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While the cop-out answer would to be that no one irreplaceable with the New England Patriots under Bill Belichick, I'd like to take this in a different direction.
Instead of the safe choice with quarterback and team MVP Tom Brady, I'd say tight end Rob Gronkowski may be a tougher player to replace.
Time travel with me back to 2008, when Brady was injured in the first game of the season. The Patriots, turning to then-backup Matt Cassell, were able to navigate through the season pretty effectively, just falling short of the playoffs despite a record well over .500.
However, the injury to Gronkowski during the 2011 playoffs was insurmountable. Gronkowski, a vital player in the team's red-zone schemes, injured his ankle during the AFC Championship Game, limiting his effectiveness during the Super Bowl. While he still managed to hit the field, the tight end was used as little more than a distraction, with the one big pass heading his way leading to an interception.
With nobody fully able to replicate that kind of production, the injury to Gronkowski could have been the difference as the Patriots would fall in a close game to the New York Giants.
Tough (if not impossible) to replace: Tom Brady, especially with the question marks about the team's current backups.