One came last November, when he decided to go for it on fourth-and-2 from the Patriots' 28-yard line while holding a six-point lead with 2:08 left at Indianapolis. Predictably, the attempt failed, Peyton Manning got the ball, and the Colts got the win.
Now, in trading Randy Moss, Belichick has again made what looks like an ill-advised gamble.
There is no disputing the Patriots are significantly weaker without Moss, that they have gotten rid of one of the best players on their roster and don't have an equal replacement.
After Monday night's blowout victory in Miami, the Patriots had surged back into top-contender status in a league that doesn't offer a clear-cut best team. After saying good-bye to Moss, they appear to have become more ordinary and a lot less threatening.
Did Moss, who had made his displeasure over his contract a public issue from the start of the season, do something to infuriate Belichick to the point where he simply couldn't tolerate having him around? Or, and this seems more likely, did Belichick simply do what he often does (what he did right before last season by sending defensive lineman Richard Seymour to Oakland) and cash out on a veteran while the getting was good? If so, the move is highly questionable given the third-round pick the Patriots received from the Vikings.
Is such a head-scratching transaction going to end up making more sense because the Patriots will get disgruntled standout San Diego Chargers receiver Vincent Jackson? Don't hold your breath on that one. Jackson wants $30 million in guaranteed money and is a behavioral risk to boot.
Even at 33, Moss is still one of the most dynamic playmakers in the NFL, which is why Brett Favre is anxious to begin throwing passes to him in Minnesota and why Tom Brady (even if he never admits as much publicly) can't be all that happy.
Moss' mere presence on the field requires opposing defenses to make certain they have an answer for him. And in having an answer for Moss, they leave questions for themselves regarding Wes Welker and other Patriot receivers.
But that win was driven by an inordinate number of big plays on special teams. Are the Patriots going to do that on a weekly basis? Doubtful. Just ask the Dolphins, whose Tuesday firing of their special-teams coach would strongly indicate that New England's success had a whole lot to do with their own failure in the kicking game.
Others who think shipping Moss out of town is a good idea cite the fact the Patriots won three Super Bowls before his arrival from Oakland. True, but the Patriots had a better defense during that run -- certainly a much stronger one than they have now.
The current version of the Patriots relies almost exclusively on offensive explosiveness to win games. Moss was a huge part of that mixture. Let's not forget the three touchdown catches he made through the first three weeks of the season, including that incredible, one-handed gem against the New York Jets. Let's not forget his ability to get open for the game-breaking play at any time.
Brady certainly won't.
Sure, he still has Welker, and second-year receiver Brandon Tate has shown promise after spending last season on injured reserve. He also has a new, exciting target in rookie tight end Aaron Hernandez, and the Patriots' passing attack is making greater use of the tight end than it has in previous years. However, tight ends benefit from Moss' ability to draw coverage just as any other New England pass-catcher. Someone with Hernandez's skills would clearly benefit more than previous tight ends who weren't as talented and, therefore, given a lesser role.
Expect opponents to adjust their coverage to focus on minimizing Welker and Hernandez. That should be a little easier to do now that they don't have Moss to worry about ... unless they have the Vikings on their schedule.