Table 1.
Allocation method explained for three different pools (A, B and C), based on ranking placements of 18 competitors.
Each column represents a complete pool with 6 fencers.
Fig 1.
Sketch of the direct elimination table of a typical competition round, from 64 up to the final, scaling with decreasing powers of 2.
Different colours identify different pistes. For clarity of the picture, larger tables (128, 256) have been omitted.
Table 2.
Scale points in the official FIE ranking.
Fig 2.
An example of athletes’ classification at the end of a simulated tournament.
Subscripts display the initial ranking of the fencers, while their pyramidal arrangement indicates their final placements. Agents in the bottom, dark-gray, part of the figure are the 30% of athletes who did not access to the direct elimination table.
Table 3.
The fixed set of parameters for each simulation run.
Fig 3.
Comparison between data and simulations (averaged over 10 runs).
Probability of having the same or a different placement the following year in Junior Men, given the associated ranking placement in the previous year. Ranking positions are arranged in groups of different sizes, to enhance visualization. Sketch of the panels: (a) data; (b) simulation with the optimal value of a; (c) simulation with a very low value of a; (d) simulation with the highest possible value of a. For each mean outcome, the corresponding standard deviation is also reported as an error bar.
Fig 4.
Comparison between data and simulations (averaged over 10 runs).
Probability of having the same or a different placement the following year in Junior Women, given the associated ranking placement in the previous year. Ranking positions are organized in groups of different sizes, to enhance visualization. Sketch of the panels: (a) data; (b) simulation with the optimal value of a; (c) simulation with a very low value of a; (d) simulation with the highest possible value of a. For each mean outcome, the corresponding standard deviation is also reported as an error bar.
Fig 5.
Trend of the average total points in Junior rankings, normalised to their maximum value, compared to simulations for male (a) and female (b) fencers.
Fig 6.
Single tournaments: Kernel density plots for initial ranking position versus final classification (top panels) and vice-versa (bottom panels) in both World Cups (a-c) and simulations (b-d) for male fencers.
In every panel, a dashed gray line shows the ideal case in which talent would be the only variable influencing both ranking placements and tournaments’ results.
Fig 7.
Single tournaments: Kernel density plots for initial ranking position versus final classification (top panels) and vice-versa (bottom panels) in both World Cups (a-c) and simulations (b-d) for female fencers.
In every panel, a dashed gray line shows the ideal case in which talent would be the only variable influencing both ranking positions and tournaments’ results.
Fig 8.
Distribution of talent as a function of fencers’ ranking in simulations, for men and women respectively panel (a) and (b).
Mean values from the seventh year of ten runs are shown, error bars (blue) representing their standard deviation.