Dividing by playing time removes part of the association it should scale: measuring the denominator gradient in eight European leagues — replication record

Replication record for a study of the denominator gradient: the slope of log recorded match minutes on recent match exposure, which measures how much of an exposure association a per-minute denominator divides out. Injury rates in football are commonly reported per minute of play. This record accompanies a study showing that dividing by playing time is not a neutral rescaling, because playing time itself responds to the exposure under study. The gradient is measured in a cohort of 88,573 appearances by 1,208 English Premier League players and replicated across 628,487 appearances in eight European domestic leagues, from appearance records alone and with no injury data. This record contains: the manuscript and its supplement; the complete analysis pipeline and its test suite at 100 per cent statement and branch coverage, in which every quantitative claim in the manuscript is recomputed from the committed data and the gates fail if text and data disagree; the derived-output tables from which every reported number is taken; the hand-built audit evidence that no script can regenerate; and a SHA256SUMS manifest of every file in the record. The raw provider snapshot is not redistributed here. Source records were public, and redistribution must follow applicable source and Transfermarkt terms; the pipeline documents how the snapshot is obtained and verified against its manifest. DE-IDENTIFICATION. No file in this record carries a person's name, the data provider's player identifier, or a match date. The hand-built audit evidence is keyed by surrogates drawn at random once and held apart from this archive, with dates coarsened to seasons; the reviewer's identified copy is retained by the authors and deposited nowhere, and row-level model diagnostics are not deposited at all. This is de-identification of the archive rather than anonymisation of the people it describes: the sampling rule is published, so a reader holding the provider's own snapshot could redraw the same appearances. LICENCE CARVE-OUT. This record contains material under different terms. The data compilation and the documentation are released under CC BY 4.0. The code is released under the MIT Licence, as stated in the LICENSE file. The manuscript and supplement files are copyright the authors and are expressly NOT released under CC BY, pending journal publication.