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I highly recommend reading Mike Freeman's "10 Point Stance". It has a lot of great nuggets on the draft, with one special focus on the Patriots:
What I continue to hear from team officials is that despite the Patriots working out a number of quarterbacks, they truly feel like that Tom Brady only has a few years left. So what the Patriots really want is a major receiving threat for him so they can take that last shot or two at the Super Bowl.
So his believe is that the Patriots could be making their traditional trade, but it might be up the draft. Belichick won't move higher than 20th, but should a top receiving talent come down the pipes (like Penn St. WR Allen Robinson, or LSU WR Odell Beckham Jr., or UNC TE Eric Ebron, or Texas Tech TE Jace Amaro), the Patriots might have to be active to jump Eagles, Chiefs, and Panthers.
Now there are a few factors:
1) The Patriots seem pretty locked up at wide receiver. Julian Edelman, Danny Amendola, Aaron Dobson, and Brandon LaFell are locked in. If the Patriots were to be aggressive for a wide receiver, it means that they're actively trying to move on from Josh Boyce and Kenbrell Thompkins. I don't blame them, but I find it hard to see the team moving on after just one season. If a top receiver talent falls to them, sure, but I have a hard time seeing them being aggressive.
2) Tight ends are a hot commodity. Eric Ebron isn't expected to fall past the New York Giants at 12th overall (although I can picture a few scenarios where it happens), and the New York Jets are apparently hot on Jace Amaro at 18th overall. Neither should pass GM Ted Thompson and the Green Bay Packers at 21, if they're available. On the back-end, the Falcons, the Buccaneers, and the Bills could all be in the market for a tight end early in the second.
There's no way the Patriots are hopping far enough up the draft board, nor should they be comfortable trading too far down the draft if a top tight end is truly their target.
3) Looking at both, the Patriots could very well just be interested in selecting the top offensive weapon available at 29th, which would make more sense than the Patriots aggressively moving up or down for a shiny hood ornament. Instead, I could see this more on the lines of Freeman's first and second points regarding "Bull---- Season."
4) The Patriots have also been heavily testing out the top quarterbacks, leading everyone to believe they're either investing in Ryan Mallett's eventual replacement or interested in a trade. While we saw last season how top quarterback prospects can slide into the middle rounds (and likely where the Patriots will actually take their future replacement for Mallett), the Patriots have been stirring the pot for trade interest ever since Belichick ascended to the throne, so this could just be more fuel for the fire.
5) Freeman is right in that Brady needs to have better receiving weapons- but to expect the same degree of injuries where all (Rob Gronkowski, Shane Vereen, Danny Amendola, Aaron Dobson, Kenbrell Thompkins, Josh Boyce) but one (Edelman) of your expected top seven receivers missed extensive time would be poorly managing your risk probabilities.
While looking at how frequently Gronk, Vereen, Amendola, Edelman, and Boyce are injured is important when evaluating where potential depth is needed (and hint: Brandon LaFell plays a similar function as the latter three names), last season was an anomaly of epic proportions.
Looking at all of this, you have to think the Patriots are still playing chess with the rest of the league and are setting up their pawns for some grand movement during the draft. The Rams, Browns, and Raiders are all interested in wide receivers and all pick before the tight end hungry Falcons/Bucs/Bills. That would be a prime location to trade down towards, while still grabbing their guy and adding another mid rounder.
The Patriots are generating trade interest with teams wanting wide receivers and quarterbacks- basically every team in the top 10. They're going to find a trade partner to move down and we're seeing Belichick starting to form his chessboard.