What battles has Tywin ever won? He's more a good politician/schemer than a commander. I mean he's not incompetent, but he's not a military genius. In the series he's mostly known for commiting a house "genocide" against one of his own vassals, betraying Aerys at the last moment and sacking King's Landing, and underestimating Robb Stark and getting owned. Not exactly a brilliant military career. He takes the entire credit for the battle of the Blackwater when clearly Tyrion was the true saviour there. If it wasn't for Edmure being a dumbass, he would have fallen for yet another trick of Robb Stark's and wouldn't even have been there.
His skill is in forging political stability through alliances and fear, not so much actual warfare.