Qualification Drama: Matchday 5 Insights & Likelihoods

We would like to announce our brand new academic partnership with OR in Sports, a working group of EURO (the association of operational research societies) which aims to bring together quantitative research related to sports in a broad sense, encourage collaboration among academics and practitioners, and increase the visibility of research in this field.


The authors of this research are the following: László Csató (Corvinus University of Budapest & HUN-REN Institute for Computer Science and Control); Karel Devriesere (Ghent University); Dries Goossens (Ghent University); András Gyimesi (University of Pecs & HUN-REN Institute for Computer Science and Control); Roel Lambers (TU Eindhoven); and Frits Spieksma (TU Eindhoven).

METHODOLOGY

Our results are derived from Monte Carlo simulations, where we generate random samples from a probability distribution to simulate the outcome of each match. A single simulation run determines the results of all scheduled matches and produces a complete ranking of the teams. To minimize the influence of randomness, we perform 1 million simulation runs. By analyzing the outcomes, we can estimate probabilities for specific events; for instance, the likelihood of Feyenoord finishing in the top 8 is determined by counting the proportion of simulations where this occurs. 

The accuracy of the results depends heavily on the details of the simulation. Match outcomes, specifically the number of goals scored, are modeled using a Poisson distribution (Maher, 1982). The expected number of goals is expressed as a polynomial function of win expectancy, which is separately estimated for home and away teams based on approximately 8,000 matches played in UEFA club competitions (Champions League, Europa League, and Conference League) and their qualifiers between 2003 and 2024. Win expectancy is derived from the Football Club Elo Ratings (see clubelo.com), which provide a more precise measure of team strength than the UEFA club coefficient (Csató, 2024a).

This modeling approach is widely applied in the tournament design literature, particularly for national football teams (Csató, 2022, 2023a,b,c, 2024b; Stronka, 2024) but also for club football (Gyimesi, 2024). Team rankings are determined in accordance with official UEFA ranking rules (UEFA, 2024, Article 19), though fair play points are excluded. The probability of qualifying for the Round of 16 is computed by simulating the play-offs, with win expectancies for two-leg matches calculated using the Football Club Elo Ratings methodology (see clubelo.com). Further details about the simulation methodology can be found in a blog post on the Football Rankings website (see http://www.football-rankings.info/2020/12/simulation-of-scheduled-football-matches.html).

UEFA CHAMPIONS LEAGUE

How did the results of the fifth matchday influence the chances of qualification for each team? The figure below shows to what extent this matchday increased or decreased the chances of each team for qualifying to top 8, compared to after matchday 4.

The next figure below shows to what extent the fifth matchday increased or decreased the chances of each team for surviving the league phase (i.e. reaching top 24), compared to right after the fourth matchday.

Next, let’s have a look at the points that are likely required to reach top 8, and to survive the league stage.

ANALYSIS RESULTS

Liverpool’s Dominance
Liverpool remains a strong favorite, with over a 98% chance of finishing in the Top 8. Their elimination is now impossible, and they are also likely to progress to the Round of 16.

Teams Eliminated from Top 8 Race
Bologna, Leipzig, S. Bratislava, and Young Boys can no longer reach the Top 8 this season.

Man City’s Setback
Man City’s chances of finishing in the Top 8 have dropped to just over 15%, a decline of more than 35 percentage points due to an unexpected draw against Feyenoord.

Feyenoord’s Recovery
Feyenoord’s draw against Man City has significantly boosted their survival prospects, reducing their chances of elimination by the highest margin in percentage points.

Top Contenders
Four teams (Liverpool, Inter Milan, Barcelona, Borussia Dortmund) now have more than a 69% chance to finish in the Top 8 and more than a 90% chance to reach the Round of 16.

Biggest Winners and Losers
The biggest winners after Matchday 5 are Atleti, Benfica, and Lille, all of which secured away victories. Meanwhile, Stuttgart, Brest, and Monaco saw the greatest decrease in their chances of reaching the Round of 16.

Survival Boost for Some Teams
Atleti (from 6.74% to 0.16%), Benfica (from 24.81% to 2.04%), and Feyenoord (from 38.83% to 15.89%) have reduced their elimination risk dramatically in the league phase.

Increased Elimination Chances
On the other hand, Girona and Sparta Praha’s elimination chances have increased by more than 10 percentage points, while Dinamo Zagreb and Stuttgart saw increases of over 15 percentage points.

Challenging Path for Leipzig and Paris
From Pot 1, Leipzig has less than a 4% chance to survive the league phase, while Paris has a less than 53% chance. In contrast, the other seven teams from Pot 1 have over a 90% chance of survival.

Surprise Teams from Pots 3 and 4
Aston Villa, Lille, PSV, and Sporting CP, drawn from Pots 3 and 4, now have over a 52.5% chance to reach the Round of 16—no such teams had this probability at the start of the league phase.

