Modifying Bradley-Terry and other ranking models to allow ties

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.

Automated summary

This paper introduces modified BT and PL models based on discrete distributions, primarily the geometric distribution, that can handle tied ranks, which are common in sports. The methodology is applied to various distributions, including some mathematically tractable ones, and illustrated using test match cricket data.