Playing time tracks recent exposure in fifteen men's and women's football leagues: the denominator gradient and what it does to per-minute injury rates
Football injury incidence is conventionally reported per 1000 hours of exposure, dividing counts by recorded playing time. Where recorded minutes track the workload under study, that division removes part of the association it should scale. We aimed to quantify the two defects contaminating a recorded-minute denominator, outcome truncation and exposure-dependent playing time, and to measure the denominator gradient across leagues and sexes. Retrospective observational cohort study of 88,573 appearances by 1208 male English Premier League players, 2017-2025, with replication from appearance records alone in 628,487 men's and 29,799 women's appearances across 15 European leagues. Changing only the offset moved the seven-day estimate from a rate ratio of 1.27 (95% CI 1.11 to 1.44) to 1.09 (0.95 to 1.25), an attenuation of 0.151 (0.140 to 0.163) that divided away 14.0% of the rate ratio; the outcome truncated recorded minutes but explained none of it (-0.095%, resampled interval -0.41 to 0.20). Independent sources confirmed attribution in 24 of 27 resolved records (88.9%, 71.9 to 96.1). The gradient exceeded the negligible threshold of 0.05 in all 15 leagues: 0.431 to 0.655 in men's competitions, 0.444 to 0.647 in women's. Restricting to starters returned it below that threshold in eight of eight men's leagues but five of seven women's, the bound reaching 0.058 in Sweden. Recorded minutes are not a neutral denominator, and the gradient should be reported before any per-minute rate. These are measurements from public records, not a tested hypothesis, and the remedy is league-specific: run the check locally.