Anomalies in Tournament Design: The Madness of March Madness

Tournament design is of crucial importance in competitive sports. The primary goal of effective tournament design is to provide incentives for the participants to maximize their performance both during the tournament and in the time period leading up to the tournament. In spectator sports, a secondary goal of tournament design is to also promote interesting match ups that generate fan interest. Seeded tournaments, in general, promote both goals. Teams or individuals with strong performances leading up to a tournament receive higher seeds which increase their chances of progressing further in the tournament. Furthermore, seeding ensures that the strongest teams or players are most likely to meet in the final rounds of the tournament when fan interest is at its peak. Under some distributions of team or player skill, however, a seeding system can introduce anomalies that could affect incentives. Our analysis of the NCAA men’s basketball tournament uncovers such an anomaly. The seeding system in this tournament gives teams with better success in the regular season more favorable first round match ups, but the tournament is not reseeded as the games progress. Therefore, while higher seeds progress to the 2nd round of the tournament at uniformly higher rates than lower seeds, this relationship breaks down in later rounds. We find that 10th and 11th seeds average more wins and typically progress farther in the tournament than 8th and 9th seeds. This finding violates the intended incentive structure of seeded tournaments.basketball, tournament design, sports, NCAA

Anomalies in Tournament Design: The Madness of March Madness

Tournament design is of crucial importance in competitive sports. The primary goal of effective tournament design is to provide incentives for the participants to maximize their performance both during the tournament and in the time period leading up to the tournament. In spectator sports, a secondary goal of tournament design is to also promote interesting match ups that generate fan interest. Seeded tournaments, in general, promote both goals. Teams or individuals with strong performances leading up to a tournament receive higher seeds which increase their chances of progressing further in the tournament. Furthermore, seeding ensures that the strongest teams or players are most likely to meet in the final rounds of the tournament when fan interest is at its peak. Under some distributions of team or player skill, however, a seeding system can introduce anomalies that could affect incentives. Our analysis of the NCAA men’s basketball tournament uncovers such an anomaly. The seeding system in this tournament gives teams with better success in the regular season more favorable first round match ups, but the tournament is not reseeded as the games progress. Therefore, while higher seeds progress to the 2nd round of the tournament at uniformly higher rates than lower seeds, this relationship breaks down in later rounds. We find that 10th and 11th seeds average more wins and typically progress farther in the tournament than 8th and 9th seeds. This finding violates the intended incentive structure of seeded tournaments.basketball, tournament design, sports, NCAA

Anomalies in Tournament Design: The Madness of March Madness

Tournament design is of crucial importance in competitive sports. The primary goal of effective tournament design is to provide incentives for the participants to maximize their performance both during the tournament and in the time period leading up to the tournament. In spectator sports, a secondary goal of tournament design is to also promote interesting match ups that generate fan interest. Seeded tournaments, in general, promote both goals. Teams or individuals with strong performances leading up to a tournament receive higher seeds which increase their chances of progressing further in the tournament. Furthermore, seeding ensures that the strongest teams or players are most likely to meet in the final rounds of the tournament when fan interest is at its peak. Under some distributions of team or player skill, however, a seeding system can introduce anomalies that could affect incentives. Our analysis of the NCAA men’s basketball tournament uncovers such an anomaly. The seeding system in this tournament gives teams with better success in the regular season more favorable first round match ups, but the tournament is not reseeded as the games progress. Therefore, while higher seeds progress to the 2nd round of the tournament at uniformly higher rates than lower seeds, this relationship breaks down in later rounds. We find that 10th and 11th seeds average more wins and typically progress farther in the tournament than 8th and 9th seeds. This finding violates the intended incentive structure of seeded tournaments

