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Here's why the Browns didn't trade down from the No. 4 overall pick
Coming into the 2018 NFL Draft, most everybody in and around the league knew the Cleveland Browns were going to select a quarterback with the No. 1 overall pick. The only question was which quarterback. It ended up being Oklahoma's Baker Mayfield, which meant the next Browns-related question was what they would do at No. 4.
Would they take Bradley Chubb to pair with Myles Garrett? Nope. Would they trade down in order to collect even more picks? Also nope. According to Peter King of The MMQB, this is why:
They got very little action on the No. 4 pick. Four teams called Dorsey with interest in moving up. None got serious. Only one team (I'd guess Arizona) offered a 2019 first-round pick as part of the package to move, which is surprising considering that two quarterbacks were still on the board when the fourth pick came up. The team willing to include its first-rounder next year said to Dorsey before the draft began: "I'm coming up for one player and one player only, and that's Baker Mayfield." As Dorsey said: "I knew all along it wasn't going to happen." So for those wondering why the Browns didn't try to pillage some team by moving down a few spots, they never had the chance.
That's definitely an interesting note. The Bills (Josh Allen) and Cardinals (Josh Rosen) both traded up for quarterbacks later in the first round, but apparently neither of them had much interest in moving ahead of the Broncos or Colts to land their guy. That strategy worked out for both of them, as they got to wait, surrender what was likely a lower price in order to move up the board, and still get their QB. (It's also interesting that the only team that was interested in moving up wanted Mayfield, considering he was not getting much buzz as the No. 1 QB in the draft until it became clear in the final days before the first round that he was the Browns' selection at No. 1.)
The Browns, meanwhile, drafted Ohio State defensive back Denzel Ward, which defensive coordinator Gregg Williams stated was due to their need for a press-man corner. They weren't able to extract additional value out of the No. 4 selection, but given that they had four picks in the top 35 and nine picks overall, they weren't exactly hurting for draft capital.