Predicting Qualification Thresholds in UEFA's incomplete round-robin tournaments

TL;DR

This paper models and predicts qualification thresholds in UEFA's new incomplete round-robin tournament format using a bivariate Dixon--Coles model and Elo ratings, providing strategic insights.

Contribution

It introduces a statistical approach to estimate qualification thresholds accounting for reduced draws, improving decision-making in UEFA's new tournament structure.

Findings

The model accurately estimates qualification thresholds for UEFA's new format.

Reduced incentives lead to fewer draws, affecting match outcome distributions.

Simulation results support strategic planning for clubs and managers.

Abstract

For the 2024/25 season, the Union of European Football Associations (UEFA) introduced an incomplete round-robin format in the Champions League and Europa League, replacing the traditional group stage with a single league table of all 36 teams. Under this structure, the top eight teams advance directly to the round of 16, while teams ranked 9th-24th qualify for a play-off round. Simulation-based analyses, such as those by commercial data analyst Opta, provide indicative point thresholds for qualification but reveal deviations when compared with actual outcomes in the first season. To overcome these discrepancies, we employ a bivariate Dixon--Coles model that accounts for the lower frequency of draws observed in the 2024/25 Champions League season, potentially driven by reduced incentives for teams to play for a draw. We proxy team strengths by Elo ratings and fit the model to different settings. This enables us to simulate match outcomes and to estimate qualification thresholds for both direct advancement and play-off participation. Our results provide scientific guidance for clubs and managers, supporting strategic decision-making under uncertainty regarding their progression prospects in the new UEFA club competition formats.

Tables

Table 1. Table 1: Final standings after the UCL league phase 2024/25.

							Goals	Goals
	Place	Team	Matches	Wins	Draws	Defeats	scored	received	Difference	Points
Round of 16	1	Liverpool FC	8	7	0	1	17	5	12	21
	2	FC Barcelona	8	6	1	1	28	13	15	19
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	7	LOSC Lille	8	5	1	2	17	10	7	16
	8	Aston Villa	8	5	1	2	13	6	7	16
Play-offs	9	Atalanta BC	8	4	3	1	20	6	14	15
	10	B. Dortmund	8	5	0	3	22	12	10	15
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	23	Sporting CP	8	3	2	3	13	12	1	11
	24	Club Brugge KV	8	3	2	3	7	11	-4	11
Elimination	25	GNK Dinamo Zagreb	8	3	2	3	12	19	-7	11
	26	Stuttgart	8	3	1	4	13	17	-4	10
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	35	S. Bratislava	8	0	0	8	7	27	-20	0
	36	BSB Young Boys	8	0	0	8	3	24	-21	0

Table 2. Table 2: Market values (in Mio) and Elo ratings for the teams participating in the 2024/25 UCL and UEL: summary statistics and allocation to seeding pots.

		Champions League					Europa League
Variable	Statistic	Pot 1	Pot 2	Pot 3	Pot 4	All	Pot 1	Pot 2	Pot 3	Pot 4	All
	Min	436	165	66	33	33	80	26	22	11	11
	Max	1310	1130	488	628	1310	836	384	266	367	836
Market values	Mean	887	514	213	236	463	350	151	78	125	176
(in Mio)	Median	923	516	149	181	381	304	118	54	104	104
	SD	306	288	148	194	361	254	112	73	114	181
	Min	1847	1601	1541	1404	1404	1618	1486	1071	1240	1071
	Max	2051	1947	1806	1808	2051	1812	1767	1726	1764	1812
Elo ratings	Mean	1921	1816	1673	1702	1778	1731	1644	1543	1562	1620
	Median	1900	1829	1651	1761	1794	1779	1640	1616	1626	1640
	SD	68	107	108	131	143	75	86	191	166	153

Table 3. Table 3: Market values (in Mio) and Elo ratings for the teams participating in the 2025/26 UCL and UEL: summary statistics and allocation to seeding pots.

		Champions League					Europa League
Variable	Statistic	Pot 1	Pot 2	Pot 3	Pot 4	All	Pot 1	Pot 2	Pot 3	Pot 4	All
	Min	402	202	55	13	13	59	32	50	25	25
	Max	1370	1320	847	665	1370	549	268	446	333	549
Market values	Mean	1038	493	307	224	516	248	115	138	126	157
(in Mio)	Median	1130	409	220	105	406	245	84	77	95	106
	SD	293	322	236	216	417	145	72	122	104	126
	Min	1818	1744	1625	1284	1284	1520	1497	1492	1475	1475
	Max	1993	1993	1839	1869	1993	1873	1745	1803	1751	1873
Elo ratings	Mean	1931	1824	1734	1639	1782	1706	1612	1597	1603	1630
	Median	1936	1806	1757	1700	1793	1742	1620	1561	1595	1611
	SD	48	71	70	172	149	111	77	108	94	108

Table 4. Table 4: Summary statistics on the distribution of wins, average number of goals, and the percentage of “lopsided matches” with a difference of at least four goals for the UCL and UEL in the 2024/25 and 2025/26 seasons.

	Outcome			Average goals			Lopsided
	Home win	Draw	Away win	Home	Away	Total	matches
UCL 2024/25	53.47%	12.50%	34.03%	1.88	1.39	3.26	15.97%
UCL 2025/26	49.31%	17.36%	33.33%	1.93	1.45	3.38	13.19%
UEL 2024/25	48.61%	24.31%	27.08%	1.64	1.19	2.83	3.47%
UEL 2025/26	52.78%	17.36%	29.86%	1.52	1.16	2.68	4.17%

Table 5. Table 5: Summary statistics on the distribution of wins, average number of goals, and the percentage of “lopsided matches” with a difference of at least four goals for the UCL seasons 2020/21 – 2025/26.

	Outcome			Average goals			Lopsided
League	Home win	Draw	Away win	Home	Away	Total	matches
UCL 2020/21	41.67%	20.83%	37.50%	1.52	1.49	3.01	12.50%
UCL 2021/22	48.96%	18.75%	32.29%	1.71	1.39	3.09	13.54%
UCL 2022/23	47.92%	19.79%	32.29%	1.68	1.49	3.17	16.67%
UCL 2023/24	46.88%	20.83%	32.29%	1.76	1.32	3.08	4.17%
UCL 2020/21 – 2023/24	46.35%	20.05%	33.59%	1.67	1.42	3.09	11.72%
UCL 2024/25	53.47%	12.50%	34.03%	1.88	1.39	3.26	15.97%
UCL 2025/26	49.31%	17.36%	33.33%	1.93	1.45	3.38	13.19%

Table 6. Table 6: Summary statistics on the distribution of wins, average number of goals, and the percentage of “lopsided matches” with a difference of at least four goals for the top four European national leagues in the 2023/24 season.

	Outcome			Average goals			Lopsided
League	Home win	Draw	Away win	Home	Away	Total	matches
Premier League 23/24	46.05%	21.58%	32.37%	1.80	1.48	3.28	8.68%
Bundesliga 23/24	43.79%	26.47%	29.74%	1.81	1.41	3.22	8.82%
Serie A 23/24	41.84%	29.47%	28.68%	1.43	1.18	2.61	4.47%
La Liga 23/24	43.95%	28.16%	27.89%	1.48	1.16	2.64	4.47%
All	43.91%	26.42%	29.67%	1.62	1.30	2.92	6.57%

Table 7. Table 7: Estimated coefficients for the independent bivariate Poisson model based on national league data.

