Penalty
Shoot-Outs

Introduction

The 2006 World Cup has moved into the knock-out phase which means every match must produce a winner - even if it means going to extra-time and possibly the dreaded penalty shoot-out. England fans know all too well the pain of losing in a penalty shoot-out. In 4 of the last 7 major tournaments that England has competed in, they have been eliminated by way of a penalty shoot-out. Hopefully they have practiced their penalties for this World Cup!

How Penalty Shoot-Outs Work

If the score of the match is level at the end of extra-time, then the tie is decided by a penalty shoot-out. Each team nominates 5 players to take penalties. The sides then take it in turns to take their penalties. The team who has converted the most penalties after 5 each have been taken is the winner. If during the shoot-out, one team establishes an unassailable lead, the shoot-out is over at that point and that side is declared the winner, even if all 5 penalties for each side have not yet been taken. If after 5 penalties for each side, the scores are level, the shoot-out then enters 'sudden death'. Now each team must match the other team's effort or they lose. A new player must take each penalty in 'sudden death' (until all players have taken a penalty when the order then returns to the start again). More information about the rules of penalty shoot-outs can be found at fifaworldcup.yahoo.com/06/en/w/doc.html

 

Penalty Shoot-Out Simulator
To use this simulator simply input the probabilities for each player scoring their penalty and then click the "Take Penalty" button until a result is determined. Don't forget to write in the name of each team as well!

TEAM 1    

Player 1   Player 2   Player 3   Player 4   Player 5  

If sudden death occurs

Player 6   Player 7   Player 8   Player 9   Player 10   Player 11  

 

TEAM 2   

Player 1   Player 2   Player 3   Player 4   Player 5  

If sudden death occurs

Player 6   Player 7   Player 8   Player 9   Player 10   Player 11  

 

SCORE
TEAM 1 - TEAM 2

 

Activity 1
Use the Penalty Shoot-Out simulator above to simulate 20 times a penalty shoot-out in which each team has a probability of 0.5 of scoring.

(a)  What was the mean number of penalties taken per shoot-out?
(b)  What is the most likely result?
(c)  How many times did you go into ‘sudden death’?

 

Activity 2
Use the Penalty Shoot-Out simulator above to simulate 20 times a penalty shoot-out in which one team (England) has a probability of 0.5 of scoring and the other team (Portugal) has a probability of 0.6 of scoring.

(a)  How many times did England win?
(b)  What is the most likely result?
(c)  How many times did you go into ‘sudden death’?

 

Activity 3
You will need two people for this simulation.

Assign a probability to each of the players on each side. You can choose a value between 0.3 and 0.7 but the overall average for each team should be 0.5. Choose the order of the penalty takers for your team and simulate the penaly shoot-out 10 times.

Is there a best strategy for using the players?

 

Activity 4
Generate some more penalty shoot-out simulations choosing your own teams and the probailities for each player to score their penalty.

Investigate an effective method for winning shoot-outs.

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Produced by R.D.Geach June 2006