A group of men play with a soccer ball at Red Square in Moscow on July 13. (Alexander Nemenov/AFP/Getty Images)

Stefan Szymanski is a professor of sports management at the University of Michigan. He is the co-author of “Soccernomics” and “It’s Football, Not Soccer (and Vice Versa).”

Of all the surprises at this World Cup, the greatest has been the performance of Croatia, a nation of only 4 million people which did not gain its independence until 1991 and has battled against the odds to reach the Sunday’s World Cup final. But in reality, the only thing surprising about it is that people find it so surprising.

It is true that before the event, Croatia were 30-1 outsiders, behind Brazil, Spain, France, Germany, Belgium, Argentina, England, Portugal and Uruguay. Only France now stands in the way. However, in a competition where teams play, at most, seven games, this is not a freakish statistical event. While statistics are central to many people’s understanding of sports, grasping these specific known-unknowns can be challenging, so here is a brief review of what we know.

Nations with larger populations do better: Of the teams from the original 32 that made it to the knockout stage, nine were from the 16 most populous nations in the competition. The most surprising eliminations were Germany and Poland, while the exits of Iran, Egypt and possibly Nigeria may be at least partially explained by the month of Ramadan preceding the tournament — which is likely to have affected the preparation of Muslim players who chose to fast during the day. Populous nations are likely to produce good teams because talent is drawn from the very tail end of the bell curve: the more people there are, the greater your chances of finding exceptional talent.

Wealth, however, matters almost as much as population: you need resources to develop the talent you have. Ten of the nations that reached the knockout stage were ranked in the top half in terms of GDP per capita — again the surprise exceptions were Germany and Poland, while the failure of Saudi Arabia, Australia and Iceland seems less shocking. Croatia and Uruguay were the only teams to reach the final 16 not on the rankings list in either population or wealth, but five of the final 16 were on both lists.

What Croatia and Uruguay lack in wealth and population, they made up for in the third key factor: experience. All the teams in the last 16 except two came from either Europe or South America, the two regions of the world where soccer was extensively played before World War I. By contrast, Mexico and Japan are from confederations that did not become properly established until after World War II. African nations, most of which did not gain autonomy until then, continue to struggle at the World Cup. Croatia and Uruguay by contrast, have long been near the core of established soccer networks. Croatia used to be a part of Yugoslavia, which for decades produced outstanding players and was well-integrated into European soccer networks. One might have thought that over time, this advantage in experience would disappear as other nations learned — but that does not seem to be the case.

Thus, this World Cup, like those before it, has largely conformed to statistical expectations — teams from more populous, wealthier nations with long experience of playing the international game have prospered while others have fallen by the wayside. But it does not follow from this logic that “England should have beaten Croatia,” or that “Germany should have beaten Mexico.” While population, wealth and experience are the leading factors that determine the outcomes of each game, there are many others that matter.

In a joint paper, Melanie Krause and I have estimated that the three factors described here, along with home advantage (which helps explain Russia’s unexpected success), account for 30 percent of the variation of team performance, which is a lot when you consider that this estimate is based on 27,000 international games played between 1950 and 2014. But obviously, it is a lot less than the remaining 70 percent, which remains unexplained.

Soccer is a very uncertain game to begin with because it is low-scoring. On any given day and with any given game, there are myriad other potential influences: weather conditions, injuries, referee mistakes, morale and so on. And then, in a game where inches decide, there is the simple randomness of a ball creeping into the corner of the net or hitting the post. Indeed, it’s this very uncertainty that makes the game so interesting to watch. The day a formula is discovered that can accurately predict the outcome of each game is the day we will all stop watching.

I’ll be cheering for Croatia on Sunday since they have played elegant football and they are the underdog. They will probably lose, but it won’t be that much of a surprise if they win. You should be relieved that a statistician can’t tell you any more than that.