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Avoid the Germans in a Penalty Shootout

July 7, 2014 Leave a comment

A particular interest of mine is game theory and penalty shootouts – see Game Theory Lesson: Man Utd v Chelsea Penalty Shootout. This involves studying the alternative strategies a person may choose to adopt depending on their assumptions about their rivals’ behaviour. The most significant research into penalty kicks has been done by Steven Levitt (co-author of Freakanomics) who co-authored a paper on mixed strategies when players are diverse in their decision making and studied 459 penalties in the Spanish and Italian leagues. Another economist Ignacio Palacios-Huerta analysed 1417 penalty kicks from several European countries during the period 1995-2000.

Approaching the business end of the Football World Cup and you have to have some sympathy for the Costa Ricans who celebrated after extra-time with the scores being tied – assuming that this was their plan from the commencement of the game and that they fancied their chances in the shootout. However why do some teams do better at penalty shootouts than others? The Economist looked at this recently and came up with the following:

1. Defeat is habit forming – players who miss regularly become fatalistic
2. Countries that are collectivist in nature rather than individualistic do much better – mindful of their public image
3. Research shows that star players tend to miss more than your average player – they feel the pressure
4. Who goes first is important as players are far more likely to miss a penalty if it to stay in the contest rather than one that will win it. The majority of the time the team going first wins the shootout.

Below is a chart from The Economist which shows that England have struggled at this part of the game but the Germans, as you would expect, are very efficient. As for the Czech Republic they have yet to miss a penalty.

Penalty Shootout stats

Psychological Preparation for Penalty Shootouts – Academic Paper

A recent piece of research from the British Association of Sport and Exercise Sciences addresses how you should prepare for Penalty Shootouts.

Players who take less than one second to place the ball on the penalty spot score on about 58% of their penalties whereas those who take longer score on about 80% of their penalties (Jordet et al., 2009).

Similarly, taking about a second or more to respond to the referee’s whistle to initiate the shot is associated with a higher probability of scoring than immediately rushing towards the ball (Jordet et al., 2009).

Developing and practising a suitable pre-shot routine is a potentially useful way to guide these timings and help protect performance under pressure. Indeed, recent research by Wood and Wilson (2012) has suggested that learning a routine involving a gaze control element (look at the point where you want to shoot prior to the run-up) helped penalty takers in a shootout task to be more accurate, maintain effective visuomotor control and increase perceptions of psychological control and contingency.

In the Shootout:

1. Don’t rush: Place the ball properly on the spot and take a breath while focusing on where you intend to shoot, before starting the run-up. Taking a deep breath is likely to ease feelings of anxiety and provides a temporal cue to ensure that sufficient processing of target-related information is enabled.
2. Trust your technique and routine – pick a spot and hit it.
3. Celebrate! It will help your team-mates who have to take the subsequent penalty kicks.

With the semi-finals coming up you’ve got to fancy the Germans if it goes to a penalty shootout.

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Game Theory Lesson: Man Utd v Chelsea Penalty Shootout

March 11, 2014 2 comments

Game theory involves studying the alternative strategies a person may choose to adopt depending on their assumptions about their rivals’ behaviour. The most significant research into penalty kicks has been done by Steven Levitt (co-author of Freakanomics) who co-authored a paper on mixed strategies when players are diverse in their decision making and studied 459 penalties in the Spanish and Italian leagues. Another economist Ignacio Palacios-Huerta analysed 1417 penalty kicks from several European countries during the period 1995-2000.

Technically the kicker and the goalkeeper play a zero-sum game – any gain for one player is exactly offset by the loss to the other side – plus one goal for me is minus one goal for you. The situation that kickers face in a penalty kick is a simultaneous-move game where they have three alternative strategies: shooting right, left, or centre. Similarly the goalkeeper also has three alternative strategies: dive to the right, dive to the left or remaining in the centre of the goal. In defining the sides of the goal researchers use the “natural side” of the kicker (which is the goalkeeper’s right, if the kicker is right-footed, and the goalkeeper’s left, if the kicker is left-footed) and the “opposite side”. Labeled like that, the strategies of both kicker and goalkeeper will be to choose the natural side of the kicker (NS), the centre (C) or the opposite side (OS).

2008 UEFA Champions League final – Chelsea v Manchester Utd.

A mutual friend of Ignacio and Chelsea manager, Avram Grant, brought the two men together and subsequently Ignacio sent Grant some facts regarding Man Utd, in particular about their goalkeeper Van der Sar. There were 4 main points:


1. Man Utd goalkeeper (Van der Sar) tended to dive to the kicker’s natural side (i.e. GK’s right for a right footed kicker)

2. Van der Sar tends to save penalties that are hit at mid-height

3. Man Utd midfielder Cristiano Ronaldo often stops in his run-up and if he does the ball is kicked towards the right hand side of the keeper. It was important that the Chelsea goalkeeper, Petr Cech, did not move early. When goalkeepers moved early Ronaldo always scored.

