Matchday 6 Insights & Likelihoods

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), 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).

Results

UEFA Champions League

How did the results of the sixth 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 5.

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

The next figure shows how many points are needed (in general) to survive the league stage (left) or reach top 8 (right). The percentages correspond with how often in our simulations the corresponding number of points was enough.

When we look at the number of points needed to survive the league stage, this in fact differs per team (mostly due to the current and expected goal difference). The colors in the plot below show, for each number of points the team can still obtain, its corresponding probability of progressing. Note that Liverpool and Barcelona are missing, as they are mathematically certain of reaching top 24. Also RB Leipzig, S. Bratislava, and Young Boys are missing: they have been eliminated. Chances for Bologna are extremely slim, even if they will their remaining games.

Comments

Guaranteed Top 24 Teams

Two teams (Liverpool and Barcelona) have secured a spot in the Top 24, with 12 clubs virtually safe from elimination.

Already Eliminated Teams

Leipzig, Young Boys, and S. Bratislava are out, and 5 more teams have minimal survival chances.

Liverpool’s Strong Position

Liverpool is almost certain for the Top 8, while Shakhtar and teams ranked lower cannot achieve this.

Man City and Real Madrid’s Struggles

The past winners face slim chances for the Top 8 and a 70% probability for the Round of 16.

Biggest Winners and Losers

Aston Villa, Brest, and Club Brugge gain the most, while Sporting CP, PSV, and Dortmund lose ground in qualification probabilities.

Drastic Risk Reduction

Juventus, Real Madrid, and Feyenoord have sharply reduced their elimination risks.

Rising Elimination Risks

GNK Dinamo and PSV see significant increases in their chances of elimination.

Top 8 Probability Shifts

Leverkusen emerges as the biggest winner, while Atalanta sees the steepest drop.

Pot 1 Disparities

Leipzig is eliminated; Paris has a moderate survival chance, while seven teams exceed 90%.

Unexpected Pot 3 and 4 Performers

Aston Villa, Lille, Brest, and Sporting CP now have a greater than 52% chance for the Round of 16.

French Teams’ Dominance

Brest and Lille’s outstanding performance eliminates their risks of elimination.

Weakest Teams’ Fates

Seven of the eight weakest teams have negligible chances for progression or survival.

Point Threshold Challenges

GNK Dinamo, Shakhtar, and Sparta Praha face tough odds with 10 points, while Benfica thrives with 90% progression probability at this mark.

UEFA Europa League

How did the results of the sixth 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 5.

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

The next figure shows how many points are needed for team to survive the league stage (left) or reach top 8 (right). The percentages correspond with how often in our simulations the corresponding number of points was enough.

When we look at the number of points needed to survive the league stage, this in fact differs per team (mostly due to the current and expected goal difference). The colors in the plot below show, for each number of points the team can still obtain, its corresponding probability of progressing. All teams ranked 1 (Lazio) to 7 (Man Utd) are missing here, as they are mathematically certain to survive the league stage. Dynamo Kyiv is already eliminated.

Comments

Guaranteed Top 24 Teams

Seven teams (Lazio, Athletic Club, Anderlecht, Lyon, Frankfurt, Galatasaray, and Man Utd) have secured a spot in the Top 24, with three more clubs virtually safe from elimination.

Already Eliminated Teams

Dynamo Kyiv is eliminated, and RFS has less than a 1% chance to survive, making the Europa League more competitive than the Champions League, where nine teams face similar odds before the last two rounds.

Strongest Teams’ Success

Lazio and Athletic Club are almost certain to reach the Top 8 and the Round of 16.

Tottenham’s Resilience

Despite earning only two points in the last three rounds, Tottenham still has a 65% probability of finishing in the Top 8.

Biggest Winners and Losers

Union SG, Anderlecht, and Roma have improved the most, while Slavia Praha, Fenerbahce, and Ferencvaros have seen the largest drops in Round of 16 qualification probabilities.

Reduced Elimination Risks

Union SG, PAOK, and Elfsborg have lowered their elimination risks by over 20 percentage points.

Rising Elimination Risks

The chances of elimination have increased by more than 15 percentage points for Slavia Praha, Hoffenheim, Braga, and Nice.

Equal Chances for Hoffenheim and Twente

Despite Hoffenheim’s six points compared to Twente’s four, both have nearly equal chances due to Twente’s easier schedule.

FCSB’s Impressive Recovery

The Romanian champion, FCSB, is almost certain to finish in the Top 24, despite a 76% chance of elimination before the first matchday.

Pot 1 Challenges for Slavia Praha

Slavia Praha has less than a 25% chance of qualifying for the Round of 16, hindered by its current total of just four points.

Underdogs’ Surprising Potential

Unlike the Champions League, two of the weakest teams, FCSB and Ferencvaros, have a reasonable chance of surviving the Europa League phase.

References

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

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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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