1950, ENIAC, the most powerful computer of the day, weighed 30 tons, cost $6 million, and could perform 385 calculations per second; today, an iPad weighs barely a pound, costs $500, and can perform tens of billions of calculations per second. Brazil has changed: Its population has grown from a shade under 52 million in 1950 to over 200 million today, and its economy, even adjusting for inflation, is almost twenty times larger in 2014 than it was back then. Even soccer, the beautiful game, has changed: Brazilian players light up the pitches for hundreds of clubs around the globe, and the World Cup tournament has doubled in size with all six populated continents represented. Still, the Maracanazo—"our Hiroshima" according to the Brazilian playwright Nelson Rodrigues—haunts the nation and suggests that hosting will hurt Brazil's chances of lifting the trophy.

We, however, are soccer scientists, and we are not Brazilian nor do we believe in ghosts. In our book, The Numbers Game: Why Everything You Know About Soccer Is Wrong, we examine what the data—cold, hard facts—say about some of the most cherished elements of soccer—corners, superstars, possession, managers—and determine whether they are all that important. Here, we will do the same thing with the Maracanazo: Was it an unprecedented loss by a home side in World Cup history? And, should Brazil fear or embrace being the host nation of the world's biggest sporting spectacle? We think the numbers and our answers provide a bit of an exorcism.


Our ghostbusting begins in an unusual place: the chessboard, whose black and white squares equal the span of years from the Maracanazo to the present. An avid chess player and physicist, Arpad Elo, invented a rating system that more accurately predicts the outcome of a match when, for example, a grandmaster takes on a master. In Elo's system, every player has a current rating that can be used to predict matches against other rated players, and then is adjusted based on the size and surprise of the actual outcomes. For instance, a player with an Elo rating 100 points greater than that of his opponent is expected to win 39 percent of the time and lose 11 percent of the time (assuming draws happen half the time). If the weaker player were to win this match, then his Elo rating would rise and the stronger's would decline. If this loss took place in a big tournament, the rise and decline would be significantly higher than if it were just a friendly match. The Elo system or one of its more sophisticated offspring is central to rating participants in many competitive arenas including Scrabble, World of Warcraft, Call of Duty, and Facemash, the predecessor to Facebook. Most importantly for us, thanks to early work by Bob Runyan and continued updating by Raoul da Silva Curiel of, we have Elo ratings for national soccer teams back into the late years of the 19th century when England and Scotland traded turns as the top-rated nation.

With these historical numbers in hand (taken from the website, we can examine the elimination games for host nations in the World Cup since 1930. First, we note that out of the 19 tournaments, six have been won by the hosts, a frequency much higher than chance. Hosting is therefore related to soccer quality but we don't necessarily know if only nations with strong enough teams are allowed to host, or whether having home field is a big advantage, or some combination of the two (we will distinguish between these arguments a bit later).


To understand the fate of the 13 hosts that did not lift the trophy, we can use the Elo ratings of their fatal match.1 The chart above displays these losing nations ordered by the amount of surprise in their loss. When France faced Italy in 1938, its Elo rating was 437 points below that of Italy's, and they suffered the expected loss 1-3. Many other hosts fell out of the tournament to favored opponents in "good" losses, but three did not—1950 Brazil, 1990 Italy, and 2002 Japan. Of these three, the Maracanazo clearly represents the biggest upset, mathematically, historically, and emotionally: Given the gap in Elo ratings of 214 points, Brazil had a 77.4 percent chance of winning the match against Uruguay. No doubt, all of Brazil was over-confident in the days before the match: These heavy odds of winning were far below the guarantee that would have justified the pre-mature actions of the newspaper headline writers, the medal stampers, and the parade planners. However, in 1990 Italy suffered a very similar defeat to Argentina—a side graded as far inferior, despite the presence of Maradona. Based on the pre-match Elo ratings, Italy, featuring a roster of Baresi, Maldini, Baggio, Donadoni, and Schillaci, had a 72 percent chance of winning, and yet they lost a desultory match on penalty kicks. In the 2002 round of 16, Japan failed to fulfill its favorite status of 64 percent as it fell to Turkey on a goal in the 12th minute. So, it might not be much comfort, but misery does appreciate company, and maybe Barbosa, the goalkeeper who made Brazil cry, can find some consolation with Maldini and Nakayama, as can the fans of each team.

One of the themes of The Numbers Game is that soccer is the team sport in which randomness plays the biggest role, and the game is full of deflections, slips, own goals, mistakes, and upsets. Soccer is coincidence and, as Johan Cruyff said, coincidence is logical. As a result, we have to refrain from making too much of a single result, even a defeat as unexpected and devastating as the Maracanazo. There should be no fear or hesitation among Brazilian supporters—hosting a World Cup is a significant advantage. The numbers are quite clear that there is a huge home field advantage in the global soccer tournament. Suppose we take the Elo ratings of every team just before the World Cup begins and rank them from strongest to weakest. So, for example, in the 1950 tournament, England and Italy were the two strongest entrants and Brazil was third. (Note that the best team in the world, Hungary, was not in attendance.) We can then compare this pre-tournament ranking to the actual outcome and judge a team's overall performance. The seventh strongest nation, for instance, should qualify for the quarterfinals and lose there. The semifinals would be an overperformance and losing in the first round would be a big disappointment.

