Application of offset ranking models to two-run ski races

In February 2024, Daniel Yule made history in Chamonix by becoming the first ever ski racer to win a two-run World Cup ski race after finishing the first run with the slowest qualifying time. A number of factors may have contributed to this achievement: the relative strengths of the competitors, the time margins from the first run and the deterioration of the snow throughout the run, amongst others. This article uses two classes of offset ranking probability models to examine the extent to which Daniel Yule's result was exceptional and identify the factors that influenced the achievement. One of the two classes is standard in ranking studies, though its application to the two-run race context is unusual; the other is a novel formulation of a Thurstone order statistics model. For the latter class, the ranking probabilities have no simple explicit expressions, but a recursive procedure is developed that enables exact calculation.