Related papers: Soccer matches as experiments: how often does the …
Predicting the winner of an election is a favorite problem both for news media pundits and computational social choice theorists. Since it is often infeasible to elicit the preferences of all the voters in a typical prediction scenario, a…
In soccer (or association football), players quickly go from heroes to zeroes, or vice-versa. Performance is not a static measure but a somewhat volatile one. Analyzing performance as a time series rather than a stationary point in time is…
This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…
Scientifically evaluating soccer players represents a challenging Machine Learning problem. Unfortunately, most existing answers have very opaque algorithm training procedures; relevant data are scarcely accessible and almost impossible to…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…
Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds…
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been…
In this work we study the ranking algorithm used by F\'ed\'eration Internationale de Football Association (FIFA); we analyze the parameters it currently uses, show the formal probabilistic model from which it can be derived, and optimize…
Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical?…
The achievement of common goals through voluntary efforts of members of a group can be challenged by the high temptation of individual defection. Here, two-person one-goal assurance games are generalized to N-person, M-goal achievement…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
A same-score streak in sports is a sequence of games where the scores are equivalent in all games. The motivating problem arose from college basketball, however due to the difficulty in collecting data, streaks in Major League Baseball…
The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player…
Boxing has a long-standing problem with biased judging, impacting both professional and Olympic bouts. "Robberies", where boxers are widely seen as being denied rightful victories, threaten to drive fans and athletes away from the sport. To…
Sports analytics -- broadly defined as the pursuit of improvement in athletic performance through the analysis of data -- has expanded its footprint both in the professional sports industry and in academia over the past 30 years. In this…
We propose a bottom-up approach to the study of possession and its outcomes for association football, based on probabilistic finite state automata with transition probabilities described by a Markov process. We show how even a very simple…
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 article we revise the football's performance score called PlayeRank, designed and evaluated by Pappalardo et al.\ in 2019. First, we analyze the weights extracted from the Linear Support Vector Machine (SVM) that solves the…