# Statisfaction

## Penalty shootout in FIFA World Cups

Posted in Sport by Julyan Arbel on 10 July 2010

the team which begins a penalty shootout is more likely to win than the following team.

Here is a so bad souvenir, with Trézeguet’s shoot on the bar… And yes, Italy went fisrt at shooting!

What do data say about that?

Here are results on penalty shootout of five main tournaments in the past decades, World Cup, European Championships, Copa América, African Cup of Nations and the Asian Cup. The trouble is a crucial point is missing: there is no mention of which team began to shoot. I managed to gather 14 data points in the following way (only for the World Cups): either using the number of penalties taken column (which provides the order information when the numbers differ), or watching relative youtube video. The outcomes are shown bellow (please comment if I misinterpreted any result, or if you know a clever way to get more data, I no football scholar!): the beginning team won 11 (out of 14) times!

Now, the question is to see whether this difference is statistically significant or not.

A simple model is the following: the random variable $X_i$ is 1 when the match labelled by $i$ is won by the first team to shoot, and is 0 otherwise ($n=14,\,i=1,...n$). Denote $p$ the probability that $X_i=1$. Then, testing $H_0 :\,p=1/2$ against $H_1 :\,p\neq 1/2$ can be done via a $\chi^2$ test (or a Wald test, with the same statistic in the case of the Bernoulli model).

Under hypothesis $H_0$, the statistic $T_n=4n(\bar X-1/2)^2$ folows a $\chi^2(1)$ distribution asymptotically. We have $T_n=4.57$. Compared to the 95% quantile of a $\chi^2(1)$ variable, $q=3.8$, we can state that the probability of success is significantly higher for the first team.

Any explanation? We can guess that the following team is more under pressure than the first, and fails more often when trying to equilize. Indeed, a player whose shoot makes win his team in case of success scores an average 93%, against an average 52% or so when it makes loose in case of failure…

PS: should Spain – Netherlands end up with a penalty shootout, football analysts say it would be in the interest of Spain. Indeed the Netherlands are among the 5 worse nations at thos (along with the UK). What if the Netherlands win the coin toss?

3 second-in winners:

 1990 SF Argentina Italy 1-1 4-3 4 & 5 1990 SF West Germany England 1-1 4-3 4 & 5 1994 Final Brazil Italy 0-0 3-2 4 & 5

against 11 first-in winners:

 1986 QF West Germany Mexico 0-0 4-1 4 & 3 1998 Last 16 Argentina England 2-2 4-3 5 each 1998 QF France Italy 0-0 4-3 5 each 1998 SF Brazil Netherlands 1-1 4-2 4 each 2002 QF South Korea Spain 0-0 5-3 5 & 4 2006 Qualifier Australia Uruguay 0-1 1-0 4-2 5 & 4 2006 Last 16 Ukraine Switzerland 0-0 3-0 4 & 3 2006 QF Germany Argentina 1-1 4-2 4 each 2006 QF Portugal England 0-0 3-1 5 & 4 2006 Final Italy France 1-1 5-3 5 & 4 2010 Last 6 Paraguay Japan 0-0 5-3 5 & 4

### 4 Responses

1. Robin Ryder said, on 12 July 2010 at 15:54

Cool question.
I think the strong signal you find might come from the data collection procedure: is it not the case that you are more likely to know which team went first when the first team won? Do you get the same result when you only use matches for which you looked at a Youtube video?

2. Pierre J said, on 13 July 2010 at 01:04

Cool post, Revolutions just blogged about the World Cup too:
http://blog.revolutionanalytics.com/2010/07/charting-the-world-cup.html
(they got data on the number of fouls and the number of goals by country)

3. Julyan said, on 13 July 2010 at 11:24

Robin you are right!! I was hesitating on that possible bias, but too lazy to check it. I think it is like this: for example a 4&5 result in the last column means that the first team failed two more times than the second, whereas a 5&4 outcome mean the second failed only one time more than the first… which occurs more often because goals are more likely than failures.
Only using the matches I got on Youtube won’t make it: there are only 4, all of them are “first-in winners”. Well, I definitely need a more comprehensive database. Les footeux?

4. Robin Ryder said, on 3 January 2011 at 09:49