Related papers: Maximising common fixtures in a round robin tourna…
We present a new type of tournament design that we call a complete mixed doubles round robin tournament, CMDRR(n,k), that generalizes spouse-avoiding mixed doubles round robin tournaments and strict Mitchell mixed doubles round robin…
The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by…
We present a new problem called the incomplete Traveling Tournament problem, which introduces the well known Traveling Tournament Problem into the realm of incomplete round-robin tournaments. We focus on the case where teams can face each…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
A tournament organizer must select one of $n$ possible teams as the winner of a competition after observing all $\binom{n}{2}$ matches between them. The organizer would like to find a tournament rule that simultaneously satisfies the…
Multi-round competitions often double or triple the points awarded in the final round, calling it a bonus, to maximize spectators' excitement. In a two-player competition with $n$ rounds, we aim to derive the optimal bonus size to maximize…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
The goal of the classic football-pool problem is to determine how many lottery tickets are to be bought in order to guarantee at least $n-r$ correct guesses out of a sequence of $n$ games played. We study a generalized (second-order)…
The incomplete round robin sports tournament format, where each team plays the same number of games but faces only a subset of the other teams, is becoming increasingly popular in both youth and professional competitions. In contrast to…
In some domestic professional sports leagues, the home stadiums are located in cities connected by a common train line running in one direction. For these instances, we can incorporate this geographical information to determine optimal or…
We consider a game with two players, consisting of a number of rounds, where the first player to win $n$ rounds becomes the overall winner. Who wins each individual round is governed by a certain urn having two types of balls (type 1 and…
According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…
Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not…
We consider the manipulability of tournament rules for round-robin tournaments of $n$ competitors. Specifically, $n$ competitors are competing for a prize, and a tournament rule $r$ maps the result of all $\binom{n}{2}$ pairwise matches…
We find an exact formula for the number of directed 5-cycles in a tournament in terms of its edge score sequence. We use this formula to find both upper and lower bounds on the number of 5-cycles in any $n$-tournament. In particular, we…
We propose a new tournament structure that combines the popular knockout tournaments and the round-robin tournaments. As opposed to the extremes of divisive elimination and no elimination, our tournament aims to eliminate the participants…
When $n$ teams play in a football league with home and away matches against every opponent there are $M = n \cdot (n-1)$ matches. There are 3 possible match results: a victory is awarded 3 points, a draw 1 point and 0 points for a defeat.…
Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decision-making and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning…
In the last round of the FIFA World Cup group stage, games for which the outcome does not affect the selection of the qualified teams are played with little enthusiasm. Furthermore, a team that has already qualified may take into account…