Battles of Norghan is supposed to be pretty much what you describe but I never got it to run
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Imagine a football manager game with fantasy world creatures such as orcs, drakes and minotaurs and turn-based strategy battles instead of football matches."
Battles of Norghan is decent. Got it on Steam, runs out of the box on my Windows 7 system.
It's got tactical turn based combat, you hire gladiators of different races/classes and they gain XP. You can train them, give them better equipment, etc. Battle victories give you prize money that you can use to buy the equipment or send your guys training. I'd say the focus is about 50/50 on battles and management.
For a more literal sports game that feels somewhat RPG-y, try Football Tactics & Glory. It combines your usual football management game with turn based tactical football matches. Each player can learn one or two special skills and specialize on various classes (defender, goalkeeper, midfielder, attacker) that give bonuses to their respective roles on the playing field. I don't care about football, don't even watch the world cup, but this game is damn fun.
Then there's Domina, a game where you play as a Roman noblewoman who inherited a gladiator school. You buy gladiators, train them, have them fight in the arena, etc. The battles are real time and can either be directly controlled like an action game or you can let the AI fight for you. Gladiators can either get wounded and surrender, or die permanently. It's usually a good idea to level up several gladiators equally rather than focusing on just pushing one guy cause if he dies, you're fucked. It's pretty basic overall, but it's good.
There's also Age of Gladiators, which has two games set in ancient Rome and one in a sci-fi setting. They're pretty mediocre tbh, although they do have tactical turn based arena combat, and a decent management layer.
I'm not aware of a game where you manage a roster of adventurers and send them dungeoneering, though.
