How the Patriots can clinch the AFC East
Control: Week 15; Patriots defeat the Texans and the Titans.
The Jets are the only other team in the AFC East still in contention and the only way for the Patriots to clinch the division prior to the week 16 match-up is if New England reaches more wins than is possible for New York. This scenario requires a Patriots victory and a Jets loss, or two New England victories to reach 12 on the year, making it impossible for the 5-loss Jets to match.
How the Patriots can clinch a first round bye
Control: Week 17; Patriots defeat the Texans, Titans, Jets, and Dolphins.
New England can't clinch a bye until the Broncos and Bengals square off in week 16. Even if the Patriots reach 12-2, and either the Broncos or Bengals fall to 10-4, Denver still holds the tiebreaker and the Bengals would still be in the running based on conference games. If the Patriots win the next three to reach 13-2, then either the Broncos or Bengals will have to fall to 10-5 for the Patriots to clinch a first round bye.
If the Patriots win out to reach 14-2, it's impossible for three teams to achieve 14-2 in the conference thanks to the Bengals and Broncos head-to-head, so the Patriots would get the 2nd seed as a minimum.
How the Patriots can clinch homefield advantage
Earliest: Week 16 Dreamland; Patriots defeat the Texans, Titans, Jets; AND Broncos AND Bengals lose next two of the next three games.
The Patriots don't have control over homefield advantage thanks to the defeat by the Broncos. If Denver wins out, they will have homefield advantage. The Patriots will need the two rivals to lose multiple games over the next three weeks to clinch prior to week 17.