# Statisfaction

## Penalty shootout in FIFA World Cups

Posted in Sport by Julyan Arbel on 10 July 2010

While looking for a post on octopus Paul, Jérôme told me about this surprising football stat:

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