4. If you win the toss you take the first penalty. 60% of teams going first win the game.

Students watch the penalty shootout between Manchester United and Chelsea and complete the following table. They have to record where the penalty taker placed the ball and which way the goalkeeper dived – NS C OS. They then answer the questions below.

Man U Chelsea Penalty Shootout

What do you notice about the Chelsea penalty takers?

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Was Ignacio correct about Cristiano Ronaldo?

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How did Man Utd goalkeeper (Van der Sar) psych out Anelka the 7th penalty taker for Chelsea? Watch the video closely.

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What did Anelka do which went against the advice of Ignacio?

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Ignacio stated in an academic paper that generally the shooter should kick to the left 38% of the time and right 62% of the time. The keeper should dive to the shooter’s left 42% of the time and to the shooter’s right 58% of the time. When both strategies are played out, the shooter will score 80% of the time. This is the best strategy for both players because any deviation from the strategy by the keeper will result in the success rate increasing while any deviation from the strategy by the shooter will result in the success rate decreasing.

Ronaldo – penalty miss vs Bayern Munich

April 27, 2012 Leave a comment

I did a post last year on game theory and penalty kicks which looked at the 2008 UEFA Champions League final – Chelsea v Manchester Utd.

From the data collected by Basque economist Ignacio Palacios-Huerta he calculated the proportion of successful penalty kicks. He also noticed that the then Man Utd midfielder Cristiano Ronaldo often pauses in his run-up and if he does the ball is kicked towards the right hand side of the keeper. Furthermore, his research showed that when he does pause 85% of the time Ronaldo kicks to the right hand side of the goalkeeper. It is important that the goalkeeper does not move early as Ronaldo seems to be able to change his mind where to put the ball at the very last instant. When a goalkeeper moves early Ronaldo always scores. Ronaldo missed a penalty in the 2008 Champions League Final v Chelsea – see above post for video. He paused in his run-up and Chelsea goalkeeper Petr Cech stayed upright for as long as possible and dived right to save the penalty.

Champions League semi-final second leg – Real Madrid v Bayern Munich

Penalty 1 – Ronaldo runs up very slowly but doesn’t pause. He puts the ball to the Bayern Munich’s goalkeeper Manuel Neuer’s left and scores. Neuer dives right maybe expecting the ball to go right

Penalty 2 (penalty shoot out) – Again Ronaldo runs up quite slowly and puts the ball to the Neuer’s right. Neuer dives right and saves. Did Neuer play the percentages and believe (like the research showed) that 85% of kicks by Ronaldo go the goalkeeper’s right (even though he didn’t actually pause) or was it guess work? One wonders if Neuer had a strategy? He dived right for 3 out of the 4 penalties in the shootout and saved 2.

Categories: Sport

Chelsea win Champions League – Petr Cech picks the correct side everytime

May 23, 2012 Leave a comment

With the disapointment of the 2008 Champions League Final behind them, Chelsea can finally claim to be the best team in Europe. As in 2008 it was decided by another penalty shoot but this time Chelsea were the victors. As always I am particularly interested in the peanlty shoot out and the strategies, if any, that are implemented by both the penalty taker and the goalkeeper.

The situation that kickers face in a penalty kick is a simultaneous-move game where they have three alternative strategies: shooting right, left, or centre. Similarly the goalkeeper also has three alternative strategies: dive to the right, dive to the left or remaining in the centre of the goal. In defining the sides of the goal researchers use the “natural side” of the kicker (which is the goalkeeper’s right, if the kicker is right-footed, and the goalkeeper’s left, if the kicker is left-footed) and the “opposite side”. Labeled like that, the strategies of both kicker and goalkeeper will be to choose the natural side of the kicker (NS), the centre (C) or the opposite side (OS).

From data compiled by Spanish economist Ignacio Palacios-Huerta he calculated the proportion of successful penalty kicks. Below is a table that shows the success rate of penalty takers when they went to their natural side and opposite side when the goalkeeper went his natural side and opposite side. Notice that when the kicker went NS and goalkeeper OS the success rates was 95% – the remaining 5% missed the target. Similarly when the kicker went OS and goalkeeper went NS – 8% missed the target.

Here is data on the peanlty kicks from last Sunday’s Champions League final

 

 

 

 

 

 

 

 

 

Notice that Chelsea keeper Petr Cech went the correct way for all penalties (including the one taken during normal time) – seemingly on the plane over he studied all Bayern penalties since 2007. He said it took nearly 2 hours – did he have a strategy?

Also Chelsea penalty takers favoured the natural side whilst Bayern the opposite side. Below is the shoot out once again.

King’s College Student Economics Magazine – “Marginal Utility”

September 23, 2011 1 comment

We recently published the first edition of “Marginal Utility” a King’s College student-driven publication that looks at current issues in the world of economics. To view click – marginal_utility.

