The role of luck in football

Imagine a 20 team league, where every team is exactly equal with equally skilled players.

Every team creates exactly 4 good chances a game, each chance has a 50% chance of being scored.

I think most people would say if every team is exactly as good, and create exactly as many chances then they’ll end up with almost exactly the same number of points. People would probably also guess that a lot of games would be draws.

Thanks to the excellent work of Danny Page we can see the truth.

A draw is he most frequent outcome (26% of the time) but that means 74% of the time we’ll have a winner by between 1 and 4 goals. This is because although our defences are all mean, they aren’t at all mean, giving up 4 good chances each. If I made it 0.5xG each the draw would be far more common.

Possible scorelines

0-0
1-0
0-1
1-1
2-0
0-2
1-2
2-1
3-0
0-3
3-1
1-3
3-2
2-3
4-0
4-1
4-2
4-3
0-4
1-4
2-4
3-4
4-4

The average team in our average league would expect to end up with 52 points, and a standard deviation of 8 points. This means that 68% of teams would be likely to end up with between 44 and 60 points in a typical season and we can be 95% sure they will get between 36 and 68 points.

Run the same scenario 1000 times and you get totals as low as 22 and as high as 82 points.

Imagine the stories that would be told of the all-conquering 82 point Champions, the greatest of all time. Or that useless idiot in charge of the 22 point team. Then remember these teams were exactly as good as each other.

The players were identically skilled, the managers were identically skilled. All that happened was the variance in whether they scored their 50/50 chances or not.

People tend to not like to talk about luck. I remember learning about beta distribution, and reading papers that showed that most fund managers don’t outperform the market in the long run. There is hardly any correlation between year to year performance of funds. Those that do beat the market in the long run might just be the equivalent of our 82 point champions. Just pure luck. This view did not make me popular in my brief time working in finance.

Likewise Paul Riley @footballfactman is famed for his ability to drag down the collective mood of any Everton forum by pointing out their underlying numbers are nowhere near as good as people think. The famous Martinez 72 point season was actually a Tim Howard/poor finishing against outlier season rather than a brave new world of dominance. And two ~50 point seasons followed.

On the other hand knowing about luck can be a comfort. Some couples trying for a baby are fortunate and manage to conceive as soon as they start trying. Other couples, with equal fertility and timing, might take years to have a baby. It can just be luck. A fertile couple not conceiving for a year is only about the same odds as flipping a coin and getting HHHH or TTTT.

But what about the phrase “you make your own luck” or the “the harder I practice the luckier I get”?

Let’s do an experiment where one team does practice harder than all the others, earning themselves an extra 0.2 chance in each and every game they play.

Well suddenly, after running the simulation, this team is winning an extra 5 points a season than their 19 identical opponents.

They are more likely to win the league than their opposing teams, but by no means guaranteed victory.

But that was achieved through better skill, not luck. It is possible to be better than your opponents in every game and be relegated.

But is luck just luck?

Perhaps the Matthew Effect is in play. Particularly in sport. Imagine that out of nowhere you have the completely luck based 82 point season in your first season in football management. You are on the front page of every paper, every player in the world wants to play for the manager who won the league by 20+ points. Suddenly Messi and Salah are offering to join the average league. Them joining increases your expected goals by 2 per game and suddenly you are winning the league each and every year.

Your managerial reputation is stellar and more and more of the best players want to play for your all-conquering side. But you remain the same manager you were. Nothing you are doing is different.

Meanwhile, that manager who got 22 points, who was equally as skilled, never got another chance in the game and has their name adopted as shorthand for somebody completely out of their depth.

In the event they did get a new job we would possibly see the xG decrease as the best players decide they don’t want to work with a known loser. The rich get richer, the poor get poorer.

So what can clubs do to ensure they are operating on skill not luck?

(1) Have people in the club with a good understanding of variance. Don’t look at just results, look at underlying numbers.
(2) Judge results against peer clubs but be fair. I wouldn’t say judging Marco Silva on Everton’s current wage bill would be fair. He isn’t responsible for the Koeman/Allardyce/Walsh spending. Make reasonable adjustments.
(3) Have an agreed plan and work towards it together. If the manager says he wants to build towards a team that plays a certain style of football then make sure he can both explain the end result and how he’ll get you to that point. If he says he wants to play a fast breaking 4-3-3 but is demanding a slow number 10 then query how it will work.
(4) Make sure the management team are pleasant people to be around. If they react to bad luck or good luck with over the top actions, like punishments or falling out with people they are unlikely to just get on with the steady improvement work that maximises chances.

Nothing will remove the variance/luck. You can do everything right and still fail. But make sure you are building towards increasing your chances of winning. That is all you can do. And MRKT Insights can help you do it.