How Bad is England at the Penalty Shootout?

Today the English woman's team fell short against France in a penalty shootout 4-3 after a hard fought and highly entertaining match. The loss immediately brought comparisons to the dismal record of the men's team in penalty shootouts. For instance, here is what The Guardian had to say:

It was a case of history repeating itself in the beautiful game as another penalty shootout ruined England's dream of World Cup glory – but this time in the women's tournament.

The national team went crashing out of the Women's World Cup in spectacular fashion at the BayArena in Leverkusen, Germany, after squandering a one-goal lead before missing two penalties in the quarter-final to send France through to the last four.

Football fans had hoped the curse of penalties, which has long plagued the men's game, would not extend to Hope Powell's squad as England looked to advance into the semi-finals. But like the 1998 men's World Cup, when Paul Ince and David Batty missed their chances against Argentina, the women's team were also defeated 4-3 on spot kicks.

But is the men's team actually cursed?   Let's look at the numbers:

In Why England Lose & Other Curious Football Phenomena Explained Simon Kuper and Stefan Syzmanski take a look at the English teams performance over time, and find that it has won just about half of its games:

England's win sequence over the 400 games [since 1980] is indistinguishable from a random series of coin tosses. (p. 48)

So let's assume a probability of winning a match for England of 0.50, just like a fair coin.  Then let's ask, what are the odds of experiencing a 1-5 (or worse) record in penalty shootouts over 6 shootout opportunities?

The answer is about 11%. Not great odds, but not very close to conventional thresholds for statistical significance either. Think of it another way, had just 2 of those 5 losses instead been wins then England would be 3-3 and the national infatuation with the penalty shootout would not have happened.

Academics have even tried to explain England's poor shootout performance via some complicated (and I'd say rather implausible) theorizing.  I've got a better explanation -- bad luck. It could be worse of course -- think of Holland. Sometimes the ball doesn't go into the net. It didn't today for England. Better luck next time.

Here is the whole penalty shootout from earlier today: