Cleveland Browns: How many picks do they have in 2019? After adding nine picks in the 2018 NFL Draft, the Cleveland Browns hope to be much improved. They can get even better in 2019 as they again have extra picks. The 2018 NFL Draft is now behind us. The Cleveland Browns added a total of nine picks. They added a potential franchise quarterback in Baker Mayfield out of Oklahoma, a top-flight corner in Denzel Ward from Ohio State and a bruising back in Nick Chubb from Georgia.