The contents in this edition are as follows:
p2. THE US DEBT CRISIS
p3. DVD REVIEW “INSIDE JOB”
p4. HAYEK V KEYNES
p5. ECONOMICS BLOGS
p6. BOOK REVIEW – “THE GREAT STAGNATION”
p7. BEHAVIOURAL ECONOMICS
p8-9. GAME THEORY AND PENALTY KICKS
p10. THE NZ DOLLAR
p11-12. KOBE AND TOHOKU QUAKES
P13. BOOK REVIEW “ECONOMIC NATURALIST”
P14-15. AIRLINES – EMIRATES
P16. QUIZ – NAME THE ECONOMIST

Students who have contributed to this issue include: Shan Jun Chang – St John’s; Andrew Grant – Marsden; Rebecca Bullen – Middlemore; Henry Black – Greenbank; Mitchell Baker – Major; Tomo Greer – Middlemore; Georgia Harrison – Taylor; Jordan Darrow – Peart; and Andrew Larkey – St John’s.

Game Theory: Penalties and the 2008 UEFA Champions League Final

March 14, 2011 1 comment

In the recent edition of econoMAX (online magazine of Tutor2u) I wrote a piece on the game theory of penalty kicks in soccer. Below is an extract from it and an example of game theory in action from the 2008 UEFA Champions League Final between Manchester Utd and Chelsea.

As we approach the business end of the football season in Europe and with the potential impact of penalty kicks deciding matches, it might be appropriate to consider the relevance of game theory – economists hold in high regard the penalty kick as a real-life example of game theory. Technically the kicker and the goalkeeper play a zero-sum game – any gain for one player is exactly offset by the loss to the other side – plus one goal for me is minus one goal for you. The situation that kickers face in a penalty kick is a simultaneous-move game where they have three alternative strategies: shooting right, left, or centre. Similarly the goalkeeper also has three alternative strategies: dive to the right, dive to the left or remaining in the centre of the goal. In defining the sides of the goal researchers use the “natural side” of the kicker (which is the goalkeeper’s right, if the kicker is right-footed, and the goalkeeper’s left, if the kicker is left-footed) and the “opposite side”. Labeled like that, the strategies of both kicker and goalkeeper will be to choose the natural side of the kicker (NS), the centre (C) or the opposite side (OS).


From the data collected by Basque economist Ignacio Palacios-Huerta he calculated the proportion of successful penalty kicks. It shows the success rate of penalty takers when they went to their natural side and opposite side when the goalkeeper went his natural side and opposite side (see right). Notice that when the kicker went NS and goalkeeper OS the success rates was 95% – the remaining 5% missed the target. Similarly when the kicker went OS and goalkeeper went NS – 8% missed the target.

2008 UEFA Champions League final – Chelsea v Manchester Utd.

If you have read Soccernomics you will be well aware of the events that unfolded in this game. Ignacio had been recording how penalties were being taken and wrote an academic paper on strategies that players and goalkeepers employed. A mutal friend of Ignacio and Chelsea manager, Avram Grant, brought the two men together and subsequently Ignacio sent Grant some facts regarding Man Utd in particular about their goalkeeper Van der Sar. There were 4 main points:
1. Man Utd goalkeeper (Van der Sar) tended to dive to the kicker’s natural side (ie GK’s right for a right footed kicker)
2. Van der Sar tends to save penalties that are hit at mid-height
3. Man Utd midfielder Cristiano Ronaldo often stops in his run-up and if he does the ball is kicked towards the right hand side of the keeper. It was important that the Chelsea goalkeeper, Petr Cech, does not move early. When goalkeepers moved early Ronaldo always scored.
4. If you win the toss you take the first penalty. 60% of teams going first win the game.

Man Utd’s Rio Ferdinand won the toss and went first – not a good omen for Chelsea. Looking at the penalties and relating it to Ignacio’s research we see the following:

Chelsea
1. Ballack – OS – left. Van der Sar dives left – GOAL
2. Belletti – OS – left. Van der Sar dives right – GOAL
3. Lampard – OS – left. Van der Sar dives right – GOAL
4. Cole – NS – left. Van der Sar dives left (as advised by Ignacio ball hit hard and low) – GOAL
5. Terry – OS – left. Van der Sar dives right – NO GOAL – hit the post
6. Kalou – OS – left. Van der Sar dives right – GOAL

Up to this point all Chelsea right footed players had taken on the advice of Ignacio and hit to their opposite side – Van der Sar’s left.

Man Utd
3. Ronaldo – paused in his run-up. Petr Cech stayed upright for as long as possible and dives right – NO GOAL – saved.

Sudden death
It seemed that Chelsea’s strategy of going to Van der Sar’s left had been hatched by someone on the Utd bench. As Anelka prepared to take Chelsea’s 7th penalty Van der Sar pointed to the left corner. Now Anelka had a terrible dilemma. This was game theory in its rawest form. So Anelka knew that Van der Sar knew that Anelka knew that Van der Sar tended to dive right against right footers. Instead Anelka kicked right but it was at mid-height which Ignacio warned against. – Soccernomics Page 127

7. Anelka – NS – right. Van der Sar dives right – NO GOAL – saved

If Anelka had taken Ignacio’s advice would Chelsea have won? Below you can see the drama unfold on YouTube.

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