Greg, there's a misconception thereāand a lot of people have the same thought. It's assumed that home field gives three points. That's the average, not what each team pulls.
When you look at a team like LSU (and this applies to Bama as well) you see they are as successful on the road as they are at home. You won't find much difference in W's and L's, not much difference in total points scored as well.
Homefield advantage compares performance against expected scores at home AND on the road to quantify the value of playing at home. The advantage a team gains at home (relative to opponent) is applied in the opposite direction on the road (data independence is treated similarly for inputs).
Due to that they don't carry as large of a home field advantage as other schools.
The rankings for home field were published in June after last seasons results. Oklahoma held the highest. Mizzou came in at #4. Bama and LSU? 104th and 106th respectively. To put that in further perspective Vandy was 115th. They lose as badly at home as they do on the road.