2021 NFL Offensive Rookie of the Year odds: No. 1 Pick Lawrence Favored May 15, 2021 | By: Covers Staff Trevor Lawrence became the latest quarterback to go first overall and, as expected, is now the favorite for Offensive Rookie of the Year. Photo By - USA TODAY Sports Trevor Lawrence became the latest quarterback to go first overall and, as expected, is now the favorite for Offensive Rookie of the Year. Photo By - USA TODAY Sports NFL Offensive Rookie of the Year odds are on the board following the NFL Draft and pro teams finally decided for this year's rookie class. Some early OROY odds are highly enticing, as even the odds-on-favorite in NFL Offensive Rookie of the Year betting has good odds.