It’s not a hat and T-shirt game, but it’s awful close.

The phrase was a favorite of former Patriots linebacker Tedy Bruschi. It was a game, explained Bruschi, where the stakes were so high that, after the winners came back to their locker room, they found a new hat and T-shirt hanging in their lockers that commemorated a milestone — division championship, conference title or Super Bowl win — because of the victory.

And despite last week’s ugly loss to the Saints in New Orleans, the Patriots can take a big step toward adding to their wardrobe on Sunday in Miami with a win over the Dolphins. A victory would put them at 8-4, and give them — at worst — a two-game lead in the division over their nearest pursuers (either Miami or New York) with only one division game remaining.

It would also allow the Patriots to post their first road win against a team that has more than one win.

“It’s a division rival, and they have some good football players who have been there for a while,” said quarterback Tom Brady when asked about Miami. “It’s a physical group and it’s a physical game and playing them on six days, everyone’s got to get in and try to get reinvigorated for the game.

“[Tuesday] was a day of reflection for everybody to get their mind back in the right perspective, but that’s right — we have to play better on road. You’re not going to do very good if you can’t take care of business on the road.”

And with New England playing one team with a plus-.500 record over the last month of the season, chances are good that after a win on Sunday, those hats and T-shirts could make for a very Merry Christmas in a week or two down the road in Foxboro.

“Everybody this time of year is playing for something that’s worth something,” said veteran running back Kevin Faulk.

Here are four other things worth keeping an eye on Sunday in Miami:

The Patriots’ pass defense. New England struggled mightily on Monday night against the Saints, suffering complete breakdowns in almost every area when it came to pass defense. The pass rushers had trouble getting any pressure on Drew Brees, the defensive backs couldn’t match up well with the New Orleans’ receivers and a lack of communication allowed the Saints to connect for several big plays (eight of 15 yards or more) in the passing game.

For the New England defensive backs, when it comes to bouncing back and regaining some confidence, there’s no better remedy than the Miami passing game. The Dolphins are averaging just 161.8 passing yards per game, the 30th best mark in the league.

“You just go about doing your job, like we’ve been doing every week. We just prepare for Miami as best that we can, and try to come out with a victory and play better than the previous week. And that’s every week,” said cornerback Leigh Bodden.

“We’re confident. There’s no need for us not to be. If you go in not confident, you’re not going to be successful. You need to still have confidence in yourself and the game and just prepare as well as we can for the game to get a win.”

New England’s quest for offensive consistency. It’s a strange statistical anomaly — the Patriots’ offense has managed to look really good early on, and then simply fade down the stretch. They are still one of the highest-scoring teams in the NFL with 307 points through 11 games (good for fourth-best in the league heading into Thursday night’s action), but they have just 101 second-half points in that span. On Monday against the Saints, they had just seven points in the second half.

Many of those second-half struggles come on the road. Aside from the relatively easy crush job they put on the Bucs in the “road game” in London, they have had major issues when it comes to scoring in the third and fourth quarter away from home. In their four road losses, the Patriots have been outscored 58-17 in the second half.

“I think that if we could put a finger on it, we’d be doing a great job of solving that problem,” Faulk told reporters this week. “But right now we’re still in the process of trying to figure out what’s going on. But that’s all you can do, you try to figure it out, and keep moving on and try to get better.”

Left tackle. Sebastian Vollmer has improved from last week, when he was out most of the time in the days leading up to the Saints game with what was being listed as a head injury. The rookie was inactive for the New Orleans game, but has practiced this week, and appears as though he might be able to go Sunday against the Dolphins.

That could lead to a tough decision for the New England coaching staff, which welcomed veteran left tackle Matt Light back for limited action for the first time since he suffered a knee injury in the loss to Denver on Oct. 11. Light rotated in in limited action against the Saints last Monday, splitting time at left tackle with Mark LeVoir. Vollmer does have some positional versatility, so if he did play, he could move to right tackle, and the Patriots could drop Nick Kaczur down the depth chart.

Regardless, if he is ready to go, Vollmer needs to be on the field — in a very short time, he’s proven that the New England offense is a better unit when he’s one of the primary blockers.

Miami defensive end Jason Taylor, who has traditionally looked at a matchup with Light in the same way a starving cartoon character looks at another person and sees a steak, said he didn’t get a whole lot of individual matchups against Vollmer when the Dolphins played in Foxboro earlier this season, was impressed by what he saw out of the rookie.

“Seeing him on tape and seeing him against us and having played a handful of plays against him, I think he’s going to be a good player. He’s a big, strong kid,” Taylor said. “I think he moves very well. I did hear about his story of not playing football his whole life and that whole thing and it’s promising when you see a guy who moves and plays as well as he does that young.

“He’s still kind of in his infancy as far as his football life is concerned. I’m not ready to say he’s Matt Light because I think Matt Light is a heck of a player, but he has the potential to be pretty good.”

Stopping Ricky. With Ronnie Brown sidelined, you would think that the dynamic Miami running attack has changed, but according to Patriots coach Bill Belichick, things look very much the same with Ricky Williams and Pat White back there. Since Brown’s injury, Williams has been a stud, posting three straight 100-yard games and picking up the slack for the missing Brown. And White remains a threat, as he did last month against the Patriots.

“I think Ricky Williams has really taken Ronnie’s spot there,” Belichick said when asked about the current state of the Miami running game. “I think when they had both players, they were comfortable with either one of them in the game, and if there was only one of them, then they were comfortable with that player in the game. So whether they shared the load or it was all Ronnie or all Rickey — based on the availability of the players — I think their offense is pretty much the same.

“They had the one Wildcat package with Ronnie and Ricky in the game with the speed sweep with Williams coming across the field. That looks like that’s died out and has been replaced with more of a Pat White package,” Belichick added. “They’ve built on that the last three weeks against Tampa, Carolina and then Buffalo. It looks to me like 95 percent of their offense is the same as it was with Ronnie and looks like they’ve maybe replaced a little bit of that Wildcat package with both of them in there with some other things, maybe the Pat White package.”