CL & EL 2025 – Matchday 07: Final-Round Odds

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).

UEFA Champions League

How did the results of the seventh matchday influence the chances of qualification for each team? The figure below shows to what extent the seventh matchday increased or decreased the chances of each team for qualifying to top 8, compared to after matchday 6.

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

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The next figure shows how many points are needed to survive the league stage, for each of the teams that are still in the running. The colors in the plot below show, for each number of points the team can still obtain, its corresponding probability of progressing. 

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Comments

• Two teams (Liverpool and Barcelona) have a guaranteed place in the Top 8 and the Round of 16, while two other clubs (Arsenal and Inter Milan) can achieve this with a probability above 98%; titleholder Real Madrid has a marginal chance to reach the Top 8. Compared to after matchday 6, the biggest winner is Atleti (from 36.29% to 80.07%) and the biggest loser is Bayern München (from 63.46% to 6.95%).

• Compared to the previous forecast before the seventh matchday, the biggest winners are Paris, Atleti, and Feyenoord, while the biggest losers are B. Dortmund, Man City, and Bayern München in terms of the probability of qualification for the Round of 16 (two of the biggest winners have won against two of the biggest losers)

Lille has found its prospects of reaching the top eight improving, even after suffering a defeat against Liverpool. This surprising outcome is due to a stroke of luck: all of Lille‘s closest competitors — B. Dortmund, Brest, Bayern München, Aston Villa, and Leverkusen — also suffered defeats in their respective matches. 

• At this point, 9 teams are eliminated, and 18 teams made sure to survive the league stage. The remaining 6 spots are contested by 9 teams: PSV, Club Brugge, Benfica, Paris, Sporting CP, Stuttgart, Man City and GNK Dinamo, and Shakhtar. Although theoretically possible, in none of our simulations Feyenoord and PSV were eliminated, while Shakhtar has less than 0.1% chance to survive the league stage.

Feyenoord (from 5.8% to 0%), PSV (from 19.34% to 0%), and Paris (from 36.6% to 14.51%) have managed to drastically reduce the threat of being eliminated in the league phase. On the other hand, the chance of elimination has increased by more than 15 percentage points for Benfica and Man City 

• While Benfica, Paris, Sporting CP, and Man City are certain to survive the league stage if they obtain 11 points (or more), and Stuttgart is almost sure (unless – amongst other things – GNK Dinamo would defeat Milan with 7 goals difference or more), this is not the case for Club Brugge and GNK Dinamo, who still risk elimination with 11 points. On the other hand, Paris, Benfica and Sporting CP still have more than 50% chance to proceed with only 10 points.

Brest, Celtic, and Lille have shown a remarkable performance since the probability of their elimination has decreased from more than 40% (before the first matchday) to zero after matchday 7. On the other hand, Bologna is already eliminated even though this was considered highly unlikely (6% chance) before the first matchday.

A note on collusion

Simulation models, including our own, generally do not account for the specific results teams need to qualify, nor the varying motivations of their opponents. This oversight can lead to skewed projections, particularly in scenarios where certain teams have little or nothing to gain from a match.

Take, for instance, Benfica and Sporting CP. Both Portuguese teams require just a single point to secure qualification, while a win will not improve their chances of reaching the top eight. Their respective opponents, Juventus and Bologna, enter the final round with no tangible stakes. While Juventus theoretically could make the top eight with a win and a string of favorable results elsewhere, this scenario is highly improbable. Under such conditions, it is arguably easier for Benfica and Sporting CP to secure a draw in these matches than if they had faced their opponents earlier in the tournament, when stakes might have been higher. This situation suggests that Club Brugge’s chances of surviving the league stage may be overestimated in conventional models.

The situation becomes even murkier with the Stuttgart–Paris fixture. In this match, Paris secures qualification with a draw. Stuttgart, on the other hand, also qualifies with a draw unless a series of extremely unlikely events unfold: unfavorable results in Benfica and Sporting CP’s matches, an unfavorable outcome in Manchester City vs. Club Brugge, and GNK Dinamo beating Milan by at least seven goals. Given these conditions, Stuttgart and Paris have a strong incentive to settle for a draw, ensuring mutual progression to the next round with minimal effort.

To better understand this dynamic, we conducted a new round of simulations where the Stuttgart–Paris match was fixed as a draw. The results reveal a significant negative impact on the qualification chances of other teams, particularly Sporting CP, Benfica, and most notably Club Brugge. This highlights how final-round motivations can disrupt the competitive balance and lead to scenarios where collaboration—or even perceived collusion—can play a decisive role in determining outcomes.

As the tournament unfolds, such dynamics remind us that not all results are created equal, and the motivations of teams in the final rounds may be as important as their skills on the field.

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The impact of collusion in the Stuttgart-Paris match is also obvious from the probability that teams survive the league stage for a given number of points.

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More information on the methodology behind these results can be found here.

UEFA Europa League

How did the results of the seventh matchday influence the chances of qualification for each team? The figure below shows to what extent the seventh matchday increased or decreased the chances of each team for qualifying to top 8, compared to after matchday 6.

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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.

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The next figure shows how many points are needed to survive the league stage, for each of the teams that are still in the running. The colors in the plot below show, for each number of points the team can still obtain, its corresponding probability of progressing. 

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Comments

• 15 teams have a guaranteed place in the Top 24, while further four clubs — those with 10 points except for Elfsborg — face elimination with less than 3% chance 

• The strongest club, Lazio, will play in the Round of 16. No other team is certain of top 8, one matchday before the end.

• Seven teams are already eliminated, while two clubs (Hoffenheim and M. Tel-Aviv) have less than 3% chance to avoid this fate.

• Compared to the previous forecast before the seventh matchday, the biggest winners are Olympiacos, FCSB, and PAOK, while the biggest losers are Porto, Slavia Praha, and Slavia Praha in terms of the probability of qualification for the Round of 16. Slavia Praha – a Pot 1 team – was among the biggest losers in three consecutive matchdays, and is now eliminated.

Elfsborg, PAOK, Midtjylland, and Twente have managed to reduce the threat of elimination in the league phase by more than 30 percentage points. On the other hand, the chance of elimination has increased by more than 30 percentage points for Slavia Praha, Porto, and Hoffenheim

• The current league phase table is misleading: Twente with 7 points has a much higher probability (62%) to finish in the Top 24 than Besiktas with 9 points (35%) as they play against each other in the Netherlands

• The Romanian champion, FCSB has reached the Top 24 despite that its chance of elimination was 76% before the first matchday.

• In stark contrast to the UEFA Champions League, three of the weakest eight teams, Elfsborg, FCSB and Ferencvaros, have a reasonable chance (exceeding 70%) to survive the league phase

• The already mentioned Elfsborg, the fifth weakest team, can reach the Top 24 with a probability of 85% even though it had the strongest opponents as calculated before the first matchday

• The upcoming match between Real Sociedad and PAOK presents a peculiar dynamic. Both teams are guaranteed progression to the next stage if the game ends in a draw. A victory offers no additional advantage for either side. With such circumstances, questions about the possibility of a prearranged surface. On the other hand, even with a loss, it is extremely unlikely that any of these teams would be eliminated.

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).

In order to determine which teams are certain to reach top 8 or top 24, or to determine which teams are eliminated with certainty from top 8 or top 24, we use integer programming. We use the same technique to determine the consequences of particular match outcomes. Note that this method can present us with a proof that certain events are guaranteed or impossible. The simulation results, on the other hand, only show what is (extremely) likely or unlikely. This, however, provides no mathematical proof or certainty. 

References

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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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