Quarterbacks at number 1 overall need to be absolute sure things like Aikman, Manning, Luck... I'm sure there are others. If there are significant doubts, I'd argue against spending a number 1 overall pick on a QB.
For me, Winston is a non-starter. He may have all the physical tools, but he is as dumb as a box of rocks and we all are familiar with his moral/ethical/behavioral issues. He's like an evil Manziel. No way I gamble the number 1 overall pick on him to see him blow his career over an incident at the Mons or a gang rape somewhere. QBs are team leaders and he's not the leader type.
As for Mariota, he seemingly checks all of the boxes on the character/behavior side, and his stats are jaw-dropping - especially his accuracy. And, he has size. However, he has taken almost 100% of his snaps in the gun or pistol and most of the snaps he takes in the NFL will be under center. He will have to learn new footwork, timing (hand-offs, progessions and reads down the field, etc.) and all at NFL speed, not college speed. Most college QBs fail in the NFL and they do not have to make the basic adjustments Mariota will have to make. Is it possible he can learn these things and have a monster career? Sure. But the odds don't favor it. And I doubt Lovie is going to change the offense to Oregon's just for him. I know, the game is changing - but really, how many college spread QBs are burning up the NFL today? RG3? Nope. Kaepernick? Not really. I'd give you Wilson. Bottom line is, there's just too much risk here.
Unless Mariota just blows everyone away with his NFL QB skills at the combine, I'd trade down for a passel of additional picks and bolster both the OL and DL - both huge weak points for the Bucs.
