Spider Football satirizes technical education in Hungary. It is set in a newly completed college building where the equipment is entirely modern, but the students achieve consistently low grades.

The devious headmaster attempts to divert attention from the poor standard of teaching by mounting an investigation into an incident in which a student was slapped by one of the teachers. The headmaster finds he is on pretty thin ice, and accuses the students of maintaining a conspiracy of silence in order to conceal the true facts of of the case.

While the investigation proceeds, the teachers agree to the introduction of an educational innovation — spider football — a new game involving physical training en masse, that has been invented by the P.E. teacher. Different teachers take different attitudes to the headmaster's stand, some refusing to go along with it. Their refusal is an implicit critique of a system that breeds subservience, hypocrisy and deceit.

Finally, the announcement of the results of the inquiry coincides with the introduction of the spider football scheme. A victory celebration is arranged, but the nature of the victory is by no means clear...