Nested Zero Inflated Generalized Poisson Regression for FIFA World Cup 2022

This article is devoted to the forecast of the FIFA World Cup 2022 via nested zero-inflated generalized Poisson regression. Our regression model incorporates the Elo points of the participating teams, the location of the matches and the of team-specific skills in attack and defense as covariates. The proposed model allows predictions in terms of probabilities in order to quantify the chances for each team to reach a certain stage of the tournament. We use Monte Carlo simulations for estimating the outcome of each single match of the tournament, from which we are able to simulate the whole tournament itself. The model is fitted on all football games of the participating teams since 2016 weighted by date and importance. Validation with previous tournaments and comparison with other Poisson models are given.Comment: 22 pages, 14 tables, 4 figures. Update October 30: including now all historic matches until 30.10.2022 for latest forecast. arXiv admin note: substantial text overlap with arXiv:2106.05174, arXiv:1806.01930, arXiv:1905.0362

An analysis of penalty kicks in elite football post 1997

The penalty kick in football is a seemingly simplistic play; however, it has increased in complexity since 1997 when the rules changed allowing goalkeepers to move laterally along their goal line before the ball was kicked. Prior to 1997 goalkeepers were required to remain still until the ball was struck. The objective of this study was to determine the importance of the penalty kick in the modern game of football. A retrospective study of the 2002, 2006 and 2010 World Cup and the 2000, 2004 and 2008 European Championship tournaments was carried out, assessing the importance of the penalty kick in match play and shootouts and the effect of the time of the game on the shooter's success rate. This study demonstrated the conversion rate of penalties was 73% in shootouts and 68% in match play. Significantly more penalties were awarded late in the game: twice as many penalties in the second half than the first and close to four times as many in the fourth quarter vs. the first. Teams awarded penalty kicks during match play won 52%, drew 30% and lost 18% of the time; chances of winning increased to 61% if the penalty was scored, but decreased to 29% if missed. Teams participating in either the World Cup or European Championship final match had roughly a 50% chance of being involved in a penalty shootout during the tournament. Penalty shots and their outcome significantly impact match results in post 1997 football

The relationships between rugby players’ tackle training attitudes and behaviour and their match tackle attitudes and behaviour

Background The tackle event in rugby is a technical and physical contest between opposing players. A player's ability to tolerate and contest during a tackle is a prerequisite for safe participation and success in rugby. Little is known about the relationship between tackle training and tackling in matches in rugby union. Therefore, we investigated the relationships between players’ training attitudes and behaviour and their match attitudes and behaviour for tackling in rugby union. Method A questionnaire was designed to assess attitude (importance) and behaviours (frequency and quantity) among junior (under 19) players on a 5-point Likert Scale. Questionnaires were handed out to 220 players (10 schools) at a tournament and 75% (9 schools, n=164) were returned for analysis. Associations between training attitudes and behaviours were tested using the χ2 test, Cramer's V and τ-b. Results The more time spent on emphasising proper technique to prevent injuries in training, the more important players rated ‘own safety’ (τ-b=0.21, moderate, z=3.1, p<0.01), ‘going for the ball only’ (τ-b=0.27, moderate, z=4.6, p<0.001) and ‘staying on feet’ (τ-b=0.23, moderate, z=3.6, p<0.001) in match play. The more time spent on emphasising proper technique to improve performance in training, the more important players rated actions ‘going for ball only’ (τ-b=0.23, moderate, z=3.7, p<0.001) and ‘preventing the ball carrier from retaining position’ (τ-b=0.20, moderate, z=3.1, p<0.01) in match play. Conclusions This is the first study to report on the relationships between players’ training attitudes and behaviour and their match attitudes and behaviours for tackling in rugby union. The importance of tackle training to prevent injury, and the amount of time spent on technique to prevent injuries, was associated with behaviours that reduce the risk of injury in matches

