If you want to talk history, then Ivy League has 3 schools in the Top 10 of most national championships.

1. Princeton - 28
2. Yale - 27
3. Notre Dame - 22
4. Alabama - 20
5. Oklahoma - 17
5. USC - 17
7. Michigan - 16
7. Ohio State - 16
9. Harvard - 12
10. Nebraska - 11
10, Pittsburgh - 11

And before you say that the Ivy League won all those championships over 100 years ago, the conference is holding its own even when DI created DI-AA (now DI-FCS). If you want to talk current, the Ivy League has had at least 1 team go 8-2 in football since 2008. Unless the Ivy League competes in the DI-FCS tournament, then it will never know how competitive its champion could be in the postseason.

As far head injuries in collegiate sports go, a study found that wrestling and ice hockey have higher rates of sports related concussions than football. FWIW the Ivy League does sponsor both wrestling and ice hockey. The article does note that football is the still the top sport in terms of sheer number.
[Post edited by VTHokie2000 at 03/01/2016 10:28PM]