Baker Mayfield Biography Latest. Baker Mayfield is a professional American football quarterback for the Cleveland Browns of the National Football League (NFL). He played college football at Oklahoma, where he was the starting quarterback for the Sooners from 2015 to 2017. Mayfield won the Heisman Trophy, given to the best player in college football, in 2017. He was drafted by the Browns with the first overall pick in the 2018 NFL Draft. Mayfield has been a starter for the Browns since his rookie season, and he has earned a reputation as a talented and competitive quarterback.