Mr. Cyril Overton of Trinity College, Cambridge, comes to Sherlock Holmes seeking his help in Godfrey Staunton's disappearance. Staunton is the star player on Overton's rugby union team (who plays at the three-quarters position, hence the story's title) and they will likely lose an important match the following day against Oxford if Staunton cannot be found. Holmes has to admit that amateur sport is outside his field, but he shows the same care he has shown to his other cases.

Staunton had seemed a bit pale and bothered earlier in the day. Later in the evening, according to a hotel porter, a rough-looking, bearded man came to the hotel with a note for Staunton; judging from the young man's reaction, the note contained rather devastating news. He immediately left the hotel with the bearded stranger; the two of them were last seen running in the direction of the Strand at about half past ten. No one has seen them since

Overton has wired to Cambridge, but Staunton has not been seen there. He has also wired Lord Mount-James, Staunton's very wealthy uncle and nearest living relative, but has heard no answer. Staunton is the almost-eighty-year-old Lord Mount-James's heir, but he must meanwhile live in relative poverty owing to his uncle's miserly behaviour.Holmes further questions the porter. The bearded man who brought the note was neither a gentleman nor a workman, and he seemed to be bothered by something too, for his hand was trembling as he handed Staunton the note. The only word that the porter overheard of their short conversation was "time".