Our Strange Relationship to World Cup Probabilities

What this World Cup reveals isn’t that the stats were wrong—far from it, they were insightfully calculated—but rather that we relate to stats and probabilities in strange ways.Photograph by Hey! Play! / Wayfair

This year’s World Cup has been full of surprises. Tournament mainstays such as the Netherlands and Italy didn’t even qualify, and Germany, the reigning world champions, finished last in their group after upsets by Mexico and South Korea. Statisticians favored powerhouses Spain and Argentina to drive into late stages of the tournament, only to see them lose to sleepers like Russia and Croatia.

Yet what this World Cup reveals isn’t that the stats were wrong—far from it, they were insightfully calculated—but rather that we relate to stats and probabilities in strange ways. Most fans, for example, enthusiastically bring up “x factors” and players who are “on fire,” while stat-wielding commentators coolly remind them that what appears to be a hot run is actually statistically regular and that a victory for the underdog remains forbiddingly unlikely. But then the whistle blows and the bizarre alchemy of the world takes over. Suddenly, a typically underwhelming team like Mexico starts to dazzle and, sensing an advantage, topples a giant.

To be sure, soccer is a sport that notoriously resists predictions. The batting averages and shooting percentages in baseball and basketball are far more reliable stats than anything in soccer for divining contest results, perhaps because the collective performance of a soccer team, as opposed to a baseball or basketball team, greatly outweighs any individual contribution from its players. This isn’t to say that probabilities in soccer are unreliable; it’s just that these probabilities apply better to classes of outcomes, like a set of coin tosses, than to this or that particular outcome, like whether the next coin flip will be heads or tails.

We say, for example, that there’s a 50 percent chance of a coin landing heads or tails. But technically, all this probability states is that in the immense class of coin-toss events, given enough tries, and all other things being equal, the coin will land heads half the time. Nevertheless, the coin could land heads 99 times in a row out of 100, and you can even expect that to happen, given enough tries.

Of course, sports matches are considerably more complex than coin-tosses. There’s no need to develop statistics about how different coin-tossers performed against others in the history of coin-tossing to calculate the probability of a coin landing tails. But the underlying nature of the probability remains the same—equally weighted teams should win about half the time against each other, and teams that have performed well against other teams in the past should, in general, perform well against them in the future.

This explains the difference in perspective between the fan and the statistician. The statistician is interested in the grand scheme of events, where “x factors” and “hot runs” simply become a part of an average, whereas the fan is interested in the unlikely series of flourishes that might make this particular match exceptional. These two conflicting perspectives are part of what makes sports matches such passionate events. We know what to expect, but we also know something else is possible, so we hope, despite the odds.

So we can, with confidence, expect Germany to beat South Korea and Spain to beat Russia, but only most of the time. However, for better or worse, “most of the time” is patently not “today” or even “this World Cup.” And this makes the upcoming match between France, the 1998 World Champions, and Croatia, first-time finalists and the second smallest nation to ever reach the championship match, all the more thrilling.

Marco Altamirano is a writer based in New Orleans and the author of Time, Technology, and Environment: An Essay on the Philosophy of Nature.