And the reason the Bucs were in the playoffs those last three years certainly wasn't their offense.
That's why the Dolphins, like everybody else, expect to see an improved Colts defense this season.
"I'm sure there'll be a dramatic change," said wide receiver Oronde Gadsden. "Dungy is one of the defensive gurus in the league. I'm sure he'll do some things to help them on the defensive side of the ball."
As expected, Dungy installed his defensive system after taking over in Indianapolis. As Peyton Manning called the Colts defense, it is now "Tampa Two."
That means you will see the Colts do a lot of stunting along the defensive line and you also will see them employ a cover two zone, designed to prevent the big plays and punish receivers after the catch.
That means patience will be important for QB Jay Fiedler and the Dolphins offense.
"The way they play, they make you earn everything you get," Fiedler said. "You have to play physical and run the ball. In the passing game, you have to take what they give you.
"They're not going to give up big chunks of yardage. But you have to make the plays when they're there.
The new-look Colts defense didn't exactly get off to a great start this season, giving up 25 points to the Jacksonville Jaguars.
But the defense also came up with a big play when outside linebacker Marcus Washington returned an interception 40 yards for a touchdown.
The Colts are banged up along the defensive line, with starting defensive tackles James Cannida and Josh Williams both expected to miss Sunday's game.
The Indy defense also isn't done fully grasping Dungy's defense, with the coach saying this week his team is more focused right now on what it's doing as opposed to what opponents are doing.
Dungy also said he expects his defense to gradually improve throughout the week.
Given his track record, you figure the Colts definitely will be better on defense, but the good news for the Dolphins is the Colts don't have the talent the Bucs and the Colts won't reach their full potential on defense until later in the season.