On Monday, Koetter's thoughts all came out. Koetter even recalled the moment he knew Winston should be taken with the No. 1 overall pick over Marcus Mariota. It came during Winston's official visit to One Buccaneer Place. Quarterbacks coach Mike Bajakian went through an installation session with Winston.
"Mike was flying," Koetter said. "Mike was going fast. Took a little break, had lunch, he met with some other people. We went back in the room and put the tape on and said "What's this? What's this? What's this?" He did really well, very impressive.
"That was probably pretty high for me right there. We had already looked at every snap for two years on both guys. That point right there because both guys are obviously very good football players, I've been around some good guys, but that was impressive -- his recall."
Koetter acknowledged what many draft experts were saying about the differences between Winston and Mariota. Winston played in a pro-style offense at Florida State. Mariota ran a spread system at Oregon.
"Even though I love watching spread football on TV, spread football doesn't necessarily prepare guys the best for the NFL," Koetter said.
When he was in Tallahassee for Winston's pro day, Koetter got a look at Florida State's playbook for a spring practice.
"Florida State was probably installing more stuff per day than we do," Koetter said. "I've known about [Florida State coach] Jimbo Fisher and his style of offense for a long time. They truly do run an NFL-style system. They ask a lot of their guys mentally. Jameis is as well-prepared as most any guy could be right now."
One of the few knocks on Winston was that he threw 18 interceptions last season.
"Turning it over at the quarterback position is the fastest way to lose games," Koetter said. "There are some throws we have to be afraid of.
"My quick analysis is that was 17 too many. There are going to be interceptions. All of the sudden a ball is batted, it's tipped, it hits the receiver right in the shoulder pads and pops up. There is crazy stuff that's going to happen. We can't have unforced errors. We give away possessions, no good."
Winston has had only three practice sessions with the Bucs. He took part in a rookie camp Friday and Saturday and worked with the veterans for the first time Monday. Koetter said the Bucs have thrown a lot at Winston in a hurry. Koetter is happy with the early results, but said there is room for Winston to improve.
"I'm going to quote him: 'Everything,'" Koetter said. "He's a rookie. He needs to work on everything and we all do. He's not alone on that. There's a lot to learn. It's like when you go from high school to college and college to pro. The game is faster. The defenses are better, the players are better, the coaches make quick adjustments. There is a lot of volume. He needs to work on everything and the good news is he wants to work on everything."