	Dependent variable:
	Goals
EloDiff	0.207∗∗∗
	(0.011)
Home	0.220∗∗∗
	(0.031)
Constant	0.225∗∗∗
	(0.023)
Note:	∗p0.1; ∗∗p0.05; ∗∗∗p0.01

Table 8. Table 8: Estimated coefficients for the Dixon–Coles (D&C) models fitted to the 2024/25 UCL and UEL season.

	Dependent variable: Goals
	UCL	UEL
EloDiff	0.286∗∗∗	0.095∗∗∗
	(0.032)	(0.035)
Home	0.301∗∗∗	0.314∗∗∗
	(0.094)	(0.101)
$\rho$	0.105	0.030
	(0.095)	(0.109)
Constant	0.242∗∗∗	0.170∗∗
	(0.073)	(0.077)
Note:	∗p0.1; ∗∗p0.05; ∗∗∗p0.01

Table 9. Table 9: Estimated coefficients for the Dixon–Coles (D&C) models fitted to the 2024/25 and 2025/26 UCL and UEL seasons.

	Dependent variable: Goals
	UCL	UEL
EloDiff	0.258∗∗∗	0.129∗∗∗
	(0.022)	(0.024)
Home	0.289∗∗∗	0.294∗∗∗
	(0.065)	(0.072)
$\rho$	0.053	0.055
	(0.069)	(0.078)
Constant	0.285∗∗∗	0.146∗∗∗
	(0.051)	(0.055)
Note:	∗p0.1; ∗∗p0.05; ∗∗∗p0.01

Table 10. Table 10: Average number of draws observed in the simulation runs for the UCL (first column) and UEL (second column) depending on the parameter value ρ \rho for randomly generated sets of participating clubs and match schedules.

Parameter value	$\rho =0$	$\rho =0.02$	$\rho =0.04$	$\rho =0.06$	$\rho =0.08$	$\rho =0.10$	$\rho =0.12$	$\rho =0.14$	$\rho =0.16$	$\rho =0.18$	$\rho =0.2$
UCL	28.32	27.79	27.29	26.78	26.26	25.74	25.24	24.74	24.22	23.70	23.18
UEL	34.83	34.20	33.53	32.86	32.20	31.53	30.89	30.20	29.52	28.87	28.20

Table 11. Table A1: Final standings after the UCL league phase 2025/26.

							Goals	Goals
	Place	Team	Matches	Wins	Draws	Defeats	scored	received	Difference	Points
Round of 16	1	Arsenal FC	8	8	0	0	23	4	19	24
	2	Bayern München	8	7	0	1	22	8	14	21
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	7	Sporting CP	8	5	1	2	17	11	6	16
	8	Manchester City	8	5	1	2	15	9	6	16
Play-offs	9	Real Madrid	8	5	0	3	21	12	9	15
	10	Inter Milan	8	5	0	3	15	7	8	15
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	23	FK Bodø/Glimt	8	2	3	3	14	15	-1	9
	24	SL Benfica	8	3	0	5	10	12	-2	9
Elimination	25	Olympique Marseille	8	3	0	5	11	14	-3	9
	26	Pafos FC	8	2	3	3	8	11	-3	9
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	35	FC Villarreal	8	0	1	7	5	18	-13	1
	36	Qairat Almaty	8	0	1	7	7	22	-15	1

Table 12. Table B1: Final standings after the UEL league phase 2024/25.

							Goals	Goals
	Place	Team	Matches	Wins	Draws	Defeats	scored	received	Difference	Points
Round of 16	1	Lazio	8	6	1	1	17	5	12	19
	2	Athletic Club	8	6	1	1	15	7	8	19
$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	7	Olympiacos	8	4	3	1	9	3	6	15
	8	Rangers	8	4	2	2	16	10	6	14
Play-offs	9	Bodö/Glimt	8	4	2	2	14	11	14	14
	10	Anderlecht	8	4	2	2	14	12	10	14
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	23	Twente	8	2	4	2	8	9	-1	10
	24	Fenerbahce	8	2	4	2	9	11	-2	10
Elimination	25	Braga	8	3	1	4	9	12	-3	10
	26	Elfsborg	8	3	1	4	9	14	-5	10
	$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	35	Nice	8	0	3	5	7	16	-9	3
	36	Qarabag	8	1	0	7	6	20	-14	3

Table 13. Table B2: Final standings after the UEL league phase 2025/26.

							Goals	Goals
	Place	Team	Matches	Wins	Draws	Defeats	scored	received	Difference	Points
Round of 16	1	Olympique Lyon	8	7	0	1	18	5	13	21
	2	Aston Villa	8	7	0	1	14	6	8	21
$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	7	SC Freiburg	8	5	2	1	10	4	6	17
	8	AS Rom	8	5	1	2	13	6	7	16
Play-offs	9	KRC Genk	8	5	1	2	11	7	4	16
	10	FC Bologna	8	4	3	1	14	7	7	15
$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	23	Dinamo Zagreb	8	3	1	4	12	16	-4	10
	24	Brann Bergen	8	2	3	3	9	11	-2	9
Elimination	25	BSC Young Boys	8	3	0	5	10	16	-6	9
	26	Sturm Graz	8	2	1	5	5	11	-6	7
$\cdots$	$\cdots$	$\cdots$		$\cdots$			$\cdots$		$\cdots$
	35	Malmö FF	8	0	1	7	4	15	-11	1
	36	Maccabi Tel Aviv	8	0	1	7	2	22	-20	1

Table 14. Table C1: Elo ratings as of 01.08.2024 and 01.08.2025 for clubs participating in the 2024/25 and 2025/26 UCL season, respectively.

Club	Elo rating 01.08.2024	Elo rating 01.08.2025
AC Milan	1839	-
AC Sparta Prague	1688	-
Ajax	-	1667
Arsenal	1947	1993
Aston Villa	1770	-
Atalanta	1884	1842
Atletico	1829	1855
Barcelona	1882	1945
Bayern	1900	1919
Benfica	1768	1795
Bilbao	-	1789
Bologna FC 1909	1795	-
Bodoe Glimt	-	1625
BSB Young Boys	1548	-
Brugge	1728	1744
Celtic FC	1639	-
Chelsea	-	1903
Crvena Zvezda (Red Star Belgrade)	1541	-
Dortmund	1869	1818
FC Kobenhavn	-	1634
Feyenoord Rotterdam	1762	-
Frankfurt	-	1746
Galatasaray	-	1700
Girona FC	1794	-
GNK Dinamo Zagreb	1563	-
Inter	1965	1934
Juventus	1828	1806
Kairat	-	1284
Karabakh Agdam	-	1517
Leverkusen	1925	1849
LOSC Lille	1751	-
Liverpool	1901	1993
Man City	2051	1960
Marseille	-	1757
Monaco	1761	1762
Napoli	-	1839
Newcastle	-	1869
Olympiakos	-	1664
Paris SG	1877	1975
Paphos	-	1479
PSV	1793	1800
RB Leipzig	1847	-
Real Madrid	1997	1936
Red Bull Salzburg	1651	-
S. Bratislava	1404	-
Shakhtar Donetsk	1601	-
SK Sturm Graz	1592	-
Slavia Praha	-	1689
Sporting	1806	1792
Stade Brestois 29	1704	-
St Gillis	-	1720
Tottenham	-	1774
VfB Stuttgart	1808	-
Villarreal	-	1786

Table 15. Table D1: Out-of-sample predictive performance of different models for the UCL and UEL, evaluated by the Brier Score, Ranked Probability Score (RPS) and Logarithmic Score (Log Loss).

