FOXBOROUGH, Mass. --With the team locked in a tight game against Miami, and in position to change its positioning in the AFC playoffs by winning its 2006 regular-season finale, Bill Belichick saw his Patriots pull closer to the Dolphins with a fourth-quarter touchdown — and sent backup quarterback Doug Flutie on the field to attempt the extra point. Via dropkick.

Later in that same game, with New England trailing by two and time about to expire, the Pats pulled within two points with another score — though on the subsequent conversion try, third-string QB Matt Cassel threw a pass that missed so badly it was obvious the sideline had been given the command to misfire.

It was six years ago, but it's a memory that remains relevant this week, as the Patriots enter the final game of the regular season with only their postseason seeding on the line — and at least some question about whether Belichick might be better off losing a game on purpose again.

The Pats wrapped up the AFC East title by beating Denver. They then secured a first-round bye by beating Miami. And they can wrap up the No. 1 seed, and homefield advantage throughout the conference tournament, by beating Buffalo this coming Sunday.

But because of the way the AFC playoffs are shaping up, there are reasons to think the Patriots might be better off losing this week, and entering the postseason as the second-ranked team behind either Pittsburgh or Baltimore. And it's because whichever of those teams doesn't win the AFC North is going to make a very dangerous No. 5 seed, even if the game is in Foxborough.

At this point, Houston is locked into the No. 3 seed, while the AFC West champion will be No. 4. That means the Texans will play a still-to-be determined wild card team, while the West winner will take on either the Steelers or the Ravens. (If the Ravens win next week, they win the division; if the Ravens lose and the Steelers win, Pittsburgh wins the division. The loser is the wild card.) Even with the teams yet to be determined, either Pittsburgh or Baltimore would be a significant favorite against the West champ (either Denver or Oakland), and is likely to win. Meanwhile, with its position locked in, Houston can use its season finale as a bye week to rest up for whichever opponent — Oakland, Tennessee or the New York Jets — is coming in a week later.

Houston has struggled lately, and is on its third quarterback of the season, though the league's fourth-ranked scoring defense is good enough to beat any of their three potential opponents on their home turf. And no matter what happens otherwise, if the Texans win their wild-card contest they're certain to play the second seed.

That's where the Patriots come in. If they were the No. 2 seed, the most likely scenario is that they would host T.J. Yates and the Texans, then have to travel to face either Pittsburgh or Baltimore in the conference championship game. If they were the No. 1 seed, however, the most likely scenario is to face either Baltimore or Pittsburgh in the divisional round, then face the other for the AFC title.

In terms of opponents, the No. 1 seed is a more difficult path, as it will most likely mean facing both of the conference heavyweights. But the No. 2 seed means traveling, and so it must be acknowledged that the Ravens were 8-0 at home (vs. 3-4 on the road) and the Steelers were 7-1 as hosts (vs. 4-3 as guests).

So if the Patriots were to choose a preference, the choice would be between a lighter schedule or the friendly confines of Gillette Stadium. On one hand it'd be a tall order to beat both Baltimore and Pittsburgh before facing the likes of a Green Bay or New Orleans in the Super Bowl. But on the other hand, the Patriots are 6-2 on the road this season, so they wouldn't be intimidated by being forced to travel.

Then, of course, there's the possibility that in this parity-stricken age of professional football, any team can beat any other and trying to pick your path is impossible.

“A bye is a bye,” Vince Wilfork said on Saturday. “We have had byes before, and it wasn't pretty; at the same time, we still have one more game to play.”

Whether they have one more game to win, however, may be up to Belichick's discretion again.

Dave D'Onofrio covers the Patriots for the New Hampshire Union Leader and Sunday News. His e-mail address is ddonof13@gmail.com.