  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.
