On Friday, Belichick pulled back the veil:
"You know, I've been asked about that before. I think it's a coincidence really. I don't go into it with an attitude like, 'We have to have a left-footed punter.' I know it's been that way.
"Lee Johnson was here when I got here. We had Tom Tupa at Cleveland. Tom didn't punt in the NFL, he punted in college and we brought him in and he became our punter. Of course he punted for us here when I was at New England in '96. He was an excellent right-footed punter. I coached Dave Jennings at the Giants and he's one of the best punters that ever punted in the NFL. I had a long relationship with Sean Landetta, as well; that's another good right-footed punter.
"I don't really have any preference toward left-footed punters. I know it's worked out that way, I can't deny it. But, I've also had the opportunity to coach and be with a lot of good right-footed punters, too, and I was more than happy with them. I loved Tupa, loved Jennings, loved Landetta. Even going all the way back to when I was involved with the special teams at Baltimore, with David Lee and at the Lions with (Herman) Weaver and John Stufflebeem who we brought in who ended up with a long career in the Navy and didn't play professionally other than in training camp. They were all good right-footed punters, too.
"... I would say coincidence."
So there you have it. Now go and impress your friends.