Hierarchy Selection: New team ranking indicators for cyclist multi-stage races

TL;DR

The paper tackles how to rank professional cycling teams in multi-stage races beyond traditional finishing-time aggregation. It introduces a family of indicators based on cumulative rider places, including adjusted measures that exclude non-finishers and rider-centric aggregates, such as $T_L^{(\#)}$, $A_L^{(\#)}$, $P_L^{(\#)}$, $B_L^{(\#)}$, $G_L^{(\#)}$, $D_L^{(\#)}$, and $U_L^{(\#)}$, to define a coherent hierarchy even when finish status varies. Applying these indicators to the 2023 VSJ race, the study shows substantial reordering of teams compared to time-based rankings and demonstrates reduced ex aequo under place-based schemes; Kendall-$\tau$ analyses quantify the degree of agreement between different measures. The findings suggest that place-based rankings can encourage more competitive behavior through the end of each stage, offer new insights for sponsorship and competition design, and have potential extensions to other domains such as academia and organizational ranking. Overall, the work provides a practical, data-driven alternative for evaluating team value in complex, multi-stage competitions.

Abstract

In this paper, I report some investigation discussing team selection, whence hierarchy, through ranking indicators, for example when measuring professional cyclist team's sportive value, in particular in multistage races. A logical, it seems, constraint is introduced on the riders: they must finish the race. Several new indicators are defined, justified, and compared. These indicators are mainly based on the arriving place of (the best 3) riders instead of their time needed for finishing the stage or the race, - as presently classically used. A case study, serving as an illustration containing the necessary ingredients for a wider discussion, is the 2023 Vuelta de San Juan, but without loss of generality. It is shown that the new indicators offer some new viewpoint for distinguishing the ranking through the cumulative sums of the places of riders rather than their finishing times. On the other hand, the indicators indicate a different team hierarchy if only the finishing riders are considered. Some consideration on the distance between ranking indicators is presented. Moreover, it is argued that these new ranking indicators should hopefully promote more competitive races, not only till the end of the race, but also until the end of each stage. Generalizations and other applications within operational research topics, like in academia, are suggested.

Figures (4)

• Figure 1: Scatter plot of the rank correlation between $T_L^{(\#)}$ and $A_L^{(\#)}$, with mention of the Kendall $\tau$ value ($\simeq 0.7969$); the best linear fit obeys : y = 0.766154 + 0.943248 x, with $R^2$$\simeq$ 0.88972.
• Figure 2: Scatter plot of the rank correlation between $B_L^{(\#)}$ and $A_L^{(\#)}$, with mention of the Kendall $\tau$ value ($\simeq 0.6246$); the best linear fit obeys : y = 2.473846 + 0.816752 x, with $R^2$$\simeq$ 0.66708. Nevertheless, notice the data points different type of clustering on each side of $r = 13$.
• Figure 3: Scatter plot of the rank correlation between $B_L^{(\#)}$ and $P_L^{(\#)}$, with mention of the Kendall $\tau$ value ($\simeq 0.8769$); the best linear fit obeys : y = 0.433846 + 0.967863 x, with $R^2$$\simeq$ 0.93676. Notice the data points disordered cluster below $r = 7$.
• Figure 4: Plot of the weight values distribution used for comparing pair dissimilarities in the indicators discussed in the main text: Csató, Ausloos, and Kendall respectively: $w_C\; =1/r$, $w_A\; = \sqrt{1/r}$, $w_K=1$, where $r$ is the lowest rank of a member of the discordant pair.