After their 4-2 loss in the quarter finals of this year’s European Championship finals, England holds a record of 6 losses and only 1 win in penalty shoot-outs in the European Championship and the World Cup finals.
(Source http://www.englandfootballonline.com/TeamPenalty/EngPenKickShootoutMtchs.html)
Journalists, players, coaches and managers often describe or compare penalty shoot-outs to draw of lots or a coin toss. If that’s true, each team of the penalty shoot-out has exactly 50% chance of winning, even England.
The probability of 0 or 1 wins out of 7 independent shoot-outs, if the chances are even, can be read from a table of binomial probabilities to P{X <= 1} = 0.0078 + 0.0547 = 0.0625. That is, if England has same chances as its opponent, the chances of winning only one (or zero) out of seven shoot-outs is 6.25%. If we look through the glasses of a 95% confidence interval or acceptance area, we can’t reject that England has just been unlucky, but the low likelihood gives some evidence to believe that England is poorer than their opponents, that is, the assumption of 50% probability of a win for England is probably false.
| World Cup Finals | 1990 | West Germany | England | 4-3 |
| European Championship Finals | 1996 | Spain | England | 2-4 |
| European Championship Finals | 1996 | Germany | England | 6-5 |
| World Cup Finals | 1998 | Argentina | England | 4-3 |
| European Championship Finals | 2004 | Portugal | England | 6-5 |
| World Cup Finals | 2006 | England | Portugal | 1-3 |
| European Championship Finals | 2012 | England | Italy | 2-4 |
Journalists, players, coaches and managers often describe or compare penalty shoot-outs to draw of lots or a coin toss. If that’s true, each team of the penalty shoot-out has exactly 50% chance of winning, even England.
The probability of 0 or 1 wins out of 7 independent shoot-outs, if the chances are even, can be read from a table of binomial probabilities to P{X <= 1} = 0.0078 + 0.0547 = 0.0625. That is, if England has same chances as its opponent, the chances of winning only one (or zero) out of seven shoot-outs is 6.25%. If we look through the glasses of a 95% confidence interval or acceptance area, we can’t reject that England has just been unlucky, but the low likelihood gives some evidence to believe that England is poorer than their opponents, that is, the assumption of 50% probability of a win for England is probably false.
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