What Are the Odds Every Team in an NFL Division Makes the Playoffs?

The NFL updated its playoff format for the 2020 season to include a third wild card team (non-division winning playoff team). The NFC West has taken that as a sign that they should all try to make it this year. Although #2 seeds may not be huge fans of the change, this is great news for teams on the playoff bubble (which I’m now realizing has a whole new meaning in contemporary sports), fans who get to enjoy a more action-packed Wild Card Weekend, and data nerds like myself who are intrigued by the possibility of all four teams in an NFL division making the playoffs together.

But is this like, “It’s possible for a college football to go undefeated,” or is it more like, “It’s possible for a Major League Baseball team to go undefeated?”

Before we look forward, let’s start by looking backward:

Historical Review

The NFL Had Three Wild Card Teams Before

Before the new division alignment took effect for the 2002 season, the NFL had just three divisions per conference, mostly five teams each. And from 1990 onward, six teams in each conference made the playoffs, three division winners and three wild cards. So there was a twelve season window where it was possible for all three wild card teams to come from the same division.

And you know what’s crazy?

It happened.

Three times.

The ’94 and ’97 NFC Central and ’98 AFC East each snagged every wild card spot.

Okay, show’s over, it’s been done, right? Well not really. See, each of these divisions featured five teams, and the fifth team had a record of 6-10, 4-12, and 3-13 respectively, each missing the #7 seed by at least three games.

It’s not enough for a division to have good teams. It cannot have any bad teams.

Best Worst Team

What’s the closest a division bottom feeder has come to securing a top seven finish in their conference?

The 1989 Bengals and 2007 Eagles each finished at the bottom of the division but missed out on a top seven finish on tiebreakers alone.

So we’re looking at something that is unprecedented, but seems pretty possible. But what are the odds?

Probability Considerations

If NFL records were independent and