	UCL			UEL
Metric	Ind. Pois.	D&C	Biv. Pois.	Ind. Pois.	D&C	Biv. Pois.
Brier Score	0.5305	0.5299	0.5340	0.5708	0.5708	0.5762
RPS	0.3899	0.3897	0.3917	0.4247	0.4247	0.4249
Log Loss	0.9036	0.9012	0.9128	0.9639	0.9638	0.9737

Table 16. Table D2: Estimated coefficients for the Dixon–Coles (D&C) models fitted to the 2024/25 UCL and UEL season with market values instead of Elo ratings.

	Dependent variable: Goals
	UCL	UEL
MVDiff	0.264∗∗∗	0.135∗∗∗
	(0.033)	(0.033)
Home	0.295∗∗∗	0.315∗∗∗
	(0.094)	(0.101)
$\rho$	0.110	0.008
	(0.093)	(0.113)
Constant	0.257∗∗∗	0.158∗∗∗
	(0.073)	(0.077)
Note:	∗p0.1; ∗∗p0.05; ∗∗∗p0.01

Equations

$$P(X=x,Y=y)=\frac{{\lambda }^x{e}^{-\lambda }}{x!}\cdot \frac{{\mu }^y{e}^{-\mu }}{y!},$$

$$P(X=x,Y=y)={\tau }_{\rho }(x,y)\cdot \frac{{\lambda }^x{e}^{-\lambda }}{x!}\cdot \frac{{\mu }^y{e}^{-\mu }}{y!},$$

$${\tau }_{\rho }(x,y)=\{\begin{array}{ll}1-\lambda \mu \rho & \text{if }x=y=0,\\ 1+\lambda \rho & \text{if }x=0,y=1,\\ 1+\mu \rho & \text{if }x=1,y=0,\\ 1-\rho & \text{if }x=y=1,\\ 1& \text{otherwise},\end{array}$$

$$\lambda$$

$$\mu$$

$$\lambda$$

$$\mu$$

Full text

Keywords: Bivariate Poisson, Dixon & Coles model, Elo rating, Incomplete round-robin tournament, Sports forecasting

1 Introduction

The UEFA Champions League (UCL) is the most prestigious competition in European club football, drawing global audiences, generating substantial commercial investment, and showcasing the highest level of competitive play. Structural changes to its format, therefore, carry far-reaching implications — not only for sporting fairness and competitive balance but also for the strategic planning of participating clubs, broadcasters, and sponsors. The 2024/25 season marks one of the most significant reforms in the tournament’s history: UEFA replaced its long-standing group stage format with the so-called incomplete round-robin format. Now, 36 clubs compete in a single league phase, fundamentally reshaping the competition dynamics. Notably, the incomplete round-robin format has also been introduced in the UEFA Europa League (UEL) and UEFA Conference League, broadening its overall impact. While this paper focuses on the UCL and UEL, the UEFA Conference League is not examined in detail due to its slightly different structure, with only six league-phase matches instead of eight per club.

Under the new system, all clubs within each competition are ranked in one table. The top eight teams qualify directly for the round of 16, while those ranked 9th to 24th enter play-offs for the remaining spots. Teams finishing 25th or lower are eliminated. Progression, therefore, requires either a top-eight finish or success in the play-offs, increasing the competitive premium of finishing near the top compared with the previous format. At the same time, the new structure creates additional opportunities for lower-ranked teams, as even a 24th-place finish results in knockout stage participation. According to Gyimesi (2024), the format alteration may enhance competitive balance and yield fewer stakeless matches.

This change in tournament design potentially also strengthens the incentive to pursue victories in single matches. Under the old group stage format, a draw meant that one of three direct opponents also collected only one point. In contrast, in the league-phase system, teams compete against 35 others in the same table, which diminishes the relative value of a draw. Similar to the introduction of awarding three points for a win instead of two (Dilger and Geyer, 2009), the format change intends to enhance competitiveness and spectator appeal. While previous literature reports mixed evidence on the effectiveness of the three-point rule (Guedes and Machado, 2002), early observations from the 2024/25 UCL season suggest stronger incentives for teams to seek a win, as we observe a considerably smaller number of matches concluding with a draw (see the descriptive statistics in Section 3).

Given the strategic implications of the new format and its altered ranking mechanism, understanding the point thresholds required for direct qualification or play-off entry in the incomplete round-robin format is of crucial importance. In particular, the frequency of draws plays a decisive role in shaping these thresholds, as highlighted in prior studies on competitive balance in sports (Fry et al., 2021; Ficcadenti et al., 2023). Moreover, since the final two league-phase matches are scheduled after the winter break, clubs must make transfer-market decisions under uncertainty regarding their progression prospects. This further underscores the need for reliable estimates of qualification thresholds in the UCL.

While the simulation-based prediction of qualification probabilities is well established in the literature (see, e.g. Groll et al., 2015, for the FIFA World Cup group stage and Karlis and Ntzoufras, 2011, for the UCL under the previous format), no peer-reviewed research has yet examined this issue in the context of UEFA’s new competition structures. To date, insights have been provided primarily by commercial analytics firms. For instance, Opta employed its proprietary simulation framework — referred to as its “supercomputer” — to estimate the points required for progression (Opta Analyst, 2024). Their forecast of the 2024/25 Champions League season indicated that “15 points is likely to be enough to progress to the last 16” and that “10 points will as good as guarantee a place in the top 24 places”. More specifically, 15 points were associated with a 73% probability of securing a top-eight finish. In comparison, 10 points ensured qualification for the play-off round with a 99% likelihood (see Figure 1).

When comparing these pre-season predictions with the actual outcomes of the first seasons (see Table 1 for an extract of the final UCL standings following the 2024/25 league phase; final standings for the 2025/26 UCL league phase (Table A1) and both UEL seasons (Tables B1 and B2) are provided in the Appendix), several unexpected results are revealed. Despite the forecasted 73% probability, teams in the UCL that collected 15 points in the 2024/25 season did not qualify directly for the round of 16 but were instead required to compete in the play-off phase (in the UEL, one team with 14 points advanced directly to the round of 16). Even more striking were the cases of VfB Stuttgart and GNK Dinamo, ranked 25th and 26th. Pre-season predictions had suggested a 99% probability (or higher) that the 10 and 11 points they achieved, respectively, would suffice to remain in the tournament. Yet, both were eliminated (in the UEL, two out of five teams with 10 points were eliminated). Reflecting on these discrepancies between forecasted and actual qualification thresholds, in a post-match interview with sports broadcaster DAZN, VfB Stuttgart’s manager Sebastian Hoeneß critically remarked that ”[…] the AI is probably not as great as everyone says“ when asked about Opta’s pre-competition forecasts.

