Now the former Steelers wideout has found a new home in Gruden's cathouse.
Asked if he has a good handle on Bryant's recent bout with migraines, Gruden responded, "I don't know. I really don't know. We're calling Martavis the white tiger."
Why the white tiger?
"I used to go to Busch Gardens in Tampa," Gruden explained. "We call (former Buccaneers receiver Joey Galloway) the white tiger in Tampa. You go to Busch Gardens and they've got a white tiger. You go 12 times or 13 times, the white tiger was always in his cage.
"But the white tiger came out today. Bryant came out. I don't know if you get that analogy but sometimes he comes out to play and sometimes he doesn't. It's good to see him because he's really special, like the white tiger. It's late in the day here."
Gruden isn't the first NFL coach to hang a nickname on the talented but enigmatic big-play threat. Former Steelers assistant coach Todd Haley once dubbed Bryant "The Alien" for a freakish combination of size, speed and coordination not found in other human beings.
If Bryant's latest appellation rings a bell, it's because Gruden's current offensive coordinator used a similar ploy in an attempt to motivate Marqise Lee when the Jaguars receiver was beset by nagging injuries three summers ago.
"He's to me like the albino tiger at the zoo," former Jacksonville assistant Greg Olson said at the time. "You get there and if you're lucky enough to get him to come out of the cage and see him, it's a good day. I've only seen him three times (in practice) since I've been here. Those three days he was very impressive, but he's only been out three days. So, we're hoping we can get him healthy and see him a little bit more."
Coincidence? We think not.
Gruden hasn't shied away from hyperbole himself, recently insisting that Bryant "is not a good talent, he's a great talent."
As we witnessed at times in Pittsburgh, Bryant is dynamic enough to increase an offense's output by a few points per game if he's healthy and motivated. That game-changing potential was behind Oakland's decision to trade a third-round pick for a one-year audition before Bryant reaches free agency in 2019.
The best NFL coaches are regarded as master manipulators, capable of pushing the right buttons to maximize the output of talented but troubled stars. On that note, it will be interesting to revisit the Gruden-Bryant-white tiger paradigm in January.