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There are a number of potential shutdown corners in the draft. The Honey Badger just isn't one of them.
Mathieu has made his name as a flashy player with electric return skills, but his upside in coverage is as a decent NFL slot corner. As a leggy 5'9" CB, Mathieu simply doesn't have the fluidity or stride length to stay with NFL receivers along the outside.
Mathieu's performance against elite college competition backs up this assertion. Consider this excerpt from an ESPN the Magazine article by Kevin Van Valkenburg:
[Football analyst KC] Joyner studied film of LSU this offseason, focusing on the seven best offensive teams the Tigers faced in 2011. In those games, Joyner found that Mathieu was targeted 25 times and allowed 14 completions for 221 yards, an average of 8.8 yards per attempt. By comparison, Mathieu's teammate, Tharold Simon, was targeted 30 times and surrendered just 12 completions for 108 yards, an average of 3.6 yards per attempt.
Mathieu's special-teams ability certainly adds value, though the Pats could have a fairly explosive KR/PR tandem simply by using Leon Washington and bringing back Julian Edelman.
Otherwise, Mathieu isn't worth a selection in the first few rounds, and since the Pats have zero picks between Round 4 and Round 6, don't expect to see the Honey Badger in New England blue and silver next season.