相关论文: Statistical Curse of the Second Half Rank

The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…

We present a new way of estimation of the role of chance in achieving success, by comparing the empirical data from 100-meter dash competitions (one of the sports disciplines with the most stringent controls of external randomness), with…

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…

Predicting the outcome of sports events is a hard task. We quantify this difficulty with a coefficient that measures the distance between the observed final results of sports leagues and idealized perfectly balanced competitions in terms of…

How much does luck matter to a criminal defendant in a jury trial? We use rich data on jury selection to causally estimate how parties who are randomly assigned a less favorable jury (as proxied by whether their attorneys exhaust their…

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…

The "significance filter" refers to focusing exclusively on statistically significant results. Since frequentist properties such as unbiasedness and coverage are valid only before the data have been observed, there are no guarantees if we…

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or…

Adversarial training tends to result in models that are less accurate on natural (unperturbed) examples compared to standard models. This can be attributed to either an algorithmic shortcoming or a fundamental property of the training data…

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…

For a directed graph, the Pagerank algorithm emulates a random walker on the graph that occasionally "jumps" to a random vertex based on a jumping parameter $\alpha$. Upon completion, the algorithm generates a stochastic vector whose…

We study a game theoretic model of standardized testing for college admissions. Students are of two types; High and Low. There is a college that would like to admit the High type students. Students take a potentially costly standardized…

We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the…

A common form of competition is one where judges grade contestants' performances which are then compiled to determine the final ranking of the contestants. Unlike in another common form of competition where two contestants play a…

Two natural ways of modelling Formula 1 race outcomes are a probabilistic approach, based on the exponential distribution, and econometric modelling of the ranks. Both approaches lead to exactly soluble race-winning probabilities. Equating…

In designing risk assessment algorithms, many scholars promote a "kitchen sink" approach, reasoning that more information yields more accurate predictions. We show, however, that this rationale often fails when algorithms are trained to…

In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a…

We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…

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…

Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…