  This note examines financial distributions to competing teams at the end of
the most famous multiple stage professional (male) bicyclist race, TOUR DE
FRANCE. A rank-size law (RSL) is calculated for the team financial gains. The
RSL is found to be hyperbolic with a surprisingly simple decay exponent (about
equal to -1). Yet, the financial gain distributions unexpectedly do not obey
Pareto principle of factor sparsity. Next, several (8) inequality indices are
considered : the Entropy, the Hirschman-Herfindahl, Theil, Pietra-Hoover, Gini,
Rosenbluth indices, the Coefficient of Variation and the Concentration Index
are calculated for outlining diversity measures. The connection between such
indices and their concentration aspects meanings are presented as support of
the RSL findings. The results emphasize that the sum of skills and team
strategies are effectively contributing to the financial gains distributions.
From theoretical and practical points of view, the findings suggest that one
should investigate other "long multiple stage races" and rewarding rules.
Indeed, money prize rules coupling to stage difficulty might influence and
maybe enhance (or deteriorate) purely sportive aspects in group competitions.
Due to the delay in the peer review process, the 2019 results can be examined.
They are discussed in an Appendix; the value of the exponent (-1.2) is pointed
out to mainly originating from the so called "king effect"; the tail of the RSL
rather looks like an exponential.
