FanPost

Possible playoff seeds for every possible record

It's late enough in the season that people are working through playoff scenarios. If the Seahawks finish 13-3, they're likely to get this or that seed. But let's back up several months (or warp ahead to the next season) and ask, if you know that a team is going to finish with a particular record, what playoff seed (or out entirely) could that possibly lead to? Or better yet, can we concoct a particular way that the season could have played out that would result in that particular record being that particular seed?

I'm going to insist on a rule of no ties. This isn't soccer, and most Americans hate ties, except for Bud Selig.

While I don't explicitly cite it below, much of the analysis appeals to the pigeonhole principle. Basically, if at least kn+1 wins are divided among n teams, then some team has at least k+1 of them. The same applies to losses. For example, if three teams have 10 wins among them, then at least one of the teams won at least four games.

How NFL schedules work

Let's start by explaining how the NFL schedule works. The NFL has 32 teams, divided into two conferences, each of which has four divisions of four teams each. Each team plays 16 games in a season. Six of those games are two each (home and away) against the other three teams in their own division. Each division is paired with one from the other conference and each team plays all four of the teams in that division. Each division is also paired with another division in their same conference, and each plays the four teams in that division as well. Division pairings rotate from one season to the next, so each team is guaranteed to play a team from the other conference every fourth year and other divisions in their own conference every third year.

The final two games are against other teams in your own conference not in the division that yours is paired with. Rather, you play the teams that finished in the same rank within the division in the previous year. For example, the four division winners in a conference are all guaranteed to play each other next year.

This is a clean, symmetric way to schedule teams. It means that for two teams in the same division, they'll play each other twice, and 12 of their remaining 14 games will be against common opponents. For teams in paired divisions, they'll play each other once, and at least 9 of their remaining 15 games are against common opponents.

So, on to the possible records:

16-0: #1 or #2

This one is pretty simple to demonstrate. All it takes is for two teams in the same conference that don't play each other to both go undefeated. This year, for example, that could be the Seahawks and Bears. One if them gets the #1 seed, and the other the #2 seed.

It's not possible for an undefeated team to rank lower than the #2 seed. A team that goes undefeated is guaranteed to win the division, as that involves handing each of the division opponents two losses. It is not possible to have three division winners all go undefeated, as some two of them would be in paired divisions, and thus play each other.

15-1: #1, #2, #3, #4, #5, or #6

A team that goes 15-1 is guaranteed to make the playoffs, but could end up as literally any seed at all. Suppose, for example, that the Seahawks, Vikings, Eagles, and Saints had each won all of their games, except against each other. Among those four teams, the home team always won. All four teams would finish 15-1. Four 15-1 division winners means that the #1, #2, #3, and #4 seeds are all 15-1.

Alternatively, suppose that the Seahawks, Cardinals, Packers, and Bears had each won all of their games except against each other. Among those four teams, the home team always won. That would mean two divisions that each had a pair of 15-1 teams. The two 15-1 teams that didn't win their division would be the wild cards, and the #5 and #6 seeds in some order.

15-1 is enough to guarantee a playoff spot, however. If it weren't, then we'd need to have at least three 15-1 or better teams that didn't win their division. If two of those are in the same division, then those two plus the division winner would be three 15-1 or better teams in the same division. That would mean at most 3 losses among the three teams, even though they play six games against each other.

Otherwise, you'd need three divisions in a conference to each have a 15-1 team that didn't win the division. The only team to be 15-1 without winning your division is for two teams to split their games against each other and win all the rest of their games. But you can't have three teams from different divisions all do that at once, as some two of those divisions will be paired with each other, so that two teams that must win all non-division games play each other.

14-2: #1, #2, #3, #4, #5, #6, or out

Suppose that the Seahawks, Rams, Saints, Falcons, Packers, Lions, Giants, and Redskins each won all of their games, except against each other. In games between any two of those teams, the home team always won. All eight teams would finish 14-2. That's your six playoff teams, plus two 14-2 teams that didn't make the playoffs. And quite a workout for the NFL tiebreaker procedures to figure out which teams landed where.

6-10: #1, #2, #3, #4, #5, #6, or out

Suppose that in every cross-conference game, the NFC team wins. Also, whenever two AFC teams play each other, the home team wins. The entire AFC then finishes 6-10. That's all of your playoff seeds, plus whoever is out.

