How did the Dolphins' loss Monday night clinch the division for the Patriots?

The simple answer: The Pats had already clinched the sixth tiebreaker with the Jets, and the Dolphins' loss allowed them to clinch at least a tie in the fifth tiebreaker, to force the process to the sixth tiebreaker.

Now the breakdown: It may have made no sense to many that the Dolphins' loss clinched the division for the Patriots, because the only team still in contention with the Patriots was the Jets, not the Dolphins. Let's break it down.

To determine when the Patriots have clinched the division, one must look at the worst case scenario for the Patriots and the best case scenario for the Jets. Only if the Jets would still finish behind the Patriots in this scenario, have the Patriots clinched the division. Let's look at it from the perspective of BEFORE Monday night. All of Sunday's games had happened, so the Jets were (and actually still are) three games behind the Patriots with three games remaining.

If the Jets win out and Pats lose out, they'd finish tied at 11-5. Now for the tiebreakers.

1) head-to-head. If the Jets win out, they'll have beaten the Patriots in the second meeting, meaning the teams split the two head-to-head meetings.

2) division record. If the Jets win out and Pats lose out, both teams' division records would be 4-2.

3) record against common opponents. The Bills and Dolphins don't matter since we already know the Pats and Jets are tied in both head-to-head and division record. The other eight common opponents are the AFC South and NFC East. If the Jets win at the Cowboys and Pats lose to the Titans (which is part of the assumption when they both finish 11-5), both teams would have a 6-2 record against the AFC South and NFC East.

4) conference record. (Note: the reason common opponents come before conference in the tiebreaking order is because common opponents record is based on 8 games, to only 6 games for the conference.) Because the two teams are tied in the division, the only 6 conference games that matter for the tiebreak are the 6 AFC games outside the division. The Pats and Jets will both have gone 3-1 against the AFC South (Jets loss to Texans, Pats loss to Titans). The other two games are the games against the AFC North and West. The Pats beat the Steelers but lost at the Broncos. The Jets beat the Browns but lost at the Raiders. Clearly then, under this scenario of the Jets' winning out and the Pats' losing out, both would finish with a conference record of 8-4. Time for the fifth tiebreaker.

5) strength of victory. This is defined as the combined records of all the teams you beat. Many of the Pats' and Jets' victories have been and would have been against the same teams, so the only teams required for comparison of strength of victory are the ones the Pats beat whom the Jets didn't, and vice versa. The teams are:

for NE: PIT, HOU, BUF
for NYJ: CLE, TEN, MIA

The reason MIA is listed for NYJ is because the Jets swept the Dolphins, and under our scenario of both Jets and Pats finishing 11-5, Pats will have split with the Dolphins, so the Dolphins' record would be added twice to the Jets' strength of victory, but only once to the Pats'.

To calculate the worst case scenario for the Pats, to determine whether or not they have clinched, we must assume PIT, HOU, and BUF all lose out, and CLE, TEN, and MIA all win out. This would give the Jets the division title, on the strength of victory tiebreaker by just 1! However, this analysis was all from the perspective of BEFORE Monday night. Now that the Dolphins have lost a game, the best case scenario for the Jets is a tie in the fifth tiebreaker.

6) strength of schedule. Two teams in the same division only play two different games, the games against the two other divisions in their own conference (not their own division or the division where they're playing everyone). This season, the AFC East is playing the AFC South, so the two different games for the Jets and Pats would be the ones they played against the AFC North and AFC West. Last year, the Pats won the division, meaning they played 1st place Pittsburgh and 1st place Denver this year. Meanwhile, the Jets finished last in the division and played 4th place Cleveland and 4th place Oakland this season. In the current standings, the Browns cannot catch the Steelers and the Raiders cannot catch the Broncos, so the Pats' strength of schedule was already guaranteed to be better than the Jets', prior to Monday's game.

Back to the simple answer from the top: The Pats had already clinched the sixth tiebreaker with the Jets, and the Dolphins' loss allowed them to clinch at least a tie in the fifth tiebreaker, to force the process to the sixth tiebreaker.