One equation allocates playing time in competitive team sports: the rulebook sets the arithmetic and the league sets the habit

This record is the complete replication object for the manuscript: the paper and its supplement, the pipeline that produced every number in them, the test suite that gates those numbers, the hand-built evidence no script can rebuild, and the derived tables each figure and table is drawn from. The manuscript is deposited inside the replication record rather than beside it, so the version of record of the evidence includes the version of the text it supports. A reader can check any sentence in the paper against the data behind it without trusting anything but arithmetic. WHAT THE PAPER DOES Every team sport that lets a team replace players rations the replacements, and the ration settles who plays and for how long. Across eight codes - association football (men's and women's), rugby union, rugby league, Australian rules (men's and women's), Gaelic football, hurling, ice hockey and baseball - the paper measures how playing time is allocated and finds one equation behind it, complete in the one-way codes, its terms separating what the rulebook fixes from what a competition chooses. Under scarcity every league behaves alike: loaded starters are kept on at the same rate on four continents. Under freedom each expresses a preference, and the size of a league's departure is priced near one-for-one by what its own withdrawal minute prices (lambda = 0.87, 95% interval 0.54 to 1.21, twelve leagues), a law confirmed in four out-of-sample predictions and refused in one. WHAT IS IN THE FILES source-paper2-v1.0.0.tar.gz - the pipeline (src/), the test suite (tests/), the manuscript and supplement sources (manuscript2/), the hand-built evidence (data/manual/), the table and split tools (tools/), and the documentation needed to rerun it. derived-outputs-paper2-v1.0.0.tar.gz - the 670 derived tables from which every number in the paper is recomputed. manuscript.pdf - the manuscript as submitted. supplement.pdf - the Supplementary Information as submitted. SHA256SUMS.txt - SHA-256 of each of the four files above. The archives are built deterministically - sorted entries, no owner, fixed timestamps - so a rebuild from the same sources reproduces the same bytes and the checksums in this record mean what they say. LICENCE CARVE-OUT Three different terms apply inside this record. The data compilation and the documentation are released under CC BY 4.0. The code is released under the MIT Licence, whose text is in LICENSE inside the source archive. The manuscript and supplement files - manuscript.pdf, supplement.pdf, and the sources under manuscript2/ - are (c) the author and are expressly NOT released under CC BY, pending journal publication. The record-level licence field reads CC BY 4.0 because Zenodo permits one value; this paragraph is the operative statement for the manuscript files. WHAT IS NOT DEPOSITED, AND WHY The third-party match records the panels are built from - Transfermarkt, Soccerdonna, FBref, itsrugby.fr, AFL Tables and the AFL match interface, the NRL match centre, the NHL statistics interface, All-Ireland final match reports and the MLB Stats interface - are publicly accessible without charge and their terms permit the research use made here, but they do not permit redistribution of the match records themselves. Those are therefore not in this record. What is deposited is the derived tables: the appearance, cell and league summaries from which every number in the paper is computed. DE-IDENTIFICATION No file in this record contains a player identifier. The deposited tables are league-, season-, cell- and panel-level summaries and model coefficients. A test in the deposited suite checks this property on every deposited table, so it is enforced rather than asserted. REPRODUCING THE PAPER Install requirements.txt, run the pipeline stages in src/, then tools/build_paper2_tables.py and tools/split_paper2_nhb.py, and compile manuscript2/manuscript2.tex and manuscript2/supplement2.tex. The test suite - 1,469 tests at 100 per cent statement and branch coverage - recomputes every headline constant from the deposited tables and fails if the text and the data disagree.