Do you have World Cup fever? We do! Then again, what’s not to love about soccer (fútbol) when the World Cup incorporates so much of our favorite thing: MATH! This post was originally written in 2018, during the FIFA men's world cup, but now it's the turn of women's teams around the world and we are just as excited!
One of the best parts of this time of year is that whether you realize it or not, the World Cup is all about math, from game play, to the scoring system, to dimensions of the field, to tournament rounds.
Keep reading to find out how it all works.
An entire soccer game is made up of two 45-minute halves, for a grand total of 90 minutes of nail-biting game play. (That’s if you’re lucky, and the two teams are well matched.) This 90 minutes can sometimes equal 100 or more minutes of viewing time when you consider the stoppage time for substitutions, injuries, and so on. If scores are tied at the end of the traditional 90 minutes, the game can go into 30 minutes of overtime, for a grand total of 120+ minutes of World Cup excitement.
During this 90+ minutes you are likely to see an impressive amount of geometry at work. Players have to mentally calculate the best angles to kick the ball to other players or into the goal for the potentially game-winning point. Feet, legs, and bodies must all be at exact angles in order to send the ball where desired. Players and goalies alike are constantly assessing and adjusting their timing to find the exact moment to send the ball into a sweet spot, or in the goalie’s case, to block that kick.
(Image from www.soccer-coaches.com)
The scoring system for soccer seems pretty simple: Get the ball into the goal, and your team gets one point. There are, however, a few points of subtlety.
“Points are not awarded if a player who kicks the ball in is in an offside position, meaning she is closer to her opponent’s goal line than both the second-last opponent and the ball. A point is not awarded if a throw-in passes the goal line, either. On an indirect free kick, a goal is only counted if the ball touches another player before crossing the goal line. A goal is awarded, though, when a direct free kick is shot directly into an opponent’s goal.” (via Livestrong)
Furthermore, goals are not counted if there is interference, meaning the ball bounces off an “outside agent” on the field. It is interesting to note, though, that referees are generally considered “neutral objects” rather than “outside agents,” which means that if the ball bounces off the referee and goes into the goal a point will still be awarded.
Where soccer scoring gets really interesting is in a tournament tie-breaking situation. If two teams in a tournament are tied with wins vs. losses, and all other things are equal (points, goal differences, and goals scored), then the team ranking is determined by which team has fewer yellow and/or red penalty cards. This happened in the 2018 World Cup tournament when Japan advanced over Senegal on a yellow card tiebreaker.
(Image via www.getdrawings.com)
A soccer pitch is 90-120 meters long by 45-90 meters wide, split into two equal sides by the halfway line. The center spot in the middle of the halfway line is where game-play begins. Each side includes a goal (2.44 meters high by 7.32 meters long) surrounded by a penalty box that is 40.3 meters long y 16.5 meters wide.
Having anywhere from 4,050 to 10,800 square meters in which to run and play, but with each player focused on only 17.8 square meters in which to score makes for some pretty exciting play.
Finally, there’s plenty of math involved in creating the World Cup tournament brackets. Pairing up and breaking down all of the world’s national teams in a fair manner until we finally arrive at the quarter and semi-finals takes time and some fancy number-work, and there is a little bit of a difference between the men's and women's tournament rounds, as you'll read below.
Women's
(Image from www.cbssports.com)
The women's FIFA World Cup begins with 24 nations split into six regions with four nations in each region.
"The four countries in each group play matches against each other during the first phase. Teams receive three points for a win and one point for a draw, and the two teams with the most points in each group advance to the round of 16 knockout phase." (via USA Today)
The knockout phase plays like any other traditional bracket tournament, with single-elimination leading to the quarterfinals, semifinals, and the highly anticipated final round.
Men's
(Image from www.cbssports.com. Click for a larger, printable image.)
Again, all the national teams are split up into six regions. They compete in regional qualifying tournaments until the best teams (theoretically) rise to the top to earn one of the 32 bracket spots at the World Cup. For some regions soccer is more of a national priority than others, and those regions (such as South America or Europe) are given a greater number of spots. Additionally, the host of the tournament receives an automatic spot.
These 32 qualifying teams are then divided into eight groups of four by a random draw.
“Once the group stage begins, the teams compete in a round-robin format, where each country plays the other three in the group just once. A win is worth 3 points; a tie, 1 point; and a loss, 0. The two teams with the highest point totals at the end of those three games move on to the knockout rounds.” (via Vox)
Here at Mathnasium, we love soccer not just for the athletic beauty and sportsmanship, but also for the math inherent in so many parts of the game; some of it obvious, some so subtle you don’t even know it’s there. We’ve heard it said that soccer players are the ballet dancers of the sports world; we would add that soccer fans are the secret mathematicians of the sports world, whether they realize it or not. Watching any sport, but the World Cup in particular, is a great way to dust off and practice, in infinitely subtle ways, the basic math skills of your youth. And for those soccer fans with kids, there’s no better way to instill the fun of math than by watching the World Cup as a family.
So tell us, which team are you rooting for?
