Who will win Euro 2020?

The European Championships are almost upon us. It’s that traditional time when the English media builds up the anticipation, and people really think that England might win an international tournament. As Stefan Szymanski wrote, though, “England never wins”. Obviously that’s not true since they managed it once in 1966. So where do we lie in between being certain to win, and having absolutely no chance?

As with previous seasons in the Football League (see here) I’ve simulated the European Championships. Why? Because it gives probability forecasts of outcomes, and hence we can get a sense of whether we should be excited or not. And why not, given that even Goldman Sachs are producing forecasts?

My forecasting model is very simple for matches — it simply asks how many goals should each team be expected to score given how strong they are, and their opponents are. More technically, it’s a double-Poisson model, using Elo ratings to measure team strength. It’s actually similar, but simpler, than the Goldman Sachs model.

If you’re interested in what the Elo ratings look like for the 24 teams in the Euros since 2018, here’s a plot:

Belgium are the best team around at the moment, at least in Europe, followed by France, who are also a little way out ahead of the chasing pack of Spain, Italy, Portugal and England. The weakest team, it won’t be a surprise to learn, is North Macedonia, just a little worse than a pack of three blue teams: Finland, Scotland and Slovakia.

As such, as we model match outcomes only based on Elo strengths, there are no nods to more recent form, no recognition of squad strength or weakness (over and above that reflected in recent match outcomes). But it’s easy to update — just the Elo rating after each match.

So we generate a number of goals in a match for each team using the Poisson distribution — that is, we create an outcome that is consistent with the strengths of the two teams involved. So, for example, a 2–0 win for Italy in their opener against Turkey on Friday. We then carry on, updating each team’s Elo ratings, until we reach the end of the group stages. Then we manage the very complicated system for determining the last 16, and go through the knock-out stages.

If a knock-out match finishes level we decide the penalty shoot out as a binomial event with the probability each team wins equal to the Elo prediction for that match (so the better team wins more than the worse team, but not always).

We then end up with a full set of results for a notional European Championships. Such as this one:

Here, Denmark channel their inner 1992, and come out as champions, beating Italy on penalties in the final after a 1–1 draw.

It’s just one replication, and we need to do this lots more to get a sense of how likely an outcome like Denmark winning is. We do it 10,000 times, and count up how often each team wins. The answer for Denmark is 480 out of 10,000. So we interpret that as a 4.8% chance that they win Euro 2020.

Below is a table collecting together the probability of winning Euro 2020 for each country, as well as the probability that country makes the final, semis, quarters and last 16.

So North Macedonia have no chance of winning, but a 0.2% chance of making the final, a 1.3% chance of making the semi-finals, and a 31% chance of progressing from their group.

England are 7% likely to win the tournament, so sixth favourites behind Belgium, France, Spain, Italy and holders Portugal.

How does all this relate to those original team strengths? Well, in the plot below I’ve plotted those winning probabilities against a team’s Elo rating at the outset of the tournament (which is also listed in the replication table).

As can be seen, there’s something of an exponential, non-linear relationship. This appears to suggest that the tournament format accentuates differences between teams at the top end of the strength range.

The difference between the Czech Republic (1150 ish) and Switzerland (1250 ish) is the same as that between Switzerland and Italy (1350ish). but the Czech Republic has a 0.2% chance, Switzerland 2% and Italy 9%.