Saban was doing it before relenting and joining in with Tua at QB.
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I'm reminded of 2012 Florida, which fits the bill you described. Under Will Muschamp, defensive guru, the offense's job was literally to just not turn the ball over. They went 11-1 and with a little different luck, could have been 12-0. Notre Dame was that type of team that year. Here's some of their outcomes:
20-17
20-3
13-6
20-13
17-14
21-6
They relied on their defense, only scored 30+ three times all year.
It got them to the NCG where they lost. I don't think it was due to the type of team they were, just a massive talent disparity with Bama.
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But that's 10 years ago now. Good teams, even ones with seemingly unremarkable offenses, tend to average at least 30-35 points per game nowadays. It seems like a program that has a fluke defensive peak season is hot garbage on offense and goes 7-5 (Iowa, Illinois, et al).