Extraordinary circumstances: Covid-19 – Italian Serie A scenario

Unpredictable and uncontrollable situations have happened throughout history. Inevitably, such situations have an impact on various spheres of life. The coronavirus disease 2019 has affected many of them, including sports. The ban on social gatherings has caused the cancellation of many sports competitions. This paper proposes a methodology based on hierarchical cluster analysis (HCA) that can be applied when a need occurs to end an interrupted tournament and the conditions for playing the remaining matches are far from ideal. The proposed methodology is based on how to conclude the season for Serie A, a top-division football league in Italy. The analysis showed that it is reasonable to play 14 instead of the 124 remaining matches of the 2019–2020 season to conclude the championship. The proposed methodology was tested on the past 10 seasons of the Serie A, and its effectiveness was confirmed. This novel approach can be used in any other sport where round-robin tournaments exist.

Irrelevant matches in round-robin tournaments

We consider tournaments played by a set of players in order to establish a ranking among them. We introduce the notion of irrelevant match, as a match that does not influence the ultimate ranking of the involved parties. After discussing the basic properties of this notion, we seek out tournaments that have no irrelevant matches, focusing on the class of tournaments where each player challenges each other exactly once. We prove that tournaments with a static schedule and at least five players always include irrelevant matches. Conversely, dynamic schedules for an arbitrary number of players can be devised that avoid irrelevant matches, at least for one of the players involved in each match. Finally, we prove by computational means that there exist tournaments where all matches are relevant to both players, at least up to eight players.

Optimal Tournament Design: Lessons From the Men’s Handball Champions League

This paper challenges the traditional seeding regime of round-robin tournaments that aims to create balanced groups. In particular, the design of the most prestigious European men’s handball club competition is compared to two alternative formats with equally strong groups via simulations. We find that it is possible to increase the quality of all matches played together with raising the uncertainty of outcome, essentially without sacrificing fairness. Our results have useful implications for the governing bodies of major sports.

Magic and Modulo Magicness of Paley Digraph

A special digraph arises in round robin tournaments. More exactly, a tournament Tq with q players 1, 2, ... , q in which there are no draws. This gives rise to a digraph in which either (u, v) or (v, u) is an arc for each pair u, v. Graham and Spencer defined the tournament as, The nodes of digraph Dp are {0, 1, ... , p -1} and Dp contains the arc (u, v) if and only if u - v is a quadratic residue modulo p where p  3(mod 4) be a prime. This digraph is referred as the Paley tournament. Raymond Paley was a person raised Hadamard matrices by using this quadratic residues. So to honor him this tournament was named as Paley tournament. These results were extended by Bollobas for prime powers. Modular super edge trimagic labeling and modular super vertex magic total labeling has been investigated in this paper.