Related papers: Football Group Draw Probabilities and Corrections
The group stage of a sports tournament is often made more appealing by introducing additional constraints in the group draw that promote an attractive and balanced group composition. For example, the number of intra-regional group matches…
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…
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…
Several sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Hence, the organisers usually use a computer-assisted random draw to avoid any dead end, a situation when the…
The group draw of a sports tournament requires assigning teams to groups of (almost) the same size. The most important criteria for a draw procedure are balance, randomness, and transparency, which could not be satisfied simultaneously if…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
The draw of some knockout tournaments requires finding a perfect matching in a balanced bipartite graph. The problem becomes challenging with draw constraints: the two draw procedures used in sports are known to be non-uniformly distributed…
We consider the urn setting with two different objects, ``good'' and ``bad'', and analyze the number of draws without replacement until a good object is picked. Although the expected number of draws for this setting is a standard textbook…
Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we…
We showcase in this paper the use of some tools from network theory to describe the strategy of football teams. Using passing data made available by FIFA during the 2010 World Cup, we construct for each team a weighted and directed network…
Graphs are used in many disciplines to model the relationships that exist between objects in a complex discrete system. Researchers may wish to compare a network of interest to a "typical" graph from a family (or ensemble) of graphs which…
A new unequal probability sampling method is proposed. This method is sequential. The decision to select or not each unit is made based on the order in which the units appear. A variant of this method allows selecting a sample from a…
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…
Many real-world scenarios require the random selection of one or more individuals from a pool of eligible candidates. One example of especial social relevance refers to the legal system, in which the jurors and judges are commonly picked…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Consider the collection of all binary matrices having a specific sequence of row and column sums and consider sampling binary matrices uniformly from this collection. Practical algorithms for exact uniform sampling are not known, but there…
A paper published in a leading journal of management science has recently analysed the mechanism used for the UEFA Champions League Round of 16 draw. Since the authors have not been familiar with the related sports analytics literature,…
In this paper we present a novel approach to optimise tactical and strategic decision making in football (soccer). We model the game of football as a multi-stage game which is made up from a Bayesian game to model the pre-match decisions…
For NCAA football, we provide a method for sports bettors to determine if they have a positive expected value bet based on the betting lines available to them and how they believe the game will end. The method we develop modifies…
The article explores the asymptotic behavior of the expected number of drawings in the Coupon Collector's Problem with group-drawing under the uniform distribution. In this variant, each draw consists of a package of $s$ distinct coupons…