These discrepancies in the first UCL season under the new format highlight the necessity for a rigorous scientific framework for estimating qualification thresholds. This paper precisely simulates league outcomes while accounting for changes in incentive structures to determine qualification thresholds, thereby offering statistically grounded guidance to teams in the UCL and UEL. We apply the bivariate Dixon–Coles (D&C) model introduced by Dixon and Coles (1997), which allows for capturing shifts in the probability distribution of scorelines and accommodates deviations in draw frequencies from their expected levels (Michels et al., 2025). Adjusting for such deviations is crucial, as the incidence of draws can materially affect predicted qualification thresholds. To account for heterogeneous team strengths, we proxy unobserved abilities using Elo ratings (see, e.g. Bosker and Gürtler, 2024; Hvattum and Arntzen, 2010; Yildirim and Bilman, 2025). The predictive validity of Elo ratings in the UCL has been demonstrated by Csató (2024). We show that our model can better predict unseen UCL and UEL matches than competitive models, forecasting the reduced number of draws more accurately and, as a consequence, providing reasonable qualification thresholds.

The remainder of the paper is structured as follows. Section 2 describes the UEFA club competitions and presents related literature. Section 3 introduces the data, Section 4 the modelling approach employed to simulate the new formats, while Section 5 presents the predicted qualification thresholds under different scenarios. Finally, Section 6 discusses the findings and their practical implications.

2 UEFA club competitions and related literature

Sports forecasting has attracted considerable attention in the academic literature (see the overview by Wunderlich and Memmert, 2021). Its primary purpose is to enhance the enjoyment of fans by providing accurate predictions on match outcomes, while also serving as a basis for sports managers to evaluate performance or traders’ decisions in the betting market (Corona et al., 2019). For the UCL in particular, the literature has addressed a range of topics, including tournament designs, the effects of qualification systems, seeding regimes, and competitive balance.

UEFA’s premier club competition, the European Champions Clubs’ Cup (European Cup), was inaugurated in 1955. Since then, its structure has been repeatedly adjusted to the evolving demands of national leagues, broadcasters, and sponsors, often to preserve a high degree of outcome uncertainty (Scarf et al., 2009). In 1992/93, the newly established UCL replaced the European Cup as UEFA’s flagship tournament. The overall tournament format remained unchanged for more than two decades preceding the 2024/25 season: the group stage consisted of eight groups of four teams, each playing a double round-robin (Rasmussen and Trick, 2008), with the top two advancing to the round of 16. However, there were different minor changes in the design that were addressed in the literature.

In 2015, the UCL implemented a change in the seeding system. While previously, the allocation to seeding pots was determined by the club coefficient, from 2015 onwards, pot 1 covered the winners of the previous UCL seasons, along with the winners of the top seven domestic leagues (Dagaev and Rudyak, 2019). Corona et al. (2019) show that this change increased uncertainty over progression from the group stage. From the 2018/19 season onwards, there was also a change in the qualifying system for the UCL. Specifically, the top leagues received an additional fixed place in the UCL, while the number of places awarded to clubs participating in the qualification reduced from ten to six. Csató (2022) demonstrates that this change resulted in a considerable decrease in the probabilities of participation in the UCL for the winners of domestic leagues in low-ranked associations, with expected prize money decreasing by more than one million Euros for some clubs.

Studies by Triguero-Ruiz and Avila-Cano (2023) and Ramchandani et al. (2023) report a decline in the ex-ante competitive balance of the UCL group stage in recent decades. By contrast, Csató and Petróczy (2025) argue that these findings may be sensitive to the chosen measurement approach and propose alternative metrics that challenge the earlier conclusions. Still, enhancing competitive balance was a central motivation for UEFA when introducing the new tournament format with a single league table. While the previous group stage format was structurally simple, it frequently produced non-competitive fixtures, including so-called dead rubbers, in the final rounds, as some teams had already secured qualification (Csató, 2024).

Unsurprisingly, the literature has devoted considerable attention to the fundamental change in the format introduced in the 2024/25 season. Gyimesi (2024) shows an increase in competitive balance for the UCL, resulting in a higher degree of match uncertainty and fewer stakeless fixtures. Similarly, Devriesere et al. (2025b) finds that the incomplete round-robin format generates more competitive matches than the former group stage format, while Guyon et al. (2025) examine the implications of the scheduling procedure using simulation data. Moreover, Csató et al. (2025) show that the qualification prospects in both formats depend on the draw procedure as well as the degree of competitive balance among participants. Beyond these findings, Csató (2024) demonstrates that replacing the current seeding regime, based on the UEFA club coefficient, with a variant of the Elo method further reduces the risk of unbalanced schedules. Nevertheless, Csató et al. (2026) argue that the newly introduced league phase format does not necessarily produce the most accurate ranking of clubs. A broader overview of tournament designs is provided by Devriesere et al. (2025a).

3 Data

In this section, we provide descriptive statistics for the teams participating in the 2024/25 and 2025/26 UCL and UEL seasons, covering their strength via market values and Elo ratings. We proceed with summary statistics on match outcomes, comparing them with data from the last four UCL seasons under the old format, as well as with figures from the 2023/24 season of the four top European domestic leagues.

3.1 Descriptive statistics for teams in the 2024/25 and 2025/26 UCL & UEL

For the draw procedure, clubs are allocated into four seeding pots of nine teams each, determined by their UEFA club coefficient (see Guyon et al., 2025 for an analysis of draw procedures in the incomplete round-robin format of the UCL, and Csató et al., 2025 for a discussion of its implications). Each team plays against eight different opponents, two from each pot, with one match at home and one away. While the first pot in both UCL seasons consists exclusively of clubs from the top five national leagues, the remaining pots are more heterogeneous in composition. A similar structure applies to the UEL, where 36 clubs from 22 (2024/25) and 23 (2025/26) associations participate, respectively.

To capture team strengths which are relevant in predicting match outcomes, Tables 2 and 3 present summary statistics on market values (sourced from www.transfermarkt.com) and Elo ratings as of 1 August 2024 and 1 August 2025, respectively, for both the UCL and UEL, separated by seeding pots and aggregated across all clubs. Elo ratings are obtained from www.clubelo.com; for an overview of individual club Elo ratings for UCL clubs, see Table C1 in the Appendix. The average market value of UCL participants is more than twice that of UEL clubs in both seasons. In both competitions, market values are strongly right-skewed, indicating that a small number of clubs possess exceptionally high market values, suggesting competitive imbalance. This pattern is particularly evident for pots 1 and 2. Moreover, the variation in market values, both within the same pot and across all clubs, is considerably greater in the UCL than in the UEL, suggesting a lower degree of competitive balance in the UCL. For the Elo ratings, summary statistics are generally higher in the UCL than in the UEL, with the exception of the standard deviation and the minimum of pot 4 in the 2025/26 season. However, differences between the UCL and UEL and across seeding pots within both competitions are smaller than those observed for market values.

