Regression to the mean in betting, explained

Regression to the mean is the reason a team on a hot streak usually cools off, and a bettor on a hot day usually has a quieter one next. Any run of results is part true level and part luck. The luck part does not carry forward, so the next run tends to sit closer to the true level. It does not mean the streak must reverse. It means you should expect less of it.

Why it happens

Think of every result as two things added together: how good a side really is, and the bounces it got. A team that wins six in a row is probably good, and probably also had a few deflections, a penalty or a goalkeeper's off day go its way. When you pick out the most extreme run, you are also picking out the run with the most luck in it. The next six games do not inherit that luck.

StatsBomb makes the point with PDO, a measure that adds a team's shooting and save percentages. Their analysis suggests a large share of a team's deviation from average on that measure is luck, but not all of it: shot quality, defending and player quality can keep the rate unusual for a while. That is regression in practice. Expect a pull back towards normal, not a return to exactly normal.

What it does to a price

If the market reads a hot run as pure skill, it prices the side too short for the next game. Gary Smith's research on football wagers looked at exactly this question: whether bettors give recent results more weight than regression to the mean says they deserve. That is the one situation where regression can be worth money. When prices already account for it, as they usually do in the biggest markets, there is nothing to take.

The useful habit is the question, not the bet. When a team is "in form", ask how much of the form came from chances created and how much came from chances taken. The first tends to last; the second tends not to. Why prices move on news like this is in why betting odds move before kick-off.

It applies to your record too

Regression works on bettors as well as teams. Our own Desk record shows it in miniature. On Friday 16 October six calls settled and five won, against 2.6 expected wins from the chances we had published. That is a good day with plenty of luck in it: three of the five turned on goals after 70 minutes. The full list is in Friday's Desk results: five from six. We do not expect the next six to go the same way, and neither should you with your own.

A losing run deserves the same treatment in reverse. How long one can honestly last before it tells you something is in how long a losing run can honestly last.

What this does not tell you

It does not tell you how much of any run is luck; that needs data on the chances behind the results, not just the results. It does not say a team on a bad run is a good bet, because the market may already have priced the bounce back in. And it does not set a timetable: luck evens out over many games, not over the next one.