An analysis of the design of the PGA Tour’s FedExCup

The FedExCup is a professional golf championship on the PGA TOUR that includes the first playoff system staged on any of the world’s profess ional golf tours. The FedExCup, incorporating elements of theory on the design of i ndividualistic sports competitions in its organisation and structure, enhances the PGA TOUR s eason by providing an additional competitive element and has to date been effective in meeting a number of its objectives. However, despite having the largest prize fund in g olf and the seventh largest first prize in all team or individual sports, the FedExCup is evidentl y considered neither by top players nor by fans to be the most important competition in gol f, thereby conflicting with theory on prize incentives in sport competition. The FedExCup canno t currently match the inherent importance and tradition of the major championship tournaments; however, its importance may be enhanced with a reorganisation of the finale tournament, ‘The TOUR Championship’, to a three day tournament and the introduction of n ew matchplay playoff competition between the top four players in the final standings after The TOUR Championship. This would serve to separate the two distinct competitio ns: (a) the competition for the event, and (b) the competition for the ‘league title’, and mak e them complementary rather than embedded. The objective of this restructure is to maintain all of the existing positive elements of the design of the FedExCup, but to also add a more dramatic context to its conclusion; critically it would make the competitio n more attractive to spectators and as a consequence, increase the perceived status of the F edExCup to a level more befitting of its prize fund

Comparing league formats with respect to match importance in Belgian football

Recently, most clubs in the highest Belgian football division have become convinced that the format of their league should be changed. Moreover, the TV station that broadcasts the league is pleading for a more attractive competition. However, the clubs have not been able to agree on a new league format, mainly because they have conflicting interests. In this paper, we compare the current league format, and three other formats that have been considered by the Royal Belgian Football Association. We simulate the course of each of these league formats, based on historical match results. We assume that the attractiveness of a format is determined by the importance of its games; our importance measure for a game is based on the number of teams for which this game can be decisive to reach a given goal. Furthermore, we provide an overview of how each league format aligns with the expectations and interests of each type of club

Indicadores de rendimiento en los Grand Slams de tenis

The objective of this research is to characterize the differences in performance indicators of Grand Slam tennis, in order to identify those technical and tactical behaviors that are more effective in real life playing situations. It is a descriptive and observational study, with a quantitative methodology. The sample was composed of 338 matches, of the absolute individual male category in the 2018 season of three Grand Slam tournaments (Roland Garros, Wimbledon and US Open). The differences in performance indicators in various situational variables (type of tournament, match result, match status and difference between sets) were analyzed through descriptive and inferential analysis. The results showed that there are significant performance indicators and differences in the analyzed tournaments in terms of tournament type, match result, match status and to a lesser extent in the difference between sets. We concluded that performance indicators are specific to each tournament or playing surface, that the importance of taking the initiative is fundamental to winning in tennis and that the form of play does not vary as the match progresses. These findings are of great interest, as they condition their setting for each tournament and the play of the players, establishing different competition strategies.&nbsp;El objetivo de la presente investigación trata de caracterizar las diferencias que se dan en indicadores de rendimiento de los Grand Slams de tenis, con el fin de identificar aquellas conductas técnicas y tácticas que resulten más eficaces en situaciones reales de juego. Se trata de un estudio descriptivo y observacional, de metodología cuantitativa. La muestra estuvo compuesta por 338 partidos, de la categoría individual absoluta masculina en la temporada 2018 de tres torneos Grand Slam (Roland Garros, Wimbledon y Open EEUU). Para ello, se analizaron las diferencias de en los indicadores de rendimiento en diversas variables situacionales (tipo de torneo, resultado del partido, match status y diferencia entre sets) a través de análisis descriptivos e inferenciales. Los resultados mostraron que existen indicadores de rendimiento y diferencias significativas en los torneos analizados en cuanto al tipo de torneo, resultado del partido, match status y en menor medida en la diferencia entre sets. Concluyendo que los indicadores de rendimiento son propios de cada torneo o superficie de juego, que la importancia de llevar la iniciativa es fundamental para ganar en tenis y que la forma de juego no varía según va transcurriendo el partido. Estos hallazgos resultan de gran interés, pues condicionan su puesta a punto para cada torneo y el juego de los tenistas, estableciéndose diferentes estrategias de competición.&nbsp