Fenton-Wilkinson Order Statistics and German Tanks: A Case Study of an Orienteering Relay Race
This is an incremental domain-specific application of order statistics to ordinal regression in sports analytics.
The authors tackled the problem of predicting final team rankings in an orienteering relay race by modeling it as a random process, achieving accurate ordinal regression predictions using a lognormal distribution for leg times and Fenton-Wilkinson approximations.
Ordinal regression falls between discrete-valued classification and continuous-valued regression. Ordinal target variables can be associated with ranked random variables. These random variables are known as order statistics and they are closely related to ordinal regression. However, the challenge of using order statistics for ordinal regression prediction is finding a suitable parent distribution. In this work, we provide a case study of a real-world orienteering relay race by viewing it as a random process. For this process, we show that accurate order statistical ordinal regression predictions of final team rankings, or places, can be obtained by assuming a lognormal distribution of individual leg times. Moreover, we apply Fenton-Wilkinson approximations to intermediate changeover times alongside an estimator for the total number of teams as in the notorious German tank problem. The purpose of this work is, in part, to spark interest in studying the applicability of order statistics in ordinal regression problems.