3.2 Summary statistics on match outcomes in the 2024/25 and 2025/26 UCL & UEL

We examine the 288 matches played per competition during the league phases of both the UCL and UEL in the 2024/25 and 2025/26 seasons. Table 4 provides summary statistics on match outcomes, including the average number of goals and the share of wins with a margin of at least four goals (“lopsided matches”). The appearance of a greater competitive imbalance in the UCL is supported by the higher average number of goals in the UCL (3.26 and 3.38) compared to only 2.83 and 2.68 in the UEL (Scarf et al., 2022). Further evidence comes from the fact that 15.97% (13.19%) of UCL matches ended with one team winning by a margin of four goals or more, whereas only 3.47% (4.17%) of UEL matches produced such lopsided outcomes. While in both competitions and seasons about 50% of the matches resulted in a home win, the frequency of away wins in the UEL is particularly lower in the 2024/25 season (difference to the UCL approximately seven percentage points). Consequently, the proportion of draws in the UEL is nearly twice as high in this season. Taken together, these findings indicate a greater imbalance in the UCL, consistent with summary statistics on the market values presented in Tables 2 and 3.

3.3 Summary statistics on previous UEFA competitions and national leagues

To place the UCL and UEL seasons under the new format into context, we calculate the same statistics for the 2020/21 – 2023/24 UCL seasons (see Table 5) as well as for the 2023/24 seasons of the top four European domestic leagues (see Table 6), namely the English Premier League, the German Bundesliga, the Italian Serie A, and the Spanish La Liga. While, on average, the national leagues (26.42%) and the 2024/25 UEL season (24.31%) recorded roughly twice as many draws as the 2024/25 UCL season (12.50%), the proportion of draws in the previous UCL seasons (20.05%) was already lower but still substantially higher than in 2024/25. The pattern assimilates for the 2025/26 season, where both leagues exhibit the same number of draws (17.36%), thus a substantially lower value than in all national leagues. This points to a lower degree of competitive balance, particularly in the UCL, compared with national leagues. A similar pattern emerges when considering the proportion of lopsided matches, i.e. wins by a margin of at least four goals. Such outcomes occur only rarely in the UEL — less frequently than in any of the national leagues — whereas their share under the new UCL format (about 15%) is more than double the average across national leagues (6.57%). However, we also observe many lopsided matches for most previous UCL seasons.

Another important finding concerns the home advantage. In the 2024/25 UCL season, the share of home wins is about ten percentage points higher than the average across national leagues, and still seven percentage points above the average of previous UCL seasons, consistent with earlier research on home advantage in the UCL (Kuvvetli and Çilengiroğlu, 2024). These differences are smaller but still positive for the 2025/26 season. The total number of goals in the UCL is approximately 14% higher, driven primarily by an increase of nearly 18% in goals scored by home teams, while away teams score only 9% more goals compared with national leagues. Relative to earlier UCL seasons, both home and total goals are higher in the 2024/25 and 2025/26 seasons.

From this descriptive analysis, we can conclude that the distribution of team strengths in the UCL is more unequal than in both the national leagues and the UEL. This imbalance is reflected in a higher proportion of (lopsided) wins, particularly for home teams, and in fewer draws. Specifically, the 2024/25 UCL exhibits a markedly lower share of draws than observed in the UEL, previous UCL seasons, or the national leagues. This result is potentially provoked by stronger incentives to play for a win rather than to settle for a draw, as already outlined in the Introduction. The frequency of draws in the UCL increases for the 2025/26 season but is still clearly below those for national league and UCL seasons under the old format. At the same time, we observe fewer draws for the second UEL season under the new format, equal to the value in the UCL.

4 Modelling approach

To model match outcomes and subsequently predict qualification thresholds, we employ two bivariate Poisson models: First, in Section 4.1, we introduce the independent version. Second, in Section 4.2, we present the bivariate Poisson model proposed by Dixon and Coles (1997). Afterwards, in Section 4.3, we outline the explicit form of the linear predictors.

4.1 Independent bivariate Poisson model

Let $X$ and $Y$ be random variables for the goals scored by the home and away team. Under the basic model, the probability of observing a particular scoreline $(x,y)$ is given by

[TABLE]

where $\lambda$ and $\mu$ are the expected number of goals for the home and away team. This formulation implicitly assumes independence between the home and away goal distributions.

4.2 Dixon–Coles model

Again, let $X$ and $Y$ denote the goals scored by both teams. Under the model proposed by Dixon and Coles (1997), the probability of observing a particular scoreline $(x,y)$ is given by

[TABLE]

where $\lambda$ and $\mu$ are the expected number of goals for the home and away team, and $\tau_{\rho}(x,y)$ is a correction factor applied to low-scoring outcomes (0-0, 0-1, 1-0, 1-1), defined as

[TABLE]

where $\rho$ is a dependence parameter that decides whether probabilities shift in one or the other direction. While the D&C model was initially developed to shift probability mass from 1–0 and 0–1 outcomes towards 0–0 and 1–1 outcomes, Michels et al. (2025) show that it can also redistribute probabilities in the opposite direction. This feature is particularly relevant for our application, as the most recent UCL season exhibited fewer draws than suggested by an independent model. Another noteworthy property is that, for $\rho=0$, the model reduces to the case of complete independence between home and away scores, i.e. the classical independent bivariate Poisson model introduced in Section 4.1.

4.3 Predictor Modelling

While Opta relied on their Power Rankings and betting odds, we follow the approach suggested in the literature and proxy team-specific attack and defence strengths using Elo ratings (Hvattum and Arntzen, 2010). This choice is motivated by the need to forecast matches between previously unseen teams, which renders team-fixed effects (as employed, for example, by Dixon and Coles, 1997 and Ötting et al., 2024) infeasible. While betting odds could also serve as proxies (Michels et al., 2023), they are typically only available shortly before matches and do not exist for randomly generated match schedules considered in our sensitivity analyses. Elo ratings, by contrast, represent a dynamic measure of team strength based on previous match results and the observed outcome given the team’s strength. They can be interpreted as a relative indicator of competitive performance on a common scale across leagues, making them particularly suitable for European tournament settings (Csató, 2024).

Thus, the expected number of home goals $\lambda$ and away goals $\mu$ are modelled as a linear function of the difference between Elo ratings of the two teams, denoted as EloDiff:

[TABLE]

where $\beta_{0},\beta_{1},\beta_{2}$ are parameters to be estimated, including the home effect $\beta_{2}$. The sign of the term that includes $\text{{EloDiff}}=\text{{Elo}}_{\text{{home}}}-\text{{Elo}}_{\text{{away}}}$ differs due to the perspective of the home and away team, respectively. This parametrisation enables the model to directly incorporate differences in team strength as measured by Elo ratings. Note that we employ standardised Elo ratings in the model, i.e. values centred by subtracting the mean and scaled by dividing by the standard deviation.

