A boy plays with a ball in the Cidade de Deus neighborhood of Port Alegre. (Reuters)

Portugal's first World Cup match Monday will be against Germany, a country with eight times Portugal's population and 16 times its gross domestic product. In international soccer, however, dominance in the sphere of economics does not reliably translate to dominance on the pitch. In this regard, the World Cup is a refreshing contrast to club competition, where successful teams often depend on wealthy owners, and to the Olympics, where national income can often be used to forecast medal counts.

Some of the strongest teams in the World Cup have weak economies. About a quarter of the Spanish labor force is unemployed. Prices in Argentina rose 28 percent last year and could rise an additional 38 percent this year. A recession, perceived corruption and shoddy public infrastructure have led to protests in Brazil, yet the tournament's host is widely recognized as the favorite. Handicappers favor Germany over Portugal, but slightly -- by much less than might be expected given the discrepancy in their national incomes.

The United States, the country with the largest population in the tournament and the largest economy in the world (for now), is not likely to beat Germany and Portugal out of Group G. China and India did not even qualify.

Social scientists have made few attempts to quantify how much a large national economy helps a national soccer team, probably because the benefits are not obvious. High incomes and a large population certainly do help, up to a point. Still, two researchers at the University of St. Andrews in the United Kingdom found that they couldn't predict a national team's strength very well without taking into account "football-specific" factors. (The R-squared value for that model was only 0.378.) There is a lot going on in soccer that has nothing to do with population or per-capita income. (See a comprehensive attempt at a quantitative model for success in soccer here.)

On the other hand, equations have been designed that can use economic data, sometimes along with information about climate, to accurately forecast total medal winnings in the Olympics. Making these predictions has almost become an Olympic sport in itself, and the competition has reached a very high level.

These plots from a recent UBS report on the World Cup emphasize the difference between rankings in international soccer and performance in the Olympics rather comically:

UBS. Used by permission.

Only emerging-market economies are shown -- but other models suggest that as population and income increase, the benefits for soccer decrease, meaning that these correlations would probably not be much stronger if developed economies were included.

The report also considered other economic factors but found no correlations. "Everything else -- how they manage their economies, how they trade, how they manage their fiscal affairs, whether there’s inflation or growth, nothing else seems to rank," said Jorge Mariscal, one of the report's authors.

The statistical reason that economic models are less useful for soccer than for the Olympics is that the Olympics involve many sports, not just one. In some nations, curling might be especially popular, just as soccer is in others. "You either are a soccer nation or you’re not," said Stefan Szymanski, an economist at the University of Michigan. Those differences cancel one another out when all of the Olympic events are considered together.

That's good news for countries like Portugal. For now, soccer remains a game of luck -- and of good players making their own luck, and in turn, of good programs creating good players. That depends on facilities, infrastructure and, of course, on less tangible factors like tradition and know-how.

The United States, for example, has a large population of young soccer players and plenty of money to pay coaches, noted Ángel Ubide of the Peterson Institute for International Economics. The problem, in his view, is a lack of institutional knowledge.

"A lot of these soccer kids are coached by parents, who really don’t know what they’re talking about," said Ubide, who played professionally as a young man in Spain and Italy.

The balance of power in world soccer could change, as Szymanski and his coauthor Simon Kuper argue in their recent book "Soccernomics." They predict that China, India and the United States will be able to use their wealth and population to develop elite soccer programs, especially if they can exploit the new quantitative techniques  common in sports such as baseball.

If that does happen, it won't be for a long time. A successful national team can't be conjured up with cash. To be sure, money goes a long way, but it isn't everything in this World Cup, as it so often seems to be in sports.