Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets What a fairer 24 team UEFA Euro could look like Julien Guyon Bloomberg L.P., Quantitative Research Columbia University, Department of Mathematics NYU, Courant Institute of Mathematical Sciences MathSport International 2017 Padua, June 26, 2017 Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Format of the UEFA Euro Since 2016: 24 teams Group stage (GS) + knockout stage (KO) starting with the round of 16 Simplest reasonable symmetrical structure: 4 groups of 6 Ro16: group winners play fourth-placed teams; group runners-up play third-placed teams Problem: 60 GS matches Assuming 3 games per day, teams would play every 4th day, GS would last 3 weeks Adding KO, tournament would last 5.5 weeks (more than the 32 team FIFA World Cup!) Would not fit in the international calendar Other symmetrical structures: 2 groups of 12: even worst... 8 groups of 3: odd number of teams per group... (cf 1982, 2026+ FIFA World Cup) = ⇒ UEFA has opted for 6 groups of 4 ; 36 GS matches can be completed in 12 days Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Problem: How to build a fair KO stage with 6 groups of 4? Number of groups is not a power of 2 16 teams must advance to the KO, ideally 16/6 teams per group should advance... UEFA has ruled that the 6 group winners + the 6 runners-up + the 4 best third-placed teams would advance In order to rank the 6 third-placed teams, UEFA considered in order: number of points obtained; goal difference; number of goals scored; fair play conduct in the final tournament; position in the UEFA national team coefficient rankings (see [2], article 18.03) Asymmetry = ⇒ it is not obvious to devise a fair, balanced knockout bracket Reproducing what FIFA did for the 1986, 1990, and 1994 World Cups, UEFA chose for the Euro 2016 the following bracket Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Bracket of the knockout stage of the UEFA Euro 2016 2A 1C 3A/B/F 2C 1D 1E 3B/E/F 2D 1B 1A 3A/C/D 3C/D/E 1F 2B 2E 2F Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Third-placed teams allocation mechanism Official rule All admissible alternative rules 4 best 3rd 1A vs 1B vs 1C vs 1D vs 1A vs 1B vs 1C vs 1D vs ABCD 3C 3D 3A 3B 3D 3C 3A 3B ABCE 3C 3A 3B 3E 3E 3C 3A 3B ABCF 3C 3A 3B 3F 3C 3A 3F 3B ABDE 3D 3A 3B 3E 3E 3D 3A 3B ABDF 3D 3A 3B 3F 3D 3A 3F 3B ABEF 3E 3A 3B 3F 3E 3A 3F 3B ACDE 3C 3D 3A 3E 3D 3C 3A 3E ACDF 3C 3D 3A 3F 3D 3C 3A 3F ACEF 3C 3A 3F 3E 3E 3C 3A 3F ADEF 3D 3A 3F 3E 3E 3D 3A 3F BCDE 3C 3D 3B 3E 3D 3C 3B 3E BCDF 3C 3D 3B 3F 3C/D/D 3D/C/C 3F/B/F 3B/F/B BCEF 3E 3C 3B 3F 3E 3C 3F 3B BDEF 3E 3D 3B 3F 3E 3D 3F 3B CDEF 3C 3D 3F 3E 3D 3C 3F 3E Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Strengths of the bracket Balance : Each half of the bracket has 3 group winners, 3 runners-up, and 2 third-placed teams Each quarter of the bracket has 1 third-placed team, and either 2 group winners and 1 runner-up, or 1 group winner and 2 runners-up Third-placed teams play against group winners in the round of 16 Group diversity : In each half of the bracket, the 3 group winners and the 3 runners-up come from the 6 different groups In each quarter of the bracket, the 4 teams come from 4 different groups. This is what motivates the third-placed teams allocation mechanism = ⇒ winner and runner-up of any given group can only meet again in the final, and any two teams from any given group cannot meet again earlier than in the semifinals Group diversity minimizes the probability of repeated matchups during the tournament Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Flaws of the bracket Group advantage : In order to advance as far as possible in the tournament, it is an advantage/disadvantage to be drawn into some groups It was a clear advantage to be drawn into Group A, and a clear disadvantage to be drawn into Group E The fact that France was automatically placed into advantageous Group A has raised criticism, see [3, 1, 6] Arbitrariness : Global structure of the bracket, i.e., distribution of the 3 following advantages: Adv1: the winner plays against a third-placed team during Ro16 (4 groups) Adv2: the runner-up plays against another runner-up during Ro16 (4 groups) Adv3: the winner cannot play against another group winner before SF (2 groups) ( = ⇒ Adv1) Third-placed teams allocation mechanism Lack of win incentive : For some groups, it is unclear whether it is better to finish first or second Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets The flaws of the UEFA Euro 2016 bracket Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Group advantage The worst case advantage W measures, for a given group, the ease of the most difficult route to winning the tournament, averaged over the winner, runner-up, and third-placed team in the group: W ≡ 3 � W 1 + W 2 + 4 � 6 W 3 8 E.g., for Group A, W 1 = 3 + 2 + 1 + 1 = 7 , W 2 = 2 + 1 + 1 + 1 = 5 For third-placed teams: W 3 ≡ p l W l 3 + p r W r 3 The average advantage A measures, for a given group, the ease of the average route to winning the tournament: � � A ≡ 3 A 1 + A 2 + 4 6 A 3 8 E.g., for Group A, A 1 = 3 + 1 2 (2 + 2) + 1 4 (1 + 1 + 2 + 3) + 1 8 (1 + 1 + 1 + 2 + 2 + 2 + 3 + 3) = 69 8 = 8 . 625 Worst case advantage assumes that the best-ranked team always advances to the next round, while average advantage assumes that each team in the bracket has a 50% chance of advancing to the next round Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Results of the knockout stage of the UEFA Euro 2016 Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Results of the knockout stages of the 1986, 1990, and 1994 FIFA World Cups 1986 FIFA World Cup 1C 1D 3B 3F 3B 1D 2D 2C 1A 1E 2A 2D 2C 3B 2C 2E – 1A 1A 2E 1A 1F 3E 2E 2E 1A 2F 1B 2B 1B 2F 3A 1990 FIFA World Cup 1C 1D 3B 3F 1D 3B 2D 2A 1E 1D 2A 2D 2C 3B 1D 1D – 3B 1F 1A 1A 1F 3E 2E 1F 1A 2F 1B 2B 1B 2F 3D 1994 FIFA World Cup 1B 1D 3A 3E 1B 3E 2C 1F 1F 2A 1B 2E 3E 2C 1B 3E – 1B 2D 2B 1A 1E D3 1A 2D 2D 1C 2B 2B 1C 2F 3F Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Statistics on the knockout stages of the 1986, 1990, and 1994 World Cups and the Euro 2016 Group ranks 1-2 1-3 2-3 Total Number of games 19 22 5 46 Best ranked team advances 10 15 0 25 Ratio 52.6% 68.2% 0% 54.3% Group rank 1 2 3 Total Nb teams reaching SF 8 4 4 16 8 4 4 16 Prob. of reaching SF 24 ≃ 33 . 3% 24 ≃ 16 . 7% 16 = 25% 64 = 25% = ⇒ The average advantage is a more realistic measure of group advantage Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Introduction The flaws of the UEFA Euro 2016 bracket Can we build a better bracket based only on group ranks? New fairer brackets Group advantage 8 7 6 5 4 3 2 1 Worst case advantage Average advantage 0 A B C D E F Group Julien Guyon Bloomberg L.P., Columbia University, and NYU What a fairer 24 team UEFA Euro could look like
Recommend
More recommend
