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Maths in football: penalty shootouts

Discuss likely, unlikely and pressure without predicting certainties.

Quick answer

Maths in football: penalty shootouts helps us understand chance, probability, and pressure. We can use maths to talk about how likely it is that a penalty will go in, and how pressure affects decision-making.

Learning outcome

By the end of this page, you will understand how chance and pressure work together in penalty shootouts, and how you can use maths to talk about how likely something is to happen. Success signs:
  • You can explain the difference between likely and unlikely
  • You can describe how pressure affects decision-making
  • You can use words like chance, probability, and prediction
  • You can think about how maths helps us understand football

Why this matters

Maths helps us understand what happens in football, especially during penalty shootouts. When players take penalties, they don't always score. We can use maths to talk about how likely it is that a goal will be scored. This is called probability. We also learn that pressure affects how people make choices. When it's a big moment, like a penalty shootout, people might make different decisions than they would in a normal game. Understanding these ideas helps us appreciate football more and think about how maths is used in real life.

How it works

In football, a penalty shootout is when teams take turns to kick the ball at goal. Each team gets five kicks. If one team scores and the other doesn't, that team wins. If both teams score the same number of goals, they keep going until one team scores and the other doesn't. We can use maths to talk about how likely it is that a penalty will go in. This is called probability. For example:
  • If a player has scored 8 out of 10 penalties, they have a high chance of scoring again.
  • If a player has scored 1 out of 10 penalties, they have a low chance of scoring again.
  • If a player has scored 5 out of 10 penalties, they have an average chance of scoring again.

Examples you can see

Let's imagine a penalty shootout between two teams. Here's what happens:
  • Team A takes the first kick. The player kicks to the left. The goalkeeper jumps to the right. The ball goes in! Team A scores.
  • Team B takes the second kick. The player kicks to the right. The goalkeeper jumps to the right. The ball goes wide. Team B misses.
  • Team A takes the third kick. The player kicks to the centre. The goalkeeper jumps to the centre. The ball goes in! Team A scores again.
  • Team B takes the fourth kick. The player kicks to the left. The goalkeeper jumps to the left. The ball goes in! Team B scores.
We can see that the players have different chances of scoring. Some players are better at scoring than others. This is because they have practiced more or they are naturally good at it.

Try it as a mini adventure

Mini Adventure: The Penalty Shootout Challenge Imagine you are the coach of a football team. You have to choose which players will take the penalties in a shootout. You have 5 players, and you want to know who has the best chance of scoring. Here's your challenge:
  1. Player A: Scored 7 out of 10 penalties
  2. Player B: Scored 2 out of 10 penalties
  3. Player C: Scored 5 out of 10 penalties
  4. Player D: Scored 9 out of 10 penalties
  5. Player E: Scored 3 out of 10 penalties
Your task is to decide who should take the first penalty. Use your maths skills to figure out who has the highest chance of scoring. Then, write down why you think that player is the best choice. How to solve it:
  • Look at how many penalties each player scored out of 10
  • Player A scored 7 out of 10 – that's 70% chance of scoring
  • Player B scored 2 out of 10 – that's 20% chance of scoring
  • Player C scored 5 out of 10 – that's 50% chance of scoring
  • Player D scored 9 out of 10 – that's 90% chance of scoring
  • Player E scored 3 out of 10 – that's 30% chance of scoring
Answer: Player D has the highest chance of scoring because they scored 9 out of 10 penalties. That means they have a 90% chance of scoring, which is the best chance.

Common mistakes

  • Mistake: Thinking that a player who scored 10 out of 10 penalties will definitely score the next one. Why it happens: Children might think that if someone is very good, they will always be good. Fix: Explain that even the best players can miss. It's still a chance, not a certainty.
  • Mistake: Not understanding that chance means "how likely something is to happen". Why it happens: Children might think that "chance" means "random" or "anything can happen". Fix: Use simple examples like "If you roll a dice, you have a 1 in 6 chance of getting a 6".
  • Mistake: Thinking that pressure makes everyone make the same choice. Why it happens: Children might think that pressure always makes people act the same way. Fix: Explain that pressure can make people think differently, but it doesn't change their skills.

Parent and carer guide

As a parent or carer, you can help your child understand penalty shootouts by:
  • Playing a game where you take turns to kick at a goal or target. Ask how many times you scored out of 10 attempts.
  • Discussing the chances of different players scoring. Ask questions like, "If a player scored 6 out of 10 penalties, what do you think their chance of scoring is?"
  • Using real-life situations to talk about chance and probability. For example, "If you roll a dice, what is the chance of getting a 6?"
  • Encouraging your child to think about how pressure might affect decisions. For example, "If you were playing a game and it was the last chance to win, how might that make you feel?"
  • Practising counting and fractions by looking at how many goals were scored out of the total attempts.

Practice questions

  1. Player X scored 4 out of 10 penalties. What is their chance of scoring?
  2. Player Y scored 8 out of 10 penalties. What is their chance of scoring?
  3. Player Z scored 3 out of 10 penalties. What is their chance of scoring?
  4. If a player scored 10 out of 10 penalties, what is their chance of scoring the next one?
  5. Why might pressure make a player choose a different direction when taking a penalty?
Answers:
  1. 40% chance
  2. 80% chance
  3. 30% chance
  4. It's still a chance, not a certainty. It's possible they might miss.
  5. Pressure might make a player feel nervous, so they might choose a safer direction or make a different decision.

FAQ

What is probability in football?

Probability is how likely something is to happen. In football, we can use probability to talk about how likely a player is to score a penalty.

Why do we use maths in football?

We use maths in football to understand how likely things are to happen, like scoring a goal or winning a game. It helps us make better decisions and understand what's going on.

What does it mean when something is "unlikely"?

When something is unlikely, it means it probably won't happen. For example, if a player has only scored 1 out of 10 penalties, it's unlikely they will score the next one.

How does pressure affect a player's decision?

Pressure can make a player feel nervous or excited. This might change how they think about their choices, like where to kick the ball or how hard to kick it.

Can we predict who will score in a penalty shootout?

We can't predict exactly who will score, but we can use maths to guess how likely it is. We look at how many goals a player has scored in the past to make our best guess.