13-3, 12-4, 11-5, 10-6, 9-7, 8-8, 7-9: #1, #2, #3, #4, #5, #6, or out

If 14-2 or 6-10 can land you with any seed at all, then it shouldn't be surprising that all of the records in between can. But let's give specific ways that they can for completeness. For 10-6 or better, take the 14-2 example and give the eight dominant teams all the same, other record against the AFC. For 10-6 or worse, take the 6-10 example and give all teams in the AFC the same, other record against the NFC.

5-11: #2, #3, #4, #5, #6, or out

That's right: you could have a 5-11 team get a bye. Suppose that in all non-divisional games involving an NFC West team, the NFC West team wins. In all non-conference games not involving an NFC West team, the AFC team wins. In all games between an NFC South team and an NFC East or North team, the NFC South team wins. In all other games, the home team wins. That would land the entire NFC West at 13-3, and the entire rest of the NFC at 5-11. That means three 5-11 division winners, which would be the #2, #3, and #4 seeds in some order. It would also mean that a 13-3 team misses the playoffs entirely.

Alternatively, let's suppose that the Seahawks, Buccaneers, Bears, and Redskins each win all of their games, except against each other. In non-conference games not involving one of those four teams, the AFC team always wins. In all other games, the home team wins. Of the twelve NFC teams who didn't win their division, six would be 5-11 and six would be 4-12. Two of the 5-11 teams would be the #5 and #6 seeds.

Showing that at 5-11 team can't get the #1 seed is easy enough. There are 96 games played among teams in a conference, so all of the teams in a conference must total at least 96 wins. That's an average of 6 wins per team, so someone must win at least six games.

4-12: #3, #4, #6, or out

Suppose that all teams in the AFC East and AFC South lose all of their games, except when they play each other. In all other games, the home team wins. Those two divisions would each have two 4-12 teams and two 3-13 teams. That gets you two 4-12 division winners, which will be the #3 and #4 seed in some order.

A 4-12 wild card doesn't have such a symmetric way to concoct it. Suppose that the Seahawks, Saints, Lions, Giants, and Packers each win all of their games, except when they play each other. In all non-conference games not involving one of those five teams, the AFC team wins. In all other games, the home team wins. The five dominant teams would obviously be the top five seeds. Meanwhile, you'd end up with the Cardinals, Rams, 49ers, Panthers, Buccaneers, Falcons, Vikings, Redskins, and Cowboys all at 4-12 exactly, while the Eagles go 3-13 and the Bears 2-14. One of the many 4-12 teams would get the #6 seed.

In order for a 4-12 team to be a #1 or #2 seed, you'd need at least three division winners to go 4-12 or worse. Two of those divisions must be paired with each other. Thus, you'd have 8 teams that each play 10 games among themselves (six in their own division and four against the other), so those teams must average at least 5 wins each. Therefore, at least one of the teams wins at least 5 games.

For a 4-12 team to be a #5 seed, you'd need all twelve teams that don't win their division to go 4-12 or worse. Thus, you'd have at most 48 wins among those twelve teams, and so most 48 conference wins. A conference plays 96 intra-conference games per season, so the four division winners would need at least 48 conference wins among themselves. That requires them to all go 12-0 in the conference, which is impossible, as two pairs of them play each other because their divisions are paired.

3-13: #4 or out

Suppose that all AFC East teams lose all of their non-divisional games. In all other games, the home team wins. The four AFC East teams would all be 3-13. Whoever wins the division gets the #4 seed.

In order for a 3-13 team to get a #3 seed or better, you'd need at least two division winners that were 3-13 or worse. Each division plays 12 intra-divisional games, so the only way for a division winner to be 3-13 or worse is for all teams in the division to go 3-3 in the division and 0-10 outside of it. But two divisions in the same conference can't do that at once because each team plays one team from the other division.

In order for a 3-13 team to get a wild card, you'd need the 10 teams that miss the playoffs to all be 3-13 or worse. Thus, you have at most 33 wins among 11 teams. That means at most 33 conference wins among 11 teams. Each conference plays 96 intra-conference games in a season, so the other 5 teams must have at least 63 wins within the conference. Thus, at least one team wins 13 games within the conference, which is impossible, because each team only plays 12 games against conference opponents.

2-14, 1-15, or 0-16: out

Each division plays 12 games within the division, so the teams in a division add up to at least 12 wins. That's an average of 3 wins per team, so some team wins at least 3 games. If it's impossible for a 3-13 team to get a wild card, then it's also impossible for worse records.