The Patriots might have a reason to play hard, and they might not: depending on the result of the Houston Texans-Indianapolis Colts game, they might have a guaranteed shot at a first-round bye with a win. They'll be rooting for Indianapolis to pull out the win, and if they don't, they'd need a very unlikely win by the Kansas City Chiefs over the Denver Broncos. Either way, they'll be going for the win. Miami, on the other hand, is just playing for pride.
As such, almost every picker sides with the Pats. Joel Thorman of SB Nation was short and sweet with his reasoning in his Week 17 NFL picks:
Miami hasn't beaten New England since 2009. That's not changing this week.
All three pickers at Yahoo and all seven pickers at CBS also sided with New England, as did Yahoo's Pick'em pool and CBS' projection machine. Things get a little bit more interesting when you factor in the spread, which gives Miami 11 points.