"From Year 1 to Year 2 is the biggest jump," Woodson, who retired this winter after 18 NFL seasons, told his young Oakland Raiders charge of life in the league.
"And then, when you hit Year 3, you're just playing ball again."
Carr is entering his third season with the Raiders and he is taking Woodson's advice to heart as Oakland prepares for its exhibition opener at the Arizona Cardinals on Friday.
"Man, it's crazy the jump that it's been each year," Carr said Wednesday.
Carr's improvement from his rookie season to last year jumps off the stat page. Consider: His completion percentage when pressured rose from 34 percent with three passing touchdowns on 125 such attempts in 2014 to 44 percent with seven TDs on 92 attempts in 2015, according to ESPN Stats & Info.
Also, his league-worst 22 percent completion rate on throws of at least 20 yards downfield as a rookie improved to 37 percent last year, his TD passes also going from two on 67 such attempts to 10, which was tied for third-most in the league, on 62 passes.
And he also improved his league-low 5.5-yards per attempt on passes from inside the pocket (a 2.8 TD percentage) as a rookie to 7.2 yards per attempt (5.6 TD percentage) from inside the pocket last year.
"He's a good football player and he works at it," said Raiders coach Jack Del Rio. "The progression that he's making, talented guys that work hard will improve. There's no question that he took a significant step forward last year and we think there's a lot of room for growth in front of him. We're excited about continuing to develop him."
The Raiders drafted Carr out of Fresno State in the second round of the 2014 draft, No. 36 overall.
"You know, it takes time. It really does," Carr said.
Think about it, while Carr is the 18th quarterback to start a game for the Raiders since 2003 -- Elias notes that only the Cleveland Browns, with 21 starting QBs, have started more in that time frame -- his 32 starts over the past two years are the most by any QB between 2003 and 2015.
"In the NFL, the organizations that are patient with people, as you can see, it helps them develop, helps them grow," Carr said. "I came into the right situation where they believed in me and trusted me, had faith in me, and have developed me and let me grow. I've got a long way to go, man. I have so many things I need to get better at.
"I'm not perfect, but I do appreciate being here and being able to be developed into my third year."