| Abstract: |
Operational research evaluates tournament formats by their efficacy, the
probability that the design identifies the stronger competitor, and computes
it almost exclusively by simulation under an assumption that is rarely tested:
that the trials a format aggregates are independent. We show that this
assumption systematically overstates what shortening a contest costs, and we
measure the correction. When trials are serially correlated, a format carries
N/[1+(N-1)rho] effective trials rather than N, so a twenty per cent cut costs
10.6 per cent of discriminating power under independence but only 5.2 per cent
at the correlation we estimate, and only 2.1 per cent in a sixty-trial format.
The ingredients are estimated from an implemented change in contest length: in
September 2023 professional Counter-Strike cut regulation rounds per map from
thirty to twenty-four. Across 72, 576 maps we measure discrimination as the
ability slope over the residual standard deviation on the first half of a map,
a contest fixed by rule at fifteen or twelve rounds with no stopping rule.
Against the calibrated benchmark of 0.948, discrimination falls by thirty-five
per cent in a ten-month window around the switch (0.648, 95 per cent interval
0.52-0.81) and by ten per cent over the full panel (0.901, 0.82-0.99). The
correction needs one number, recoverable from ordinary results data as a
design effect. |