A Brief Look at Goal Distributions in International Tournaments

The 2024 Euros has been in full swing over the past few weeks. A friend whose interest in football is limited to major international tournaments and not particularly keen in watching matches in their entirety asked me what parts of matches they should focus on catching to maximise entertainment and excitement.

In some sports, there is a pretty clear answer. In fact, in many sports (including cycling or most other "racing" sports), the most exciting moments usually come towards the end. It was not immediately obvious to me that this is the case in football. Of course, the tension increases as we get closer to the final whistle. But in terms of goals scored (which is what I think they partially meant by entertainment), it is not clear that more goals are scored towards the end of matches, or even that there is any discernable pattern in the distribution of goals in matches. There is then only one good way to answer the question -> let's take a look at the data!

We consider data from the World Cup 2018, the Euros 2020 (2021) and the World Cup 2022. and consider group-stage and knockout matches separately. By knockout matches, I mean a last-16, quarter-final, semi-final or final. I was also curious about the differences with club/league football so let's also include a comparison to data from the top 5 European leagues (England, Spain, Italy, Germany, France) during the 2015/16 season (which is the seasons statsbomb has available data for). All the code used to produce this analysis is available here.

From the table below, knockout matches have had the most goals per match, which is not surprising given they can include 30 minutes of extra-time in the case of a draw after 90 minutes. Group-stage and knockout matches are relatively close in terms of second half goals. The surprising figure to me from this table is the low amount of goals in the first half of group-stage matches (0.95). In general, fewer goals are scored in the first half but this is particularly the case for group-stage matches.

	Group-Stage	Knockout	Leagues
Goals / match	2.55	3.13	2.67
Goals / First Half	0.95	1.26	1.18
Goals / Second Half	1.60	1.57	1.49
Goals / Extra-Time	NA	0.78	NA
Number of Matches	132	47	1823
Number of Goals	336	147	4863

Let's take a more refined look in the below plots.

Much could be said from these plots but due to the limited amount of matches considered (especially knockout matches), it is unclear how representative it would be of a true underlying distribution of goals. Nevertheless, here are a few observations

• group-stage: few goals at the start and most at the start of the second half.

• knockout: most goals either side of half-time. Dip in the 15-30 minute window.

• in both cases, a higher goal to minute ratio in injury-time of the second half.
  

A possible explanation for these differences is that in group-stage matches, there does need to be a winner and teams might be satisfied with a draw and therefore be more cautious (in the first half / beginning of the match). It could also be argued that we expect teams to actually play more cautiously in knockout matches since they might rather go to penalties than expose themselves and risk losing. However, the data suggests that this is not the case in the first half - perhaps the influence of the prospect of penalties on tactics only sets in later in the match.

We again also include below a plot for the European leagues. Note that the much larger dataset provides smaller variance and more accurate representations of the true distributions.

The patterns are interestingly quite different for the league games with the likelihood of a goal increasing steadily throughout the match.

There are many more interesting questions to ask / patterns to look into:

• How does this vary for finals, semi-finals... etc ?

• What about the relative strength of teams facing each other ? And home vs away teams ?

• What about the context of the match ? If a team is one goal up or if they are drawing ? Also, what is the distribution of the first goal ? The second ? ... etc

• Can we carry out tests to reach statistical conclusions about some of these claims ?

We may explore some of these ideas in future posts. For now, the main takeaway is that my friend should probably aim watch the second half of matches. Thanks for reading!