5 Results

In this section, we provide simulations of the final standings and the points required to proceed to the knockout stage. First, we outline the simulation setup. We then fit the independent bivariate Poisson model from Section 4.1 to data from the 2023/24 season of top European domestic leagues in order to mimic the Opta forecast for the 2024/25 UCL season under the official match schedule. Afterwards, we apply the D&C model from Section 4.2 to data from the 2024/25 UCL and UEL seasons. Subsequently, we provide model checks and extend our out-of-sample analysis by randomly generating match schedules to examine whether the results are driven by the official schedule, enabling more reliable predictions of the point thresholds in both competitions. Finally, we perform sensitivity analyses.

5.1 Simulation set up

To estimate the number of points required to progress to the play-offs and the round of 16, in each simulation experiment, we use a match schedule of 36 teams allocated to four seeding pots. Each club plays two opponents from each pot, with one match at home and one away. Seeding pots and schedules are either given by the official schedules for the 2024/25 season (Section 5.2), the 2025/26 season (Sections 5.3), or randomly generated schedules (Sections 5.4 and 5.5). Outcome probabilities for each match are derived from the underlying regression model.

In each simulation run, we randomly draw an outcome for each match according to the underlying probability distribution. A win awards three points, a draw one point to each team, and a loss zero points. After simulating all matches, the teams are ranked in descending order according to the points accumulated. Cut-off values for qualification to the round of 16 and the play-offs are then determined. For each simulation run, qualification is coded as 1, and non-qualification as 0. In cases where multiple teams finish with the same number of points but not all progress to the next round, we calculate qualification chances as $1/n$, where $n$ is the number of teams with the same points total at the qualification threshold. We repeat each simulation 10,000 times. Averaging across all runs yields an estimate of the likelihood of qualification for each possible points total. Note that, for simplicity, we do not account for the exact match schedule, as our model relies on fixed Elo ratings from the start of the season (Krumer and Lechner, 2017).

5.2 Predicting UEFA competitions based on national league data

As a first step, we use data from the top four European domestic leagues to fit an independent bivariate Poisson model based on Elo ratings, as introduced in Sections 4.1 and 4.3. The estimated coefficients are reported in Table 7 together with corresponding standard errors. As expected, a higher (lower) difference in Elo ratings between the observed team and its opponent increases (decreases) the average goals of the observed team. Furthermore, playing at home raises the average number of goals for the team. For a balanced match with average Elo ratings of 1,405 for both teams, the model predicts, on average, $1.56$ goals for the home team and $1.25$ goals for the away team.

We use these estimates to simulate the number of goals from two independent Poisson distributions and determine the match outcome in each simulation run. By conducting a sufficiently large number of runs, we can estimate the win probability distribution for each match based on the relative frequencies of simulated outcomes. For the example given above of teams with identical Elo ratings, we obtain probabilities of 44.3% for a home win, 24.9% for a draw, and 30.8% for an away win.

We now use the estimated coefficients from Table 7 to predict match outcomes for the 2024/25 UCL and UEL season based on the official match schedule and Elo ratings for clubs. The procedure follows the approach outlined in Section 5.1. Figure 2 presents the resulting qualification thresholds for the round of 16 and play-offs in both competitions. Comparing our findings to the pre-competition forecasts by Opta based on their Power Rankings and betting odds (see Figure 1 in the Introduction), we observe slight differences. For the UCL, both approaches indicate a probability close to 100% of qualifying for the round of 16 with 17 points or more. However, for lower point totals, the predictions diverge: Opta suggests probabilities of 73% (28%) for 15 (14) points, whereas our approach, using domestic league data, yields only 59% (14%). Similarly, for qualification to the play-off round, Opta suggests probabilities of 69% (16%) for 9 (8) points, compared with our values of 47% (6%).

Likely driven by the difference in competitive balance between the UCL and UEL (see Section 3), we observe corresponding variations in the qualification thresholds. For the round of 16, qualification is slightly more likely in the UEL than in the UCL for the same number of points, indicating that a higher point total is required to advance in the UCL. Specifically, the qualification probability in the UEL exceeds that in the UCL by six percentage points at 15 points and by two percentage points at 14 points. Notably, we find a reverse result for the play-off round: Qualification probabilities in the UEL are lower by up to 12 percentage points (at nine points) compared with the UCL. The requirement of higher point totals to reach the round of 16 in the UCL can potentially be explained by the greater competitive imbalance at the top (see Table 4) and the resulting lower number of draws compared with the UEL. In contrast, teams in the lower part of the UCL table collect fewer points than in the UEL, which leads to slightly higher qualification probabilities for the play-off round for a given point total in the UCL, compared to the UEL.

In conclusion, the predicted threshold point totals for both competitions are similar to the ones reported by Opta. Slightly lower qualification probabilities can be explained by our use of Elo ratings. Nevertheless, the predicted thresholds still do not align with the number of points that were necessary to advance to the upcoming rounds in the 2024/25 season, particularly in the UCL. We suggest that the main reason for this discrepancy is that the independent bivariate Poisson model predicts, on average, 32 draws for the UCL — more than 75% above the 18 draws actually observed during the 2024/25 season.

5.3 Predicting UEFA competitions with the Dixon–Coles Model

Given the results of the first season under the new competition, and our findings from Section 5.2, we now aim to enhance the prediction accuracy of qualification thresholds in the UCL and UEL league phases. For this purpose, we replace the independent bivarite Poisson model with the model suggested by Dixon and Coles (1997). This approach specifically allows probabilities to be shifted from draws to home and away wins, thereby accounting for the relatively low number of draws observed in the 2024/25 UCL season (see Section 4.3). We estimate the model based on this data and (1) conduct an in-sample analysis using the official 2024/25 match schedule, comparing results to those obtained in the previous section, and (2) perform out-of-sample simulations using the 2025/26 match schedule. Moreover, in the Appendix, we conduct model comparisons using different proper scoring rules (Gneiting and Raftery, 2007).

Table 8 provides parameter estimates for the models fitted to data from the 2024/25 UCL (left column) and UEL (right column) seasons together with corresponding standard errors. We find a stronger effect of the difference in Elo ratings in the UCL, suggesting a higher likelihood of (lopsided) wins in more imbalanced matches than in the UEL. The estimated correlation parameter, which governs the redistribution of probability mass from draws to wins, is denoted by $\hat{\rho}$. It is estimated to be close to zero in the UEL, implying that the more complex model offers little advantage over the independent bivariate Poisson model. In contrast, for the UCL, we obtain $\hat{\rho}=0.105$, indicating that, for teams with average Elo ratings, the probability of a 1:1 is reduced by 10.5%, relative to the independent model, and that of a 0:0 draw by 23.0%. Given that the model includes only one season under the incomplete round-robin format, yielding 144 observations per competition, it is unsurprising that the effect is statistically insignificant even for the UCL.