Brest’s Remarkable Performance
Brest has earned 10 points from five matches, with their chances of elimination plummeting from 52.29% before the first matchday to just 0.61%.

Weakest Teams Struggling
Seven of the eight weakest teams have less than a 1% chance of advancing to the Round of 16 or avoiding elimination from the league phase.

Points Required for Survival
Achieving 8 points is unlikely to be enough to survive the league stage. Even 9 points will only guarantee survival in less than half of the cases, while 10 points offers no guarantee either.

UEFA EUROPA LEAGUE

How did the results of the fifth matchday influence the chances of qualification for each team? The figure below shows to what extent the this matchday increased or decreased the chances of each team for qualifying to top 8, compared to after matchday 4.

The next figure below shows to what extent the fifth matchday increased or decreased the chances of each team for surviving the league phase (i.e. reaching top 24), compared to right after the previous matchday.

Next, we’ll have a look at the points that are likely required to reach top 8, and to survive the league stage.

ANALYSIS RESULTS

Lazio’s Dominance
Lazio has the highest chance to reach the Top 8, Top 24, and the Round of 16, as it is the second strongest team and leads the league table.

No Certainties Yet
Surprisingly, no team is absolutely certain to survive the league stage after 5 rounds.

Tottenham’s Resilience
Tottenham, the second strongest team, still has more than a 75% probability of finishing in the Top 8 despite earning only one point in the last two rounds.

Biggest Winners and Losers
The biggest winners after Matchday 5 are Rangers, Fenerbahce, and Union SG, all of which secured away victories. The biggest losers in terms of Round of 16 qualification chances are Nice, Slavia Praha, and Hoffenheim.

Survival Boost for Some Teams
Union SG, Fenerbahce, Braga, Ferencvaros, and Rangers have reduced their threat of elimination in the league phase by more than 20 percentage points.

Increased Elimination Chances
On the other hand, the chance of elimination has increased by more than 20 percentage points for Nice, Besiktas, Twente, and Hoffenheim.

Challenging Path for Viktoria Plzen
Viktoria Plzen faces a higher chance of elimination than the weaker Ferencvaros, despite both teams having nine points. Plzen’s more difficult schedule and fewer home matches contribute to their increased risk.

Eastern European Champions Thrive
Two Eastern European champions, FCSB (Romania) and Ferencvaros (Hungary), have won three of the first five rounds, dramatically reducing their chances of elimination from over 76% to 1.25% and 2.84%, respectively.

Slavia Praha’s Struggles
From Pot 1, Slavia Praha has only a 40% chance of qualifying for the Round of 16, as it has only four points.

Athletic Club’s Strong Position
From Pot 4, Athletic Club has more than a 94% chance to finish in the Top 8, benefiting from its high Elo rating, which highlights an issue with UEFA club coefficients.

Survival Odds in Contrast
In stark contrast to the Champions League, two of the weakest eight teams, FCSB and Ferencvaros, have very high chances of surviving the league phase.

Points Required for Survival
In the Europa League, obtaining 9 points is likely to be enough to survive the league stage with a 75% chance, while collecting 10 points almost guarantees survival.

REFERENCES

Chater, M., Arrondel, L., Gayant, J.-P., and Laslier, J.-F. (2021). Fixing match-fixing: Optimal schedules to promote competitiveness. European Journal of Operational Research, 294(2):673–683. 

Csato, L. (2022). Quantifying incentive (in)compatibility: A case study from sports. European Journal of Operational Research, 302(2):717–726. 

Csato, L. (2023a). Group draw with unknown qualified teams: A lesson from the 2022 FIFA World Cup. International Journal of Sports Science & Coaching, 18(2):539–551. 

Csato, L. (2023b). How to avoid uncompetitive games? The importance of tie-breaking rules. European Journal of Operational Research, 307(3):1260–1269. 

Csato, L. (2023c). Quantifying the unfairness of the 2018 FIFA World Cup qualification. International Journal of Sports Science & Coaching, 18(1):183–196. 

Csato, L. (2024a). Club coefficients in the UEFA Champions League: Time for shift to an Elo-based formula. International Journal of Performance Analysis in Sport, 24(2):119–134. 

Csato, L. (2024b). On head-to-head results as tie-breaker and consequent opportunities for collusion. IMA Journal of Management Mathematics, in press. DOI: 10.1093/imaman/dpae016. 

Csato, L., Molontay, R., and Pinter, J. (2024). Tournament schedules and incentives in a double round-robin tournament with four teams. International Transactions in Operational Research, 31(3):1486–1514. 

Gyimesi, A. (2024). Competitive balance in the post-2024 Champions League and the European Super League: A simulation study. Journal of Sports Economics, 25(6):707734. 

Maher, M. J. (1982). Modelling association football scores. Statistica Neerlandica, 36(3):109118. 

Stronka, W. (2024). Demonstration of the collusion risk mitigation effect of random tie-breaking and dynamic scheduling. Sports Economics Review, 5:100025. UEFA (2024). 

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