What a Shorter Contest Really Costs: Serial Dependence, Effective Trials, and Evidence from a Rule Change in Professional Esports

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.