We first use the estimated coefficients for an in-sample simulation to predict qualification thresholds for the 2024/25 season. Results are presented in Figure 3. For the UCL, the model produces, on average, only 25 draws — more than 20% fewer than the model trained on domestic league data, and closer to the 18 draws observed empirically. Consequently, qualification thresholds for specific point totals change substantially. For instance, the probability of directly reaching the round of 16 with 16 points decreases from 94.1% to 74.5%. Even stronger effects are observed for 15 (14) points, where probabilities decline from 59.2% (14.1%) to 22.3% (2.2%). For the UEL, however, the effect is reversed: qualification probabilities increase markedly, from 64.8% (16.2%) to 89.1% (44.6%) for 15 (14) points. Indeed, empirical results for the first season show that all teams with 15 points advanced directly to the round of 16 in the UEL, whereas all teams collecting 15 points in the UCL had to compete in the play-off round. Regarding progression to the play-offs, the two approaches yield only minor differences in qualification probabilities for the UCL. For the UEL, however, the likelihood of reaching the play-off round with nine points decreases by about eight percentage points from 35.1% to 27.5%. In the 2024/25 UEL season, both teams finishing with nine points were eliminated.

In the following, we employ the same estimation model and apply it to the official match schedule from the 2025/26 season for two main reasons: First, we aim to evaluate the predictive power of our approach using an out-of-sample dataset. Second, we seek to investigate whether the composition of participating clubs and the match schedule affect qualification thresholds. Our model predicts, on average, 26 draws in the UCL, which is fairly close to the 25 draws observed empirically. Moreover, Figure 4 illustrates the predicted qualification thresholds. When comparing these thresholds with those from the previous season, we observe differences of up to 15 percentage points in the UCL. While the probability of qualifying for the play-offs with a given points total is higher in the 2024/25 season, the probability of reaching the round of 16 is higher in the 2025/26 season. For instance, the predicted qualification probability for 16 points is 74.5% in the 2024/25 season, compared with 86.1% in the 2025/26 season. In both seasons, all teams with 16 points qualified directly for the round of 16.

We find a reverse pattern for the UEL, where teams with nine points had a 66.9% probability to qualifying for the play-offs in the 2025/26 season (only 27.5% in the 2024/25 season). However, the 65.5% probability of directly advancing to the play-offs with 15 points in the 2025/26 season is clearly lower than the 89.1% observed in the preceding season. This pattern is consistent with the empirical results. In the 2024/25 season, two of the five teams with ten points were eliminated, whereas in 2025/26 one team with only nine points reached the play-offs. Conversely, in 2024/25, one team with 14 points qualified directly for the round of 16, while in 2025/26 even one team with 16 points had to take part in the play-offs. These findings confirm that the (D&C) model can generate realistic qualification thresholds in an out-of-sample dataset (for model checks and comparisons, see Appendix D). Nevertheless, the differences between the two seasons demonstrate that the composition of participating teams affects qualification thresholds.

5.4 Simulating UEFA competition results

As our results in the previous section indicate that the composition of clubs participating in the competition affects qualification thresholds, we now aim to generalise our findings. To this end, we first estimate the D&C using data pooled from both seasons. Table 9 presents results on the D&C model fitted to the combined dataset. Compared with the model estimated for the 2024/25 season alone, we observe slight differences across all estimated coefficients. In particular, $\hat{\rho}$ decreases from 0.105 to 0.053. This change is plausible, given the higher number of draws in the 2025/26 season compared with the previous one. Nevertheless, the positive value still indicates a probability shift from draws towards wins. As expected, the larger sample size results in smaller standard errors, yet the conclusions regarding statistical significance remain unchanged.

We now use these results to simulate 10,000 repetitions of the UCL and UEL. In each run, we randomly draw participating clubs and construct match schedules in accordance with the official draw procedure. To generate participating clubs, we combine those that took part in the 2024/25 and 2025/26 seasons, grouped by seeding pots. For each pot, we assume the Elo ratings of the clubs are uniformly distributed between the minimum and maximum Elo ratings observed within that pot across both seasons. To perform draws under the new UCL competition format, Devriesere et al. (2025b) propose an programming model. As our analyses rely on fixed Elo ratings, the specific match sequence does not influence the results; we are only interested in the set of opponents assigned to each team. Our simulation design ensures that every club faces exactly two teams from each seeding pot, one at home and one away. However, for simplicity, we do not account for association-related constraints, such as the restriction preventing clubs from the same association from meeting in the league phase. Finally, we predict match outcomes and qualification probabilities using the underlying prediction model.

Figure 5 provides qualification thresholds for randomly drawn sets of participating clubs and match schedules. The results for the UCL and UEL are broadly similar, with only minor differences. For a given point total, qualification prospects are slightly higher in the UCL, by up to ten percentage points (at nine points) for the play-off phase, whereas for the round of 16, the outcomes are almost identical. Nevertheless, there is considerable variation across simulation runs. In single runs, seven points were sufficient to reach the play-off phase in both competitions, while in others, even 11 points led to elimination. The variation is even more striking for the round of 16: in certain runs, 13 (12) points sufficed in the UCL (UEL), whereas in others, 18 (17) points still resulted in elimination. Comparing these findings with the empirical observations from the first two seasons under the new system, the eliminations of VfB Stuttgart and GNK Dinamo in the 2024/25 season, despite having collected ten and even 11 points respectively, appear to have been very rare events, largely driven by the exceptionally low number of draws in that season. According to our simulations, their qualification probabilities were 90.4% (99.9%).

5.5 Sensitivity Analysis

Given that the estimated coefficient for the parameter shifting probabilities from draws to wins, $\hat{\rho}$, is statistically insignificant, likely due to the limited number of observations, we conduct a sensitivity analysis to assess the effect of different values of $\rho$ on the qualification probabilities for specific point totals. In this analysis, we refer to the same procedure as in Section 5.4, but vary $\rho\in[0,0.2]$ while holding all other parameter values constant (see Table 9).

Table 10 reports the average number of draws observed in the simulation runs for the UCL and UEL, depending on the parameter value $\rho$. Even under an independent bivariate Poisson model ($\rho=0$), we find more draws in the UEL compared with the UCL. As implied by the model properties, an increase in the value of $\rho$ shifts probability mass from draws to wins for either team. Accordingly, the average number of draws declines from 28.32 to 23.18 in the UCL and from 34.83 to 28.20 in the UEL when $\rho$ is increased to $0.2$. Recall that we estimated $\hat{\rho}=0.053$ for the UCL and $\hat{\rho}=0.055$ for the UEL (see Table 9).

To illustrate how this affects qualification thresholds, Figure 6 shows the relationship between the value of the parameter shifting probability mass from draws to wins $\rho$ and the qualification probabilities for specific point totals in the UCL, both for progression to the round of 16 (a) and play-offs (b). While only minor differences arise when qualification probabilities are already close to 100% (17 points and above) or 0% (14 points or less), substantial differences emerge for 15 (16) points. For $\rho=0$, we obtain a qualification probability of approximately 36% (84%); however, the likelihood reduces to around 26% (78%) for $\rho=0.2$. A similar pattern is observed for the play-off round, where the qualification probability at 9 points reduces from 53% to 43%. The corresponding results for the UEL are provided in Figure E1 in the Appendix. These findings demonstrate that the probability mass on draws can influence qualification probabilities at critical point totals by up to 10 percentage points, underscoring the importance of employing a prediction model capable of integrating the frequency of draws in the new UEFA competition formats to predict thresholds for qualification accurately.

