(h/t to name78 on /r/Patriots)
Bill Belichick owns a sterling 199-105 record over the 11th most coaching attempts (304) in NFL history. Out of coaches with 200+ games under their belt, Belichick has posted the 5th best career winning percentage at 65.5%, although he'd have to go 16-0 this upcoming season to pass Dungy (although Dungy has coached far fewer games).
He's a winner on the field. Turns out that he's a winner in Vegas, too.
According to Nate Silver at FiveThirtyEight, we should be putting our money where our fandom is. Belichick has beaten the spread 56.6% of his time with the Patriots.
Vegas's job is to provide a line where people will bet an even amount for and against the spread, which generally coincides with an expectation for a game's final score. So if Vegas predicts the Patriots will win by 7 points, it's because Vegas believes roughly the same amount of money will flow in bets that the Patriots will win by more than 7 and by less than 7.
Belichick has beaten that line 56.6% of the time, which means that Belichick's Patriots score more than projected a statistically significant amount of the time (his record against the spread is 139-102-5, according to Pro Football Reference, which is 58.2%, and a game or two different from Silver's).
Silver attributes this significance to Belichick's coaching acumen, where Belichick is able to take advantage of match-ups better than his contemporaries. I agree with this take, although last season's 8-8 output was the definition of average.
Look for Belichick to get back on track against the spread next season as he gets to play with all of the new toys from this off-season.