We evaluate the sporting effects of the seeding system reforms in the Champions League, the major football club tournament organized by the Union of European Football Associations (UEFA). Before the 2015–2016 season, the teams were seeded in the group stage by their ratings. Starting from the 2015–2016 season, national champions of the Top-7 associations are seeded in the first pot, whereas other teams are seeded by their rating as before. Taking effect from the season 2018–2019, the team’s rating no longer includes 20% of the rating of the association that the team represents. Using the prediction model, we simulate the whole UEFA season and obtain numerical estimates for competitiveness changes in the UEFA tournaments caused by these seeding reforms. We report only marginal changes in tournament metrics that characterize ability of the tournament to select the best teams and competitive balance. Probability of changes in the UEFA national association ranking does not exceed several percent for any association.
Appendix contains supplementary information on the UEFA tournaments format and rankings in the 2015–2018 tournament cycle.
A.1 National association coefficient
All clubs participating in the Champions League and Europa League collect points for the national association they represent. In the qualifying rounds, each win adds 1 point to the association’s total, a draw – 0.5 points, a loss – 0 points. Starting from the group stage, these numbers are 2, 1 and 0, respectively. After the season, the total number of points is divided by the number of participants from this association. The resulting average is the association’s yearly coefficient. It is calculated over the last 5 seasons; the sum is an association’s 5-year coefficient.
A.2 Club coefficient
A UEFA team coefficient consists of two terms: number of points gained by this team in the Champions League and Europa League for the last 5 years and 20% of the coefficient of the association this club belongs to. Starting from the group stage, a win adds 2 points to the team’s coefficient, a draw – 1 point, a loss – 0 points. Bonus points are awarded for qualification into the latter stages of the tournaments. In the Champions League, it’s 4 points for reaching the group stage, plus 5 points for the Last-16 stage, plus 1 point for the quarterfinals, plus 1 point for the semifinals, plus 1 point for the final. In the Europa League, it’s 2 points for reaching the group stage, plus 1 point for the quarterfinals, plus 1 point for the semifinals, plus 1 point for the final. As an exception from all other bonus points, 2 points for reaching the group stage of the Europa League are partly awarded only if a team fails to obtain more than 2 points. More precisely, if a team gets x normal points during the group stage, it gets points instead. Thus, a total of 2 points is a guaranteed minimum number for the teams that reached the group stage of the Europa League. The participants that fail to reach the group stage get points on a different basis. Namely, a team that leaves the Champions League from the 1st qualifying round gets a fixed amount of 0.5 points, from the 2nd qualifying round – 1 point. A team that finishes its participation in the Europa League in the 1st qualifying round gets 0.25 points, in the 2nd qualifying round – 0.5 points, in the 3rd qualifying round – 1 point, in the 4th qualifying round – 1.5 points.
A.3 Monte-Carlo specification
The starting values of parameters are random. On i-th Monte-Carlo step, the new set of parameters is tested. The new set of parameters is generated by adding a random normally distributed fluctuation to the previous set :
where TMC is Metropolis “temperature” (it regulates the degree of allowed fluctuations in the system), and σ is a coefficient, the value of which is chosen to obtain a mean acceptance ratio equal to 0.5. The step acceptance probability is equal to
During optimization, we decreased TMC from to in steps, which corresponds to a random walk in the parameter space at the beginning of optimization and negligibly small parameter fluctuations in the end.
Since scores follow a Poisson distribution, λh and λa must always be positive; parameters that lead to negative λh or λa are considered invalid. During Monte-Carlo optimization, we used only valid sets of parameters . New fluctuations (and, thus, new sets of parameter values) were generated at each step until a valid set was obtained.
Beichl, I. and F. Sullivan. 2000. “The Metropolis Algorithm.” Computing in Science & Engineering 2(1):65–69.Search in Google Scholar
Boyko, R. H., A. R. Boyko, and M. G. Boyko. 2007. “Referee Bias Contributes to Home Advantage in English Premiership Football.” Journal of Sports Sciences 25(11):1185–1194.Search in Google Scholar
Buraimo, B. and R. Simmons. 2009. “A Tale of Two Audiences: Spectators, Television Viewers and Outcome Uncertainty in Spanish Football.” Journal of Economics and Business 61(4):326–338.Search in Google Scholar
Corona, F., D. Forrest, J. D. Tena, and M. Wiper. 2018. “Bayesian Forecasting of UEFA Champions League under Alternative Seeding Regimes.” International Journal of Forecasting. (To appear). DOI: https://doi.org/10.1016/j.ijforecast.2018.07.009Search in Google Scholar
Dixon, M. J. and S. G. Coles. 1997. “Modelling Association Football Scores and Inefficiencies in the Football Betting Market.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 46(2):265–280.Search in Google Scholar
Garcia, J. and P. Rodriguez. 2002. “The Determinants of Football Match Attendance Revisited: Empirical Evidence from the Spanish Football League.” Journal of Sports Economics 3(1):18–38.Search in Google Scholar
Goossens, D. R., J. Beliën, and F. C. R. Spieksma. 2012. “Comparing League Formats with Respect to Match Importance in Belgian Football.” Annals of Operations Research 194(1):223–240.Search in Google Scholar
Hart, R. A., J. Hutton, and T. Sharot. 1975. “A Statistical Analysis of Association Football Attendances.” Journal of the Royal Statistical Society: Series C (Applied Statistics) 24(1):17–27.Search in Google Scholar
Horen, J. and R. Riezman. 1985. “Comparing Draws for Single Elimination Tournaments.” Operations Research 33(2):249–262.Search in Google Scholar
Kirkpatrick, S., C. D. Gelatt, and M. P. Vecchi. 1983. “Optimization by Simulated Annealing.” Science 220(4598):671–680.Search in Google Scholar
Koning, R. H., M. Koolhaas, G. Renes, and G. Ridder. 2003. “A Simulation Model for Football Championships.” European Journal of Operational Research 148(2):268–276.Search in Google Scholar
Koopman, S. J. and R. Lit. 2015. “A Dynamic Bivariate Poisson Model for Analysing and Forecasting Match Results in the English Premier League.” Journal of the Royal Statistical Society. Series A: Statistics in Society 178(1):167–186.Search in Google Scholar
Maher, M. J. 1982. “Modelling Association Football Scores.” Statistica Neerlandica 36(3):109–118.Search in Google Scholar
Pawlowski, T., G. Nalbantis, and D. Coates. 2018. “Perceived Game Uncertainty, Suspense and the Demand for Sport.” Economic Inquiry 56(1):173–192.Search in Google Scholar
Pollard, R. (1986). “Home Advantage in Soccer: A Retrospective Analysis.” Journal of Sports Sciences 4(3):237–248.Search in Google Scholar
Scarf, P. A., M. M. Yusof, and M. Bilbao. 2009. “A Numerical Study of Design for Sporting Contests.” European Journal of Operational Research 198(1):190–198.Search in Google Scholar
Schreyer, D., S. L. Schmidt, and B. Torgler. 2018. “Game Outcome Uncertainty in the English Premier League: Do German Fans Care?” Journal of Sports Economics 19(5):625–644.Search in Google Scholar
Vu, T. D. 2010. “Knockout Tournament Design: A Computational Approach.” PhD diss., Stanford University.Search in Google Scholar
©2019 Walter de Gruyter GmbH, Berlin/Boston