6 Discussion

With the 2024/25 season, UEFA introduced the incomplete round-robin format for the Champions League (UCL) and Europa League (UEL), with the aim of increasing competitiveness and fan engagement. Given the relevance of progressing to the next round for strategic planning of clubs, this evokes demand for scientific guidance for clubs and managers on qualification thresholds. This paper seeks to develop a model that improves upon existing prediction approaches, which lack validation from the actual outcomes of the 2024/25 UCL season. For this purpose, we consider the difference in competitive balance between the UCL and UEL and explicitly account for the increased incentive of playing for a win instead of resting on a draw under the new format by shifting probability mass from draws to wins via the bivariate D&C model when predicting qualification thresholds.

Our results demonstrate that this approach allows us to predict outcomes more accurately. For instance, for a point total of 15, we obtain a qualification probability for the round of 16 of about 20% in the 2024/25 UCL season compared to more than 70% predicted by Opta. Indeed, all teams finishing with 15 points in the UCL missed direct qualification for the round of 16 and had to compete in the play-offs. While the approach used in this study offers several advantages — most notable its ability to adjust for unexpected draw rates and account for differences in team strength using Elo ratings — the first UCL season under the new format may present an extreme case in this regard, requiring caution when interpreting results. To address this, we have not only extended our analysis to an out-of-sample simulation with data from the 2025/26 season, but also presented a simulation based on randomly generated clubs and match schedules, as well as conducted a sensitivity analysis with alternative scenarios that result in different thresholds. These thresholds provide valuable guidelines for teams in planning and refining their strategies.

Still, some limitations remain: First, the simulation model does not account for association-specific restrictions in the draw procedure, i.e. it does not prevent clubs from being paired with teams from the same association in the league phase. Second, the simulation of matches does not incorporate the schedule of the generated fixtures, as the model relies on static Elo ratings fixed at the beginning of the season. Consequently, dynamic factors such as transfers and roster changes, team motivation, or short-term variations in form are not captured, which may lead to either over- or underestimation of win probabilities.

Despite these limitations, our approach provides valuable guidance for teams and managers. Predicting qualification thresholds can support decision-making regarding transfers, squad rotation, or tactical approaches during the league phase under the uncertainty of progression. Looking ahead, several avenues for further research arise. Methodologically, the D&C model is only one of several approaches for redistributing probabilities across scorelines. With the accumulation of additional seasons, future research could apply more advanced models, such as those proposed by Michels et al. (2025). These models not only allow probability mass to be shifted from 0:0 and 1:1 to 0:1 and 1:0, but also enable adjustments for scorelines with more than one goal per team. Such extensions can potentially capture the underlying data-generating process even more accurately, thereby enhancing predictive performance and the robustness of estimated qualification thresholds.

Appendix

Appendix A UEFA Champions League 2025/26: Final standings

Appendix B UEFA Europa League 2024/25 and 2025/26: Final standings

Appendix C Elo rating of UCL clubs

Appendix D Model comparison

D.1 Model frameworks

To assess whether the Dixon–Coles (D&C) model provides the most suitable structural specification for predicting match outcomes in the new UEFA formats, we compare its forecasting performance with the independent Poisson and the well-known bivariate Poisson model (Karlis and Ntzoufras, 2005).

Models are evaluated using strictly proper scoring rules (Gneiting and Raftery, 2007) to assess their probabilistic forecasting performance. In particular, we consider the Brier Score, the Rank Probability Score (RPS), and the Logarithmic Score (Log Loss). The Brier Score measures the mean squared deviation between predicted probabilities and observed outcomes in a multi-class setting. The Rank Probability Score extends this concept to ordered categorical outcomes and evaluates cumulative probability discrepancies, making it particularly suitable for football results (home win, draw, away win). The Logarithmic Score evaluates the log-likelihood assigned to the realised outcome and is closely related to maximum likelihood estimation. All three scoring rules are strictly proper, meaning that they are minimised in expectation by the true data-generating distribution (Gneiting and Raftery, 2007). Lower values of these metrics indicate superior probabilistic calibration and sharpness. The comparison is conducted out of sample, using the 24/25 season as training data and the 25/26 season as test data.

Table D1 reports the out-of-sample predictive performance of the competing models for both competitions, the UCL and the UEL. For the UCL, the D&C specification performs best across all three scoring rules. While the improvements are numerically small — what is to be expected given that we only predict one season — they are consistent across all metrics. For the UEL sample, the picture is largely the same. With respect to the Log Loss, the D&C model again performs best (0.9638), albeit with only a marginal improvement over the independent Poisson model (0.9639). For the Brier Score and RPS, the independent Poisson and D&C models are virtually indistinguishable, both clearly outperforming the bivariate Poisson specification.

Across both competitions, the D&C model either strictly dominates or matches the best-performing specification in all cases. The consistency of this ordering across two different competition environments strengthens the conclusion that accounting for low-score dependence improves probabilistic forecasts in this setting. Importantly, while the absolute performance differences are moderate, they are stable across scoring rules and competitions. This robustness supports the interpretation that the structural adjustment embedded in the D&C model captures relevant features of goal dependence that the standard independent Poisson framework does not sufficiently address.

D.2 Covariate modelling

To ensure that our conclusions are not driven by the specific choice of team-strength proxy, we again predict qualification thresholds in an out-of-sample analysis using data from the 2024/25 season and evaluate the 2025/26 season for model comparison. Instead of relying on Elo ratings, we now use market values (MVs) as an alternative explanatory variable. While the suitability of Elo ratings for European club tournaments has been demonstrated (Csató, 2024), we do not claim that they are a perfect proxy for match outcomes. Similarly, MVs are only an indirect measure of team quality. However, the objective of this robustness check is not to identify the optimal strength indicator, but rather to examine whether the model comparison remains stable across different covariate specifications. Similar to Section 4.3, we estimate the D&C model with the following properties:

[TABLE]

with $\text{{MVDiff}}=\text{{MV}}_{\text{{home}}}-\text{{MV}}_{\text{{away}}}$. The parameter shifting probability mass from draws to 1:0 and 0:1 is estimated as 0.110 for the UCL and 0.008 for the UEL (see Table D2). This is fairly close to the values obtained with Elo ratings (0.105 for the UCL and 0.030 for the UEL; see Table 8 in Section 5.3). Unsurprisingly, for most point totals, qualification thresholds reported in Figure D1 are similar to those obtained when using Elo ratings (see Figure 4 in Section 5.3). Specifically, deviations in qualification probabilities are smaller than eight percentage points in the UEL. In the UCL, we obtain deviations of up to 14 percentage points, with one exception: When using Elo ratings, we predict a probability of 39.1% to advance to the play-offs with nine points, whereas this probability is predicted at 71.2% when using MVs. Indeed, in the 2025/26 season, two out of five teams (40%) with nine teams reached the play-offs.

These results indicated that the D&C model with Elo ratings is suitable for predicting qualification thresholds in UEFA club competitions. However, future research may focus on the model specification itself. In particular, non-linear effects, interaction terms, or more flexible functional forms could be incorporated to better capture the relationship between team strength and scoring intensity.

Appendix E Qualification probabilities depending on $\rho$ for the UEL