I watch a lot of detective shows on TV. And I’ve being considering the relationships between the principal detective and her or his offsider.
There are detectives who manage to fill the screen with enough panache or gravitas not to need a companion: Poirot and Miss Marple come to mind. But the sleuth usually needs someone to explain things to (Dr Watson) or be assisted (Joe/Aiden, in Vera) or thwarted by (Valentine/Sullivan/Mallory, in Father Brown).
If the principal detective is not a professional (Fr Brown) the companion may be a policeman, in which case he (the cop) will see the amateur as an impediment and/or a competitor.
DI Geordie Keating (Robson Green) and Rev. Sidney Chambers (James Norton) on Clare College bridge
Said ‘companion’ will, however, always come round to seeing the strengths of the detective. In the last episode of Grantchester with James Norton as the vicar Sidney Chambers, his adversary in the force, Geordie Keating, is just about crying into his beer when Norton was leaving the show.
If it’s a policeperson who is the main character, the companion is never (?) a layman, but always another officer, whose function is therefore to admire the deducer, and sometimes care for her (Vera) or him (Poole/Goodman/Mooney, in Death and Paradise; Jimmy Perez in Shetland).
Anne-Marie Medcalf adds another, different kind of analysis:
I think the detective couples are a version of mythical dyads. Myths of origin dyads could be siblings of whatever mix, spouses, parent and child. They are usually immortal and live in some kind of beatitude. They are complementary and often represent two different faces of humanity. The wise and the happy-go-lucky for instance. Then one of them does something stupid – say, eat an apple, or break the jug containing the water of immortality. They are no longer immortal as individuals but thanks to all that going forth and multiplying, humanity keeps on going, becomes immortal itself … well until further notice anyway.
The police series dyads are often made up of complementary and opposite characters. They are not family but their relations reproduce family ties -mentor/father and disciple/son or daughter, for instance. Or brothers – I think the relation between Chambers and Geordie is a sibling one, Geordie being the older one. Their relations are complementary: the wise and the quirky, the aristocrat/ middle class and the working class, the intellectual and the doer. In the series Inspector Morse, Morse is an upperclass Oxbridge man, fond of fast cars, crosswords and poetry. His methods are offbeat. His offshoot /son/ disciple, Lewis, is working class and the epitome of the plod, with a systematic, no-stone-unturned approach. Poetry is not in his blood. The Inspector Morse series is replaced by Lewis. Lewis has his own offshoot, Sergeant Hathaway, an ex-seminarist Cambridge graduate, hyper-erudite and a misfit. Lewis is now the father; together they perform miracles. In the later series, Lewis is now retired, Hathaway’s sergeant is a no-nonsense young woman. And the beat goes on. They all complement and contradict each other. They never succeed in establishing a haven of peace and order, but they insure in some ways the continuation of society within their beat.