Related papers: A comparative study of scoring systems by simulati…
We propose a simple method for combining together voting rules that performs a run-off between the different winners of each voting rule. We prove that this combinator has several good properties. For instance, even if just one of the base…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
The availability of massive data about sports activities offers nowadays the opportunity to quantify the relation between performance and success. In this study, we analyze more than 6,000 games and 10 million events in six European leagues…
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…
We introduce a class of proper scoring rules for evaluating spatial point process forecasts based on summary statistics. These scoring rules rely on Monte-Carlo approximations of expectations and can therefore easily be evaluated for any…
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.…
Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory…
Prediction markets are well-studied in the case where predictions are probabilities or expectations of future random variables. In 2008, Lambert, et al. proposed a generalization, which we call "scoring rule markets" (SRMs), in which…
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…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
Rapid technological advancements in AI as well as the growing deployment of intelligent technologies in new application domains are currently driving the competition between businesses, nations and regions. This race for technological…
Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probability distributions. In this article, we review the…
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…
Tennis is one of the world's biggest and most popular sports. Multiple researchers have, with limited success, modeled the outcome of matches using probability modelling or machine learning approaches. The approach presented here predicts…
Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules,…
Risk-sharing is one way to pool risks without the need for a third party. To ensure the attractiveness of such a system, the rule should be accepted and understood by all participants. A desirable risk-sharing rule should fulfill actuarial…
Using a simple game-theoretical model of contests, we compare the effort exerted by rugby teams under three different point systems used in tournaments around the world. The scoring systems under consideration are NB, +4 and 3+. We state…
Though athletics statistics are abundant, it is a difficult task to quantitatively compare performances from different events of track, field, and road running in a meaningful way. There are several commonly-used methods, but each has its…
In peer mechanisms, the competitors for a prize also determine who wins. Each competitor may be asked to rank, grade, or nominate peers for the prize. Since the prize can be valuable, such as financial aid, course grades, or an award at a…
We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety…