Goal Get It: The Math Behind Soccer

Soccer fans unite – it’s time for the FIFA Women’s World Cup! Soccer, or futbol as a lot of the world calls it, is such a fast-paced sport with incredible displays of athleticism and, you know what our favorite thing about it is? It involves MATH! Much like many sports, from game play to scoring, to the dimensions of the field to the way the tournament rounds breakdown, math is a huge part of soccer. Let’s dig in! 

Gameplay

Soccer games are made up of two 45 minute halves for a total of 90 minutes. 90 minutes is the actual game time, but total time you watch the game can take more because of injuries, penalties, substitutions etc. If at the end of 90 minutes of playing time scores are tied, 30 extra minutes are played to try and break the tie. That means games can go up to 120 minutes of playing time! Can you imagine running around that hard for 120 minutes? Talk about conditioning. 

During the game, there is quite a lot of geometry going on. Feet, legs and bodies must all be at certain angles in order for players to make the ball go where they want it to. Players who are frequently passing or striking have to mentally calculate and eye the best angles to kick the ball to other players or into the goal, and players and goal keepers are constantly speeding up or slowing down to try and find the exact moment to send the ball to an advantageous position to either block a goal or score a goal.

Scoring

Scoring for soccer isn’t complicated. When the ball goes across the line into the goal, 1 point is scored. However when and how scoring can occur has some technicalities:

1. Offsides is called when a player who kicks the ball is closer to her opponent’s goal line than both the ball second last opponent and the ball. Goals that are made from offsides aren’t awarded. 
2. Goals can’t be made from throw-ins (when players throw the ball in because it went out of bounds). 
3. Goals that are indirectly free kicked are only counted if the ball touches another player before crossing the goal line. In other words, the ball pretty much has to be passed or shot directly at the goal in order to be counted as a goal. 
4. Goals must be clear of interference. If the ball bounces off an “outside agent” on the field it’s considered interreference and won’t count. Interestingly enough, referees aren’t considered “outside agents” they’re considered neutral, which means if the ball bounces off of the refs and goes in into a goal, the point will count. 

Lastly, in tournament tiebreaking situations, red and yellow penalty cards matter! This is because if two teams in a tournament are tied with wins vs. losses and their points, goal differences and goals scored are all equal too, the team with the least amount of red and yellow cards advances in the tournament. This happened in the 2018 Men’s World Cup when Japan advanced past Senegal because Senegal had one more yellow card than Japan. 

The Field

An in-bounds soccer playing area is typically  90 – 120 meters long and 45 – 90 meters wide and it’s split into 2 equal sides with a line running down the middle going width wise. In the center middle of the halfway line is where game-play begins. Each side includes a goal, which is 2.44 meters high and 7.32 meters long that then has a penalty box around it, which is 40.3 meters long by 16.5 meters wide. Players then have up to 10,800 square meters to play, yet they generally only focus on about 17.8 square meters when it comes to most game play and trying to score. 

Tournament Rounds

Last of all, tournaments are almost pure luck, well, and skill of the players and teams who work their way to the top. Pairing up and breaking down all of the world’s national teams is quite a tack. It takes a lot of time and a lot of statistics work and it’s done a bit differently for the women’s FIFA World Cup v. the men’s. Let’s review how the women’s works, since they’re currently playing in FIFA World Cup. 

The women’s begins with 24 countries split into six regions, so that 4 different countries are in each group. Then just like in the men’s FIFA World Cup, the four countries play games against each other during the first phase. A win is worth 3 points, a tie is worth 1 point and a loss is worth 0 points and the two teams with the highest points in the group at the end of those games move onto the next round, playing the winners from the five other groups. 

So, now that that secret is out about how much math is involved is soccer, you’ve probably put together that watching the women’s FIFA World Cup is sort of a way for you to brush off some old math skills and put them to use. And for those with kids who love soccer and are watching games with you, bring them into the math fun!