Duff was the son of Colonel James Duff, a retired army officer living in Aberdeenshire, and Jane Bracken Dunlop.
He and his twin brother Alan were among the first boys at Fettes College, Edinburgh; he came as a scholar to Trinity College, Cambridge, in 1878 and was elected a Classical Fellow in 1883, a post he held until his death.
[1] Teaching Latin and Greek at Trinity, and also at Girton, was the main work of his life; and he is best known to classical scholars for what A. E. Housman praised as his 'unpretending school edition' of Juvenal.
He was over forty years old when he taught himself Russian, in order to read in the original the novels of Tolstoy and especially Turgenev, which he had greatly admired in French translations.
He never visited Russia, but had Russian friends, with whom he corresponded in their own language: notably Alexandra Grigorievna Pashkova, the wife of a Russian landowner, whose two sons were Trinity undergraduates.