A sports day is several different competitions sharing a field. Track events run as heats into finals and are ranked by time. Field events are attempt-based — three jumps or three throws, ranked by the best one. Relays are team events scored by house. They all finish at different times, all feed the same house tally, and all have to be recorded by whichever teacher happens to be standing there.
The usual system is a paper slip per event, carried to a desk where one person types everything into a master spreadsheet. That person is also the bottleneck, and usually also judging something. When the day overruns, the tally is the thing that slips.
Running each event type in its proper scoring model — timed, attempt-based, or head-to-head — means the house tally is a live consequence of results rather than an end-of-day reconciliation job.