Abstract

This study classifies cooperative and non-competitive ball games, keep-up circle games and sports warm-up drills by their scoring unit. Some sports score when an exchange ends; others score when it continues. A circulation sport is defined by three properties held as rules: it scores the completed pass rather than the termination; it guarantees that every participant receives the ball (by mandatory rotation, a called receiver or an all-must-touch rule); and it keeps no individual statistics. Below three participants a forward pass cannot be told from a return, a floor cited from work on generalized exchange and indirect reciprocity. A three-step rule-modification procedure (re-seat the scoring unit; guarantee reach; delete accumulation) comes with worked conversions of basketball, volleyball, soccer and tennis, and a boundary (Ultimate Frisbee, the rondo, golf). Members include kemari, chinlone and the Malay circle game sepak raga bulatan, whose conversion into the net sport sepak takraw (Penang, 1945, with earlier net forms in Siam and at Seremban) is read as the procedure run in reverse. A pre-registered coded survey of 22 published warm-up and icebreaker formats (2026-08-07) falsified the authors' prediction that guaranteed turn distribution is rare: it was found in four architectures (queue, role rotation, round completion, turn-taking norm), each of which makes the turn order predictable. The paper states a drill/sport differentia (a sport's ending is supplied by its own rules), distinguishes the class from cooperative games while carrying an open question against that distinction, and pre-registers six predictions.

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Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

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