The World Cup draw was unfair to several teams, including the United States, but there’s a better way. See for yourself in our interactive simulator.

The United States has drawn one tough World Cup group, which includes Germany (currently the second-ranked team in the world), Portugal (ranked third) and Ghana (38th). (In the October rankings used for the Dec. 6 draw, Portugal was ranked 14th and Ghana 23rd.)

That much is known.

But here is something many fans don’t know: The difficulty of the United States’ group is not merely a byproduct of bad luck. It’s a perfectly normal outcome from the selection rules created by FIFA, soccer’s governing body.

FIFA seeded eight top teams and drew them to separate groups, but after that, geography, not skill, dictated the rest: teams from the same continent cannot be drawn into the same group, with the exception of European teams – a maximum of two of them per group is allowed.

For instance, Brazil, given automatic elite status as the host country, had an equal chance of drawing the United States (ranked No. 13 at the time) as drawing Honduras (ranked No. 34) simply because both teams are from North America. Or Spain could just as likely have drawn Ghana as Cameroon (No. 59 at the time, lowest in the tournament). Ultimately, this method produces groups with a huge variance in strength, and this year’s tournament is no different.

What if there were a better way?

Julien Guyon, a French mathematician, has come up with a method of drawing World Cup teams that produces more balanced groups. In the table above, we’ve made an interactive version of his method along with FIFA‘s so you can see for yourself. The Guyon method isn’t better every single time, but on average, the groups are much more balanced.

The Guyon method differs from FIFA’s in a very simple way: All the teams are seeded, according to their world ranking, 1 through 32. The teams are then assigned groups in a manner similar to any other large tournament, like the N.C.A.A. basketball tournaments, with an attempt to group higher-rated teams with lower-rated ones.

Guyon keeps FIFA’s geographical constraints by randomly selecting continental groupings ahead of time. We’ve published a fuller description of the methodology, written by Mr. Guyon, and there’s an even more detailed academic paper here.

Relative to FIFA’s process, this method particularly rewards strong teams who were not in the top eight, like England, Italy, Portugal and the United States.

Here’s what groups the two methods would have produced for the United States if you had pressed the simulate button above 10,000 times.

The dark blue area represents the Guyon method, and light blue areas represent the traditional FIFA method. The dark blue area is skinnier than the light blue area, which means draws for the United States are more consistent under the Guyon method. The United States is less likely to find itself in a very easy group (toward the left of the chart) or a very hard one (toward the right).

Likelihood of United States’ World Cup Draw Guyon

method ——— Fifa method Draws under the Guyon method have much less variance

As you can see, the United States’ actual draw was not particularly unlucky. Its weakest potential group would have included France, Cameroon and Brazil. Its strongest potential group would have included Argentina, Italy and the Netherlands. (Australia drew a similar combination in real life, so please observe a moment of silence for the Socceroos.)

With Mr. Guyon’s rules, by contrast, the options are much more limited. A draw as difficult as the actual one facing the United States or Australia simply would not have been possible.

What’s the downside to this new method? In a word, variety. Some fans enjoy the commentary surrounding what’s known as the Group of Death every four years, and the Guyon method makes even the toughest group less lethal. It also reduces the chance of a team finding itself with an especially easy draw. (We're looking at you, Group H.)

Below, how the FIFA and Guyon methods compare for every country in the World Cup, based on 10,000 simulations. The charts below are just like the one for the United States: They show how likely it is that a country will have an easy or hard group.

Likelihood of Every Country’s World Cup Draw