But Josh Heupel led the Sooners to the 2000 National Championship.
And Jason White won the 2003 Heisman Trophy and was the third place finisher in the 2004 ceremony.
So, the Sooners have had two Heisman Trophy-winning quarterbacks in the last five years, and it could have been three in the last eight, had Heupel, now the Sooners' quarterbacks coach, won it in 2000.
"Yeah [it could have been three]; Jason should have won it again his second year," Heupel joked, when asked about the Sooners potentially having three recipients of the award in the current decade.
Regardless, OU has been a powerhouse team for quarterbacks lately.
"Well, I think what we're able to sell here is that I don't know if there's a program that's had as much success on the college level with their quarterbacks as we've had," Heupel said. "And [many] guys have been up for the Heisman Trophy. We've won numerous player of the year awards, All-Americans."
He said that's something a lot of quarterbacks don't get the opportunity of experiencing.
"It's been a special run here at the quarterback position," Heupel said. "They're surrounded by great players."
And it's one many signal callers thrive to have.
"Great quarterbacks want to have that," Heupel said. "They want to have an opportunity for success. Hopefully, we'll be able to continue that with guys that are coming in that are in our program right now."
Bradford continues to solidify his game with all his talent and the personnel around him.
In fact, while it's something that may be hard to believe for everyone that witnessed Bradford's breakout sophomore season last year, Heupel said there's been noticeable strides in his game since the 24-14 National Championship loss to Florida.
"Yeah, he was a better football player day one in spring ball than he was at the end of the season against Florida," Heupel said. "He's a lot better football player right now than he was at the beginning of the spring."
It's hard to imagine what a player that threw for more than 4,700 yards and 50 touchdowns a year ago could have improved upon, but there are things.
"It's film; it's having total command of understanding what defenses are trying to do, understanding why they're lining up in certain alignments and having a better grasp of what you're seeing on the back end," Heupel said. "He's gotten better as we've gone through the spring. He has better command of all his protections, everything that we're doing."
However, it's hard to expect any better numbers than he put up last year.
"Is [his improvement] going to roll over to better numbers? I couldn't foresee that, especially from his sophomore year," Heupel said. "I can't see that from his sophomore for his junior year, but he is a better football player, and he will be when he comes back in August."