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Don’t be fooled by a cold streak

Anyone who watches soccer knows that even the world’s best strikers may sometimes fail to score for a few matches in a row. But not every club has the luxury of employing one of the world’s best strikers. Let’s say your club has a fairly average striker. What will his cold streaks look like?

To answer this question, let’s create an imaginary striker who takes four shots per match in 25 league matches per season. Two of his shots in each match have a 5% chance of scoring, one has a 10% chance, and the last one has a 40% chance. So in total, he takes 100 shots per season, with each shot averaging a 15% chance of scoring. If he played infinite seasons, we’d expect him to average 15 goals per season. These are good if not extraordinary numbers.

Plenty of people have shown that such a striker may score many more or fewer goals than 15 in a given season, depending on his luck. But how long might he go without a goal? If we simulate the same season 10,000 times – that is, he takes the same shots in the same 25 matches 10,000 times over – we see that he has a goalless streak of at least four matches in more than half of the iterations. In 14% of the iterations, he’ll go without scoring for at least six matches in a row.

Let’s say the striker plays seven such seasons in his career. There’s close to a 50-50 chance that he’ll suffer at least one slump that lasts six matches or longer. And he’ll suffer the moans of the supporters, pundits, and perhaps even teammates for no reason other than a statistical idiosyncrasy.

Now let’s change the scenario a bit – what if our striker is playing for a lousy team? The players around him simply can’t manufacture chances that well. So instead of a 40% chance of scoring, perhaps his big opportunity in each match leads to a shot with only a 20% chance of going in. Now we’d expect him to score 10 times per season on average. In a new simulation, we find that more than half of his seasons include a goalless streak of six matches or more. In 14% of them, he goes at least nine matches without a goal.

That’s quite a drought. But remember, these two simulations are for the same striker. Nothing about his talent or effort has changed. Yet on a bad team, he’s likely to have quite a few dry spells.

I wrote this post as a word of caution to coaches and recruiters. It’s important to consider context when assessing a player. Understanding how much a players’ teammates may affect his performance is crucial. And so is trying not to be fooled by quirks that may be nothing more than randomness.