Just an FYI, drawing on the excellent work of /u/NFLPlayoffScenarios here. N.B. All of the rooting interests described below benefit the Patriots from the perspective of maximizing their seed, without reference to which other teams make the playoffs, with which seeds. It's conceivable, therefore, that you might nonetheless wish to root for some different outcomes on the basis of how other teams will do, in the hope of setting up the playoff matchups you feel are most favourable to the Patriots.

1. It's quite obvious that a Patriots win on Sunday over the Jets would be beneficial for the Patriots. Because of the chance that they fail to obtain one, it would be likewise beneficial for

2. the Jacksonville Jaguars to defeat the Houston Texans, ensuring that the Texans cannot finish with a better record than the Patriots.

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   Provided that either of the above two results occurs, we would like

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3. the Oakland Raiders to beat the Kansas City Chiefs. (If the Patriots have beaten the Jets, then this will give them a chance of capturing the top seed. Even if the Patriots have lost to the Jets, if the Texans have lost to the Jaguars, a Raiders victory has potential to benefit the Patriots for complex reasons involving a strength-of-victory tiebreaker between Texans and Ravens.)

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   Provided that the Patriots have defeated the Jets, we would also like

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4. the Denver Broncos to beat the Los Angeles Chargers, since in that case, if the Raiders also defeat the Chiefs, then the Patriots will gain the top seed in the playoffs.

   I don't expect that most of the above comes as news to you. However, you may not be aware of some of the games that the Patriots have a subtler interest in.

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   All of the remaining rooting interests apply only if the Patriots lose to the Jets (or may yet do so):

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5. Cleveland Browns to tie or beat the Baltimore Ravens (ensuring that the champion of the North will be seeded below the Patriots, based on overall record).

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   All of the remaining rooting interests apply only if, additionally, the Jaguars defeat the Texans (or may yet do so):

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6. Indianapolis Colts to beat the Tennessee Titans (ensuring that the champion of the South will be seeded below the Patriots based on head-to-head record, as the Patriots have defeated the Colts, but lost to the Titans).

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   The remaining rooting interests apply only if, additionally, the Ravens may yet defeat the Browns (or have already done so):

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7. Buffalo Bills to beat the Miami Dolphins. (This, along with the following three outcomes, will weaken the Texans' strength of victory. In the unlikely case that the Colts and Titans tie their game in the evening, this may help the Patriots gain a higher seed than the Texans.)

8. Philadelphia Eagles to beat the Washington Redskins

9. New York Giants to beat the Dallas Cowboys

10. Los Angeles Chargers to beat the Denver Broncos. (N.B. Although, if the Patriots win against the Jets, we will root for the Broncos to beat the Chargers, to give the Patriots a chance of winning the top seed, in the case that they have lost against the Jets, they will be unable to gain a higher seed than the champion of the West in any case, whilst, on the other hand, the Chargers beating the Broncos will weaken the Texans' strength of victory, as noted.)

Our interests in the latter games, especially, involve esoteric ties in the final standings that are quite unlikely to occur in practice, but even so, I figure it's always nice to have some interest in the outcome of a game your team is not directly involved in.