Related papers: Catch-Up: A Rule that Makes Service Sports More Co…
With the aid of mathematical modelling (basic tool is the random walk with absorbing barriers) we derive subsequent formulas to study the effect of different versions of possible rules. For different rules the probability of winning a game,…
In pickleball doubles with conventional side-out scoring, points are scored only by the serving team. The serve alternates during a game, with each team serving until it has faulted twice, except at the beginning of the game, in which case…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
Serves, especially first serves, are very important in professional tennis. Servers choose their serve directions strategically to maximize their winning chances while trying to be unpredictable. On the other hand, returners try to predict…
Tennis, like other games and sports, is governed by rules, including the rules that determine the winner of points, games, sets, and matches. If the two players are equally skilled -- each has the same probability of winning a point when…
Penalty shootout in soccer is recognized to be unfair because the team kicking first in all rounds enjoys a significant advantage. The so-called Catch-Up Rule has been suggested recently to solve this problem but is shown here not to be…
We consider two-person sports where each rally is initiated by a \emph{server}, the other player (the \emph{receiver}) becoming the server when he/she wins a rally. Historically, these sports used a scoring based on the \emph{side-out…
We propose a definition of generalized Cops and Robbers games where there are two players, the Pursuer and the Evader, who each move via prescribed rules. If the Pursuer can ensure that the game enters into a fixed set of final positions,…
From the viewpoint of networks, a ranking system for players or teams in sports is equivalent to a centrality measure for sports networks, whereby a directed link represents the result of a single game. Previously proposed network-based…
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given…
The presence of momentum in sports, where the outcome of a previous event affects a following event, is a belief often held by fans, and has been the subject of statistical study for many sports. This paper investigates the presence and…
Professional team sports provide an excellent domain for studying the dynamics of social competitions. These games are constructed with simple, well-defined rules and payoffs that admit a high-dimensional set of possible actions and…
In many competitive settings, from education to politics, rules do not reward effort evenly, and thresholds (e.g., grade cutoffs or electoral majorities) make some moments disproportionately important. Success thus depends on efficiently…
We introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2.…
We consider two-player contests with the possibility of ties and study the effect of different tie-breaking rules on effort. For ratio-form and difference-form contests that admit pure-strategy Nash equilibrium, we find that the effort of…
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…
As predictive models are deployed into the real world, they must increasingly contend with strategic behavior. A growing body of work on strategic classification treats this problem as a Stackelberg game: the decision-maker "leads" in the…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
The usual $n$-in-a-row game is a positional game in which two player alternately claim points in $\bb{Z}^2$ with the winner being the first player to claim $n$ consecutive points in a line. We consider a variant of the game, suggested by…
Usually a voting rule requires agents to give their preferences as linear orders. However, in some cases it is impractical for an agent to give a linear order over all the alternatives. It has been suggested to let agents submit partial…