The CHEERS intelligence graph

Compliments of Neatogama.com.

As someone who wrote these characters for nine years, this would be my order:

Lilith
Frasier
Diane

(now comes a big drop)

Sam
Rebecca
Carla
Norm
Cliff

Coach
Woody
 
Sam was dumbed down over the years but at least during the first few seasons he was very smart and savvy.  So if you average his IQ over the seasons he still comes out way ahead, certainly better than Cliff.

I can't believe they put Cliff anywhere near the top.

Why Coach over Woody?   They were both pretty addled.  But you figure that before he was hit in the head by too many fastballs, the Coach was probably smarter.  Although, now that I think about it, how intelligent do you have to be to just get out of the way?