The New England Patriots are 9-3 and in first place in the AFC East, as well as the entire conference.
The Miami Dolphins are 7-5, second in the AFC East, and the current holder of the 6th and final playoff spot, winning a sixway tie due to their conference record of 6-3.
The Buffalo Bills are also 7-5, good for third in the AFC East, and are in 8th place in the conference, ahead of the clusterbomb that is considered the AFC North, with only the Chiefs separating them from the Dolphins.
Then there are the New York Jets at 2-10, but we don't talk about them. It's not polite.
With four games to go, the Patriots seem to be in great position to win the division, even while they're walking a tightrope against the other division leaders. New England holds the tie breaker against all three leaders, but they share the same record as the Broncos, have the same amount of losses as the Bengals, and are a game ahead of the Colts. In other words, the Patriots need to win out to get home field advantage.
But if we just want the Patriots to first win their division and clinch a playoff spot, they have a pretty straight path ahead of them. They have a remaining schedule of @Chargers, Dolphins, @Jets, Bills.
Let's look at their rivals.
In order for the Bills to win the division, they need to get through a final schedule of @Broncos, Packers, @Raiders, @Patriots. That's insane. They won both their games against the Jets and they split their season against the Dolphins. The Patriots have the early season victory in hand.
For the Bills to win the division, they need at least three victories, including the season finale against the Patriots, including three losses by the Patriots. If they don't beat the Patriots, they cannot win the division as if the Patriots lost three, but beat the Bills, they would share a 10-6 record, but the Patriots would hold the head-to-head tiebreaker.
The Patriots losing three, including against the Bills, would mean at least 2 divisional losses, making their divisional record a 3-3 at best, which would tie the Bills. This would lead to the next tiebreaker, record against common opponents. They currently both share a 6-3 record, with the Patriots still playing the Dolphins, Jets, and Chargers, while the Bills have the Broncos, Packers, and Raiders. In this hypothetical scenario, the Bills would wind up with the better record against common opponents and hold the tiebreaker.
If the Bills lose next week against the Broncos and the Patriots beat the Chargers, the Patriots will have a three game lead and the Patriots will need to lose out for the Bills to win the division. Regardless, the Patriots cannot knock the Bills out this week; the earliest will be if the Patriots beat both the Chargers and the Dolphins, and the Bills lose to one of the Broncos or the Packers. This is possible, if not probable.
If the Patriots split against the Chargers and the Dolphins, they will need the Bills to lose to both the Broncos and Packers to eliminate them from the division. Again, it's very likely the Bills will be out of the divisional race in two weeks.
Of course, this is all assuming the Dolphins can't keep pace, or surpass the Bills.
With Miami holding the head-to-head over the Bills, the Bills would need them to lose at least one of their final games (note: Miami and Buffalo split this season), The Dolphins finish the year against the Ravens, @Patriots, Vikings, and Jets, which is a much easier schedule than the Bills.
The Dolphins are a different issue for the Patriots. They hold the current head-to-head tiebreaker due to Week 1, and they already have three divisional wins; if the Patriots beat the Dolphins, then the Dolphins will need the Patriots to lose their other three games to force a tiebreaker at 10-6, which Miami would win due to divisional record.
If the Dolphins beat the Patriots, then they would hold the head-to-head tiebreaker and the Patriots would need to finish the season with a better overall record to win the title. If the Dolphins lose to the Ravens this week, and the Patriots beat the Chargers, then Miami would need to win out and the Patriots would need to lose out in order for the Dolphins to win the division.
Of course, in this situation, the Dolphins would be 10-6, along with the Patriots at 10-6. It would still be possible for the Bills to be 10-6 as well, but Miami would have the head-to-head tiebreaker against the Patriots win the division due to the best head-to-head record. In fact, the Patriots would finish in third, as the Dolphins (3-1) and Bills (2-2) would have a better record than Patriots (1-3) in this scenario.
If the Patriots beat the Dolphins, then Miami would need to win out and the Patriots to lose their other three games. This 10-6 tiebreaker would eliminate the Patriots as their divisional record (3-3) would be worse than the Dolphins and Bills (4-2). As this has the Bills beating the Patriots, the Bills can lose to any of the Broncos, Packers, or Raiders and still claim the division due to records against common opponents.
The reality is that the earliest the Patriots can clinch the division would be after beating the Chargers and Dolphins, assuming that the Bills lose to one of the Broncos or Packers- which would give the Patriots an 11-5 minimum record, while the Dolphins and Bills (assuming a Buffalo loss) couldn't crack 10-6.
The earliest the Patriots can win if Miami and Buffalo win the non-head-to-head matchups would be Week 16 after the Jets game. If the Bills beat the Broncos, Packers, and Raiders they will stand at 10-5 (and also be a ridiculously dangerous team), so the Patriots winning their next three would put them out of reach of a Week 17 head-to-head tiebreaker.
In all likelihood, the Bills will lose to either the Packers or the Broncos. The Patriots chances at a divisional crown will come down to the Week 15 rematch against the Dolphins. Let's just hope the Patriots win their next two games and seal another division title.
TL;DR: Fastest way to win the division is to beat the Chargers and the Dolphins, and watch the Bills lose to either the Broncos or Packers.