When the Seahawks defeated the Browns on Sunday, it was announced broadly that the Seahawks had clinched a playoff berth. Nowhere, however, was it explained how this was determined. It appeared to be taken on faith, generally without a source, though in some cases the information was cited as coming from “the league”. This is not good enough for me.

When the same thing happened in 2013, I took it upon myself to investigate, and produced How the Seahawks Clinched. At the time I imagined that it couldn’t get much more complicated to prove that a team had clinched a playoff berth. I was wrong. Hold on for the ride.

Let’s start by excluding the scenario where the Seahawks win the NFC West division. As of this writing it is moot due to Arizona’s victory on Sunday night, but when the Seahawks-Browns game was completed, it was still theoretically possible. (Obviously had the Seahawks won the NFC West, they would have had a playoff berth.) This means that we only have to concern ourselves with how the Seahawks clinched a wildcard berth.

Because the Seahawks are 9-5, they can only be defeated for a wildcard berth by a team that has lost at most seven games and isn’t going to win its division. Not counting the NFC East for the moment, this limits the teams to Green Bay (10-4), Minnesota (9-5) and Atlanta (7-7).

Now let’s dispatch the NFC East. Washington can go 9-7, but if they do then they win the division title and thus aren’t part of wildcard consideration. Philadelphia could also have gone 9-7 had they not lost to Arizona on Sunday night (which occurred after the Seahawks clinched). However, in order for the Eagles to have finished 9-7, they would also have had to have defeated Washington next weekend. In this case, Washington would do no better than 8-8, Philadelphia would win the NFC East, and Washington would not be part of the wildcard picture. To summarize, no NFC East team can qualify for a wildcard position.

This leaves three detailed scenarios to consider, which I will cover in increasing order of complexity.

The first and simplest scenario is where Seattle wins (or ties) at least one more game or Atlanta loses (or ties) at least one more game. If Seattle wins or ties one more game, it is at least 10-6 (or 9-6-1) and Atlanta’s theoretical 9-7 best is not good enough. Similarly, if Atlanta loses (or ties) at least one more game, it can finish no better than 8-8 (or 8-7-1) so Seattle’s theoretical 9-7 worst is good enough. In either case Seattle is guaranteed one of the two wild card slots, and the other goes to either Minnesota or Green Bay (whichever of these two doesn’t win the NFC North).

As a result of this, in the remaining scenarios we only have to consider cases where Atlanta wins out and Seattle loses out and thus they both finish 9-7.

The second scenario is where Minnesota wins (or ties) at least one more game. In this scenario, Minnesota and Green Bay are both 10-6 (or 9-6-1) or better and Atlanta and Seattle are both 9-7. The better of Minnesota and Green Bay wins the NFC North, and the worse gets the higher wild card position, i.e. 5th seed overall. This leaves Atlanta and Seattle competing for the final wild card position.

Atlanta and Seattle didn’t play each other, so there’s no direct head-to-head, and they are in different divisions, so intra-divisional records aren’t compared. The next tiebreaker is conference record; in this scenario both teams would be 6-6. After that the next tiebreaker is record against common opponents, with a minimum of four. It turns out that Atlanta and Seattle have exactly four common opponents this year — Carolina, Dallas, Minnesota, and San Francisco — and the Seahawks are 4-1 (3-1 if you count the 49ers only once) while the Falcons are 1-3. Even if you include the Panthers a second time, and the Falcons defeat them in the rematch next weekend to finish 2-3 (which they need to do in order to finish 9-7), it’s not good enough. So the Seahawks win this tiebreaker and are in the playoffs.

The third scenario is where Minnesota loses both of its remaining games, leaving them tied with Atlanta and Seattle at 9-7. Figuring out who wins this three-way tiebreaker is quite involved. None of these teams defeated both of the other two, so there’s no winner based on sweeping the head-to-head games. Minnesota would also have a 6-6 conference record in this scenario, so that doesn’t help either. And these three teams do not play at least four common opponents in 2015.

The next step in the tiebreaker is strength of victory. This is where things get really gnarly. Strength of victory involves taking the combined won-lost-tied records of all of the teams that each team defeated and computing an aggregate won-lost-tied percentage. This means that even a meaningless Week 17 game like Chicago vs. Detroit could have an effect on the tiebreaker because it could improve one team’s strength of victory at the expense of another.

The good news is that who wins the three-way tiebreaker amongst Atlanta, Minnesota, and Seattle is moot as it affects the Seahawks playoff chances. Here’s why: Let’s assume that one of the three teams has the best strength of victory. If it’s the Seahawks, then they win the 5th seed by virtue of this tiebreaker. And if it’s not the Seahawks, then either Atlanta or Minnesota wins the 5th seed, leaving the Seahawks in a two-way tie with the other team to determine the 6th seed.

If Minnesota wins the three-way tiebreaker, then Atlanta and Seattle are competing for the 6th seed. This is the same as the second scenario, where we’ve already shown that Seattle wins over Atlanta by virtue of record against common opponents. If Atlanta wins the three-way tiebreaker, then Minnesota and Seattle are competing for the 6th seed, which Seattle takes on the basis of its 38-7 victory over Minnesota on December 6th.

Even in the unlikely case that no team won the strength of victory tiebreaker (and I’m not even sure if this is mathematically possible at this point), eventually one of the three teams would have to win one of the lower tiebreakers — coin toss, anyone? — and the above logic still applies: Either the Seahawks win the three-way tiebreaker and get the 5th seed, or they’re competing one-on-one against either Atlanta or Minnesota for the 6th seed and win that two-way tiebreaker.

So to recap, in any season-ending scenario that was possible at the time that the Seattle-Cleveland game ended on Sunday afternoon, the Seahawks would have a playoff berth. Q.E.D. And phew!

[Updated 2015-12-24: Added image and made minor text edits.]