Modifying Bradley–Terry and other ranking models to allow ties

IF 1.9 3区工程技术 Q3 MANAGEMENT

IMA Journal of Management Mathematics Pub Date : 2021-08-01 DOI:10.1093/imaman/dpaa027

Rose Baker;Philip Scarf

引用次数: 6

Abstract

Models derived from distributions of order-statistics are useful for modelling ranked data. The well-known Bradley–Terry (BT) and Plackett–Luce (PL) models can be derived from the order statistics of the exponential distribution but cannot handle ties. However, ties often occur in sports, and the ability to accommodate them leads to more useful ranking models. In this paper, we use discrete distributions, principally the geometric distribution, to obtain modified BT and PL models and some others that allow tied ranks. Our methodology is introduced for some mathematically tractable and some less tractable distributions and is illustrated using test match cricket.

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修改Bradley–Terry和其他排名模型以允许平局

从顺序统计分布中导出的模型对于建模排序数据很有用。众所周知的Bradley–Terry（BT）和Plackett–Luce（PL）模型可以从指数分布的阶统计量中导出，但不能处理平局。然而，在体育运动中经常会出现平局，而适应平局的能力会带来更有用的排名模型。在本文中，我们使用离散分布，主要是几何分布，来获得修改的BT和PL模型以及其他一些允许并列的模型。我们的方法介绍了一些数学上可处理的和一些不太可处理的分布，并用板球测试赛进行了说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IMA Journal of Management Mathematics OPERATIONS RESEARCH & MANAGEMENT SCIENCE-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The mission of this quarterly journal is to publish mathematical research of the highest quality, impact and relevance that can be directly utilised or have demonstrable potential to be employed by managers in profit, not-for-profit, third party and governmental/public organisations to improve their practices. Thus the research must be quantitative and of the highest quality if it is to be published in the journal. Furthermore, the outcome of the research must be ultimately useful for managers. The journal also publishes novel meta-analyses of the literature, reviews of the "state-of-the art" in a manner that provides new insight, and genuine applications of mathematics to real-world problems in the form of case studies. The journal welcomes papers dealing with topics in Operational Research and Management Science, Operations Management, Decision Sciences, Transportation Science, Marketing Science, Analytics, and Financial and Risk Modelling.