Dude, Carroll won't even be eligible for 5 years, if he is eligible he will 100 percent not be first ballot. He's not getting in over a guy like Mike Shanahan who has multiple rings to his name as well as a similar regular seaso n and better playoff record. He also created his own distinct spin on the WCO that was considered innovative for his time. If Carroll does get in, it'll likely be 10 or 15 years in the future, or even longer. Especially since Billichick was forced out at the same exact time and now Reid is getting up there in age.
The reason I mention Shanahan is he has yet to be nominated to the HOF, despite not coaching for over 10 years now. A guy with the credentials like Shanahan is having trouble getting into the HOF and certainly wasn't a first ballot.