相关论文: A comparison of penalty shootout designs in soccer

The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares seven soccer penalty shootout rules that determine the kicking order, from a theoretical perspective.…

We compare conversion rates of association football (soccer) penalties during regulation or extra time with those during shootouts. Our data consists of roughly 50,000 penalties from the eleven~most recent seasons in European men's football…

Winning the coin toss at the end of a tied soccer game gives a team the right to choose whether to kick either first or second on all five rounds of penalty kicks, when each team is allowed one kick per round. There is considerable evidence…

Penalty shootouts play a crucial role in the knockout stage of major football tournaments. Their importance has substantially increased from the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals…

Penalties are fraught and game-changing moments in soccer games that teams explicitly prepare for. Consequently, there has been substantial interest in analyzing them in order to provide advice to practitioners. From a data science…

This note proposes a penalty criterion for assessing correct score forecasting in a soccer match. The penalty is based on hierarchical priorities for such a forecast i.e., i) Win, Draw and Loss exact prediction and ii) normalized Euclidian…

Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this…

In this paper, a new continuous scoring system for soccer is proposed, based on the proportion of time that a team is winning, losing or tied. Several simulations are made applying this technique to complete seasons of different leagues. As…

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…

Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…

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…

Soccer is a sparse rewarding game: any smart or careless action in critical situations can change the result of the match. Therefore players, coaches, and scouts are all curious about the best action to be performed in critical situations,…

Analysis of the popular expected goals (xG) metric in soccer has determined that a (slightly) smaller number of high-quality attempts will likely yield more goals than a slew of low-quality ones. This observation has driven a change in…

The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by European club football competitions, where the organiser generally imposes an association constraint in the first…

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…

Fairness has several interpretations in sports, one of them being that the rules should guarantee incentive compatibility, namely, a team cannot be worse off due to better results in any feasible scenario. The current seeding regime of the…

Tanking, the act of deliberately dropping points or losing a game in order to gain some other advantage, is usually seen as being against the spirit of sports. It can be even more serious if playing a draw is a (weakly) dominant strategy…

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…

A question is raised on whether some implied regularity or structure, as found in soccer team ranking by the Union of European Football Associations (UEFA), is due to implicit game result value or score competition conditions. The analysis…

In the game of cricket, the result of coin toss is assumed to be one of the determinants of match outcome. The decision to bat first after winning the toss is often taken to make the best use of superior pitch conditions and set a big…