**Reform of the Champions League: advantages and disadvantages of the “incomplete championship”**

Mathematician Julien Guyon deciphers the new format imagined by UEFA for the flagship European competition.

In the future Champions League format, 36 clubs would compete in a first phase in a league, each of them playing ten matches. MATTHEW CHILDS / REUTERS

UEFA is expected to ratify in March a reform of the Champions League format which would come into force in 2024. The group stage is over with eight groups of four teams competing in a mini-championship by two-way matches ( six days, 96 games in total): it would be replaced by a single championship of 36 teams.

Each team would only play against a small number N of opponents (once each, no round trip), i.e. 18 N matches spread over N days: a format inspired by the “Swiss system” (so named because it was used). for the first time at a chess championship in Zurich at the end of the 19th century), which we call “incomplete championship”.

UEFA seems to have set its sights on N = 10: ten league days for a total of 180 matches, almost double the current format. It is interesting to note that in ten days we have a classic group stage with six groups of six teams (ten days, 180 matches).

The abandonment of the classic group stage and the adoption of the incomplete championship are therefore not the result of an insurmountable constraint linked to the calendar or the number of teams entered, but are indeed deliberate choices of UEFA. So what are the advantages and disadvantages of this new format?

**Not too many matches to establish a first ranking**

The major advantage of the incomplete championship is that it makes it possible to establish a complete classification of a large number of teams, without having to organize too many days of the championship or too many matches (“only” 10 days and 180 matches in the place of 35 days and 630 matches).

However, it is useful, before the knockout phase, to have a complete classification of qualified teams. At the moment, we only have internal rankings for the 8 groups: a weak *posterior* group qualifies as many teams (2) for the knockout phase as a *successful posterior* group .

With the new formula, 4 teams which, in the current format, could all have found themselves in a strong group, can hope to qualify all four.

Another advantage of this format is its flexibility: if UEFA wants to go, for example, to 40 teams and 12 matches, no problem! This format is also interesting for spectators, since it offers a greater variety of matches: each team meets a new opponent every day.

**No more meetings between big cars**

Another interest for UEFA, big clubs, broadcasters and spectators: more matches (in proportion and in absolute) between big engines. In the version that UEFA seems to favor, the 36 teams would be divided into 4 hats of 9 teams, essentially by level: the 9 best teams according to the UEFA coefficient of the clubs in hat 1, the next 9 in hat 2, etc. .

In reality, UEFA could continue to reserve hat 1 for the winners of the best leagues, which tends to weaken hat 1 compared to hat 2.

Each team of the extreme hats (1 and 4) would meet 4 other teams of these same hats (2 + 2) and 6 teams (3 + 3) of the middle hats (hats 2 and 3); symmetrically, each team of the middle hats would meet 4 teams of those same hats (2 + 2) and 6 teams (3 + 3) of the extreme hats.

This means that teams in hat 1 will be able to compete against each other, as well as teams in hat 2, which is currently not possible.

The proportion of matches between teams of the top two hats would drop from 1/6 (16 games out of 96) in the current format to 1/4 (45 games out of 180) in the new format. The same applies to the matches between teams of the two weaker hats: matches attracting less audience, but *a priori* well balanced.

The proportion of the most unbalanced matches (hat 1 against hat 4), which do not generate much interest, would drop from 17% to 10%.

**A problem of equity**

The major drawback of the incomplete championship is its lack of fairness: at the end of the 10 days, the teams are classified according to the number of points acquired. However, they did not all play against the same opponents!

If the hats are well built, the range of strength *a priori* of the 10 opponents is fairly evenly distributed. But it may be that Team A finishes before a B team because opponents of A were *retrospectively* revealed low (their accumulated points at the end of the 10 days is low) while those in B are *retrospectively* disclosed strong (cumulative high points).

In such a case, is it fair to classify A before B? Shouldn’t the points won by each team be weighted by taking into account the cumulative points of their opponents? At the very least, this shows that to decide between two teams with equal points, the cumulative points of the opponents would be better than the traditional criterion of goal difference.

**The question of the a priori measurement of the strength of the competing clubs**

The incomplete championship is in fact a truncated championship. When Ligue 1 shut down in the spring of 2020 due to the coronavirus epidemic, I had proposed a method to correct for truncated ranking biases, using the Elo formula, which could also be used here by UEFA.

Even if we consider that the performance of the teams will be in line with their strength *a priori* , and therefore that the cumulative points of the opponents will not vary too much from one team to another, it is still necessary to know how to measure the *a priori* strength of teams!

Since the new formula compares performances that are not exactly comparable, its success depends on the quality of this classification a priori. In this sense, the exceptional rule used to define hat 1 is regrettable.

The UEFA coefficient, which today measures the *a priori* strength of clubs, seems quite old-fashioned, while more efficient alternatives (with better predictive power) have proven their worth, such as the Elo method which, unlike the UEFA coefficient, is ‘self-correcting taking into account the strength of opponents, and was adopted in 2018 by FIFA for its ranking of national teams.

**The risk of games without stakes distorting the ranking**

Another flaw in the new formula proposed by UEFA is the risk of games without stakes. For example, during the last days, teams may already be guaranteed to finish one of the last 12 eliminatory places, or one of the first eight directly qualifying places for the round of 16 (the other eight tickets would be awarded following play-offs between the teams ranked 9 to 24).

They can thus play their second team, which risks distorting the final classification, the opponents of the second team being unfairly favored. The “Choose Your Opponent” format that I recently proposed would solve this problem: the best ranked teams would choose, in order, their opponent in the round of 16, which would encourage them to win all their matches to finish in the first. square.

Another important aspect of the reform concerns the access list to the championship phase. UEFA each season could recover two big guns *in principle* not qualify for the Champions League based on their UEFA coefficient.

Thus, Manchester United could be drafted if they finish 6th in the Premier League, behind, say, Leicester City, 5th, who would have to settle for the Europa League, even if they finished ahead of the Mancuniens. Another fairness issue, but that’s another story …

**Not a real “Swiss system”**

The true “Swiss system” differs from the incomplete championship offered by UEFA. In this system, the matches are determined as the days go by according to the results of the teams, so that the matches always oppose two teams having had similar performances – with the constraint that two teams do not meet more than one. times.

For example, assuming for simplicity that draws are prohibited, after day one, day two matches win against winner, and loser against loser, to the extent possible; then, on the third day, double winner against double winner, double loser against double loser, the remaining matches between teams with one win and one defeat; etc.

Thus, the cumulative points of the opponents of two neighboring teams in the classification are similar, and the classification is therefore valid *a posteriori* .

UEFA should consider adopting the real Swiss system. Admittedly, one would not know the agenda of a day until the end of the previous day, which complicates the logistics and planning for UEFA, clubs, broadcasters and spectators. But that would guarantee more fairness as well as a better competitive balance, and in particular more matches between the best teams.

*Julien Guyon is a mathematician and football fan. A quantitative analyst, he is also an associate professor in the mathematics department at Columbia University and at the Courant Institute of Mathematical Sciences at New York University. His work is available on his web page: **http://cermics.enpc.fr/~guyon/** and on his Twitter account: @ julienguyon1977*