Like their neighbours at Nottingham Forest, Derby fans still dine out on the deeds of Brian Clough. But the idea that those days might return in the current era is as far fetched as to suggest that this year's title will not be won by Manchester United, Arsenal or Chelsea.
Under Smith's shrewd stewardship they have at times been close enough to sniff the aromas. A result or two in their favour in either of the last two seasons could have taken them into Europe.
It has all been done on prayers and a shoestring budget, which is commendable, but also means it could all go rapidly and horribly wrong.
Derby have lost four times at home already. Saturday's defeat did not register alongside the 5-0 humbling by Sunderland on the catastrophe scale but was embarrassing nonetheless, inflicted as it was by a team likely to have a limited life in the Premiership.
Smith's side expended a good deal of energy but made an abundance of possession count for nothing. Francesco Baiano, whose Derby career has blown hot and cold, produced one of his better performances, but the support for him was inadequate, particularly after Esteban Fuertes was sent off in the first half for a crime of pure petulance against Bradford's David Wetherall.
Seth Johnson is a tenacious scrapper in the Lee Bowyer mould and at 20-years-old, a player to watch. But Derby lack a schemer in midfield, not to mention a reliable goalscorer. Smith says he has funds to reinforce his squad but admits most of his targets are priced higher than he can afford.
Paul Jewell praised his Bradford team for their "magnificent defending" and Gary Walsh for his excellent goalkeeping, but even he conceded that they failed to create much of an attacking threat.
Not that they needed to with Derby in a mood of extraordinary generosity. Fuertes lashing out at Wetherall balanced the numbers after Andy Myers had picked up a second yellow card. Then Horacio Carbonari, aided by some goalkeeping indecision, headed a Gunnar Halle free kick into his own net.
Goal: Carbonari o.g. 66 (0-1).
Derby County (3-4-1-2): Hoult; Prior, Carbonari, Elliott; Borbokis (Harper 65), Delap, Johnson, Dorigo; Baiano (Murray 83); Fuertes, Sturridge (Christie 78). Substitutes not used: Knight (gk), Schnoor.
Bradford City (4-4-2): Walsh; Halle, Wetherall, O'Brien, Myers; Blake (Windass 78), Whalley, Beagrie (Westwood 76); Saunders (Jacobs 61), Mills. Substitutes not used: Clarke (gk), Rodriguez.
Referee: M Halsey (Welwyn).
Bradford: Myers. Bookings: Derby: Johnson, Baiano; Bradford: Myers. Sending- off: Derby: Fuertes.
Man of the match: Walsh.