Are Penalty Shootouts a Lottery? What the Numbers Say

After the World Cup, penalty shootouts are back in everyone's nightmares, and with them an old argument: are they a lottery, or can skill, nerves and the order of kicking tilt the result? Statistics cannot calm the nerves, but it can tell us how much evidence the argument really has.

The math of five kicks

Suppose each kick is scored with probability 0.75. The binomial distribution calculator shows that a team scores at least 4 of its first 5 kicks about 63% of the time, and all five about 24%. If both teams have the same chance, the five rounds end level roughly 29% of the time, which means sudden death is common.

If order did not matter, both teams would win exactly half of all shootouts. That is the starting point, the null hypothesis, for any test.

One study found an advantage

A well-known paper reported that teams kicking first won 60.5% of shootouts, and explained it psychologically: leading in the score puts pressure on the team that kicks second (Apesteguia and Palacios-Huerta, 2010). Professionals also reported preferring to kick first when given the choice.

Another found nothing

A later study extended the sample to 540 shootouts and failed to detect any significant first-mover advantage (Kocher, Lenz and Sutter, 2012). An earlier comment from the same authors found that first kickers won only 53.4% of shootouts in a broader dataset, which was not significantly different from chance.

How can two studies disagree? Part of the answer is sample selection. Using specific subsamples without a coherent criterion can produce unrepresentative findings, as the comment pointed out.

The sample-size problem

Take a hypothetical 57.1% first-kicker win rate based on 80 wins in 140 shootouts. The one-sample proportion test gives p ≈ 0.11, not significant. A 53.3% rate over 540 shootouts gives p ≈ 0.13.

To detect a true 55% win rate against 50% with 80% power, you would need about 780 shootouts, more than the 540 shootouts in the larger study. An advantage that small, if it exists, would be nearly impossible to prove.

The sensible conclusion is modest: kicking first may help a little, but the evidence is weaker than a headline suggests.

A large effect has not survived larger samples.

Skill still matters

Treating every kick as an identical 75% chance is a simplification. Takers differ, goalkeepers differ, and conditions differ. Players and coaches who prepare carefully, by choosing who kicks and where to aim, can shift the odds even if kicking order does not.

Rules matter as well. A recent change in regulations let the winner of the coin toss choose the kicking order, and the original study noted that players rationally chose to kick first. That choice is itself data about what professionals believe, though belief is not proof.

A fair statistical summary is that a shootout is closer to a coin flip than most fans would like, with a small and unproven edge for preparation. The mix of chance and skill is precisely what makes the format so tense.

Players still prefer to kick first, and that is rational even without proof, since it costs nothing. As with the hot hand, our piece on football goals and streaks shows how often intuition sees patterns in randomness.