Tag Archives: Penalty Shoot Out

Action bias and penalty kicks – is it best if the goalkeeper does nothing?

Action bias is a situation where we would rather be seen doing something than doing nothing. This has been the case in numerous government elections as the voting population like to see some action from politicians when in some cases the best option is to let the economy run its course. President Nixon (US President 1969-74) was a great one for doing something even though it would have been better to do nothing – I refer to the wage and price controls introduced in 1971 – the controls produced food shortages, as meat disappeared from supermarket shelves and farmers drowned chickens rather than sell them at a loss. So when the economy is doing badly the government maybe tempted to intervene, even if the risks associated with the changes not necessarily outweigh the possible benefits. Furthermore if an economy is doing well policy makers may feel that they shouldn’t do anything even though the changes could improve the economy further.

According to classical assumptions in economics, when a people face decision problems involving uncertainty, they should choose what to do according to their utility from the possible outcomes and the probability distribution of outcomes that follows each possible action. Bar-Eli, Azar, Ritov, Keidar-Levin, & Schein, 2007

In a 2007 study, Michael Bari-Eli at the Ben Gurion University of the Negev, Israel, analyzed 286 professional soccer penalty kicks. They discovered that goalkeepers almost always jump right or left because the norm is to jump — a preference for action (”action bias”). The goalkeepers jumped to the left 49.3% of the time, to the right 44.4% of the time, but stayed in the centre only 6.3% of the time. Analysis revealed that the kicks went to the left 32.2%, to the right 39.2% and to the centre 28.7% of the time. This means that the goalkeepers were much more likely to stop a kick if they had just stayed put – see table below.

The table above suggests that the decisions taken by the kicker and goalkeeper are made roughly simultaneously. The fact that the directions of the kick and the jump match in 43% of kicks rather than in 0% or 100% of the kicks suggests that neither kicker nor goalkeeper can clearly observe what the other chose when choosing their action.

A goalkeepers’ decision making.

In order to suggest a best option for goalkeepers it is necessary to examine the probability of stopping the ball following each combination of kick and jump directions. The table below presents the average saving chances using the formula

Number of penalty kicks saved ÷ Number of penalty kicks x 100

Jumping left = 20 ÷ 141 x 100 = 14.2%
Staying Centre = 6 ÷ 18 x 100 = 33.3%
Jumping right = 16 ÷ 127 x 100 = 12.6%

The research conclusions state that goalkeepers jump to the right or the left during penalty kicks more than they should. In analysing the 286 kicks Bar-Eli et al show that while the utility-maximising behaviour for goalkeepers is to stay in the goal’s centre during the kick, in 93.7% of the kicks the goalkeepers chose to jump to their right or left. This non-optimal behaviour suggests that a bias in goalkeeper’ decision making might be present. The reason that they suggest is ‘action bias’. However you also need to look at the psychological aspects of a goalkeeper. Arsenal and former Chelsea goalkeeper Petr Cech said that he never liked to stay in the centre as it might look to the fans that he wasn’t trying. Although he would be in a good position to save a penalty that was kicked down the centre, he would feel a lot worse if he stayed in the centre and the ball went into the goal either side of him.

Sources:

Bar-Eli, M., Azar, O. H., Ritov, I., Keidar-Levin, Y., & Schein, G. (2007). Action Bias Among Elite Soccer Goalkeepers: The Case of Penalty Kicks. Journal of Economic Psychology, 28(5), 606-621.

An “Action Bias” Can Be Counterproductive

Game Theory Lesson: Man Utd v Chelsea Penalty Shootout

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.

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

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.