The chart below shows this comparison for each hosting nation in World Cup history. Along the bottom, we have the pre-tournament ordering based on the country's Elo rating, and from top to bottom, we have the final positions in the tournament with losers in a given round ranked, as in league play, by goal difference. The diagonal line represents a team meeting expectations; below the line is under-performance, and above is, not a miracle, but a pleasant surprise.


There are no countries below the diagonal line. Hosts do not under-perform; they, in fact, usually over-perform. South Korea in 2002 and Sweden in 1958, followed closely by Chile in 1962, were the nations that surpassed their pre-tournament ranking by the greatest margin. Of course, if a team is highly ranked, then there is little room to exceed expectations but much room to disappoint. However, looking at the upper right-hand corner of the chart, we can see that no highly ranked host failed to deliver. Even Brazil in 1950, taking the broad tournament view, did not disappoint since they were the third strongest team and finished runner-up.

We did more sophisticated analyses that examined the factors that determine where competitors finished in every World Cup. There were three factors that explained much of why some nations lose in the group stage and a couple make the finals: pretournament Elo ranking, being the home nation, and the cultural distance of a nation from the host. The statistics show that being the host results in the equivalent of a 50 percent improvement from your Elo ranking, so if a hosting nation was the 15th strongest in the World Cup then they could expect to make the quarterfinals, and every host, even the very weakest, could expect to survive the group stage. South Africa in 2010 was a bit of a disappointment in that respect, the U.S.A. in 1994 performed as a weak host should, and Korea in 2002 had an amazing, but not miraculous, run.


A perceptive reader will note a couple of omissions from this analysis. First, the FIFA rankings. These rankings, which presently have a top four of Spain, Germany, Portugal, and Brazil, have been shown to be inferior to the Elo ratings in predicting the outcomes of international matches. Second, the physical distance a team has to travel to the World Cup did not, with statistical significance, impact its final performance in the tournament. This is good news for Japan, Korea, Australia, Russia, and Iran who have the longest trips to this year's Cup. This finding fits with other research in soccer and team sports that has usually found that travel distance is not the primary source of the home field advantage.

Instead, there is a growing consensus among scientists that the major source of home advantage is the referee and the other match officials. The numbers show that there is consistently more extra time added when any home team (not just Manchester United under Sir Alex Ferguson) is behind by a goal, and less is added when the home team is ahead by a single score. A clever study by the German economist Thomas Dohmen showed that social pressure from the crowd was partly responsible for this unconscious bias by the officials: In stadia in the German Bundesliga where the crowd is further back from the pitch because of a running track, there was less distortion of injury time in favor of the home team.

Chartered jets, fine hotels, and plenty of support staff may help visiting players avoid jetlag and the fatigue of travel, but they are still strangers in a foreign land, and they might feel discomfited, unsure, and alienated. We find that the visitor disadvantage in the World Cup rises with the cultural distance between the visitor's land and the host nation. Geert Hofstede, a Dutch social psychologist, has pioneered the research in this area, and he has shown that there are a number of dimensions that characterize culture or, as he defines it, the "collective mental programming" of a group of people. Some of the dimensions that distinguish how countries differ in perceiving and thinking about the world are the importance of the individual relative to the community, the expectation of who legitimately gets power, masculinity, and orientation toward the long-term or the short-term. We created a single cultural distance measure from four of Hofstede's dimensions that have the most available data.


This distance measure leads to some surprises: Cameroon, not Mexico, is more similar to the United States; Russia, not Honduras, is closer to Spain; the Korea Republic, not Colombia, is more like Chile. In our statistical analysis, cultural distance is significantly and negatively related to a nation's final World Cup position. The more its culture differs from the host's, the more likely a visiting nation is to disappoint in the World Cup. We would expect, for example, Portugal's national team, all else being equal, to perform 33 percent better in Brazil than they did in South Africa because of a greater cultural affinity.

Both the cultural distances and the current Elo ratings are shown in the graph above for most of the participants in this summer's tournament.2 The good news for Brazil is that the current Elo ratings, pending the pre-World Cup friendlies, have them on top trailed by Spain, Germany, and Argentina. The numbers say Spain is clearly a threat and both Germany and Argentina have gaps to overcome. The United States is unlikely to overcome either Germany's rating advantage or Portugal's cultural advantage to advance out of the group stage. If we wanted to identify a dark horse for the Cup, Croatia pops out due to their surprising cultural closeness, and the brilliance of Luka Modric and Mario Mandzukic.


The numerical factors, especially the benefit of hosting, all point to Brazil lifting the trophy on July 13. Of course, it is soccer, the coincidental game, so anything can happen, but the good news for Brazilian fans is that they don't need their saints to perform miracles at home, they just need them to let their natural advantages come to the fore.

1For Spain in 1982 and South Africa in 2010, we used the single loss each team suffered in the second round and first round, respectively.

2Algeria, Bosnia, and Ivory Coast are missing because we could not find cultural dimension information for them.


Excerpted from the new book, The Numbers Game: Why Everything You Know About Soccer Is Wrong by Chris Anderson and David Sally.