Look at how the Patriots succeed, for example. On paper, they are nowhere near the best NFL team. But they contend for championships almost every year.
The only example I can think of recently is Kimi Raikkonen in F1. Ferrari paid him his usual salary after removing him from the first team (each team in F1 only has two seats, then sometimes there is a reserve and an additional test driver role, mostly for the simulator). The agreement was they would continue to pay him his regular F1 driver salary, as long as he didn't race for any other F1 team.
He spent a year doing rally, did a couple of NASCAR races, snowmobile, motocross, and came back the following year for Renault.
Funnily enough, a few years later he returned as a first team driver for Ferrari for a few additional years and now races for Alfa Romeo.
His main thing is he hates promotional appearances (stuff like commercials and autograph signings) and restrictions (he has a private motocross track and shop, and he refuses to race for any team that won't let him ride motorcycles and snowmobiles and whatever the F else he wants to do).