Complex dynamics in the distribution of players’ scoring performance in Rugby Union world cups

Abstract

The evolution of the scoring performance of Rugby Union players is investigated over the seven rugby world cups (RWC) that took place from 1987 to 2011, and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995. The distribution of the points scored by individual players, Ps, ranked in order of performance were well described by the simplified canonical law Ps∝(r+ϕ)−α, where r is the rank, and ϕ and α are the parameters of the distribution. The parameter α did not significantly change from 1987 to 2007 (α=0.92±0.03), indicating a negligible effect of professionalism on players’ scoring performance. In contrast, the parameter ϕ significantly increased from ϕ=1.32 for 1987 RWC, ϕ=2.30 for 1999 to 2003 RWC and ϕ=5.60 for 2007 RWC, suggesting a progressive decrease in the relative performance of the best players. Finally, the sharp decreases observed in both α(α=0.38) and ϕ(ϕ=0.70) in the 2011 RWC indicate a more even distribution of the performance of individuals among scorers, compared to the more heterogeneous distributions observed from 1987 to 2007, and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players. Note that neither α nor ϕ significantly correlate with traditional performance indicators such as the number of points scored by the best players, the number of games played by the best players, the number of points scored by the team of the best players or the total number of points scored over each RWC. This indicates that the dynamics of the scoring performance of Rugby Union players is influenced by hidden processes hitherto inaccessible through standard performance metrics; this suggests that players’ scoring performance is connected to ubiquitous phenomena such as anomalous diffusion.