I don't understand certified autographs
 

What criteria does PSA use to "certify" an autograph as authentic?

I ask this because I happened to see this "Certified Authentic" Billy Sullivan autograph for sale on eBay: http://www.ebay.com/itm/Billy-Sulliv...YAAOSwrklVFbWS and, as his grandson, I can tell you that I don't think I've ever seen him sign his name like that. He always signed it Billy, not Bill, and usually with much more flourish. Here's are two examples of what his signature ordinarily looked like
http://www.ebay.com/itm/VINTAGE-BASE...AAAMXQxKxSBohN and http://www.ebay.com/itm/1941-DIZZY-T...MAAOSwu4BVjx~q.

So I'm just curious what would make PSA think it is authentic.

I think this is the autograph of the former AFL/NFL owner and not the baseball player/your grandfather.

However, it is possible that the teenager making minimal wage knows more about grandfather's signature than you do. :D

I am familiar with the former Pats owner. But was he a Junior?

Yes:

https://en.wikipedia.org/wiki/Billy_...rican_football)

I think you may be right.

In which case it is listed incorrectly on eBay since it is under Baseball-MLB signatures, by a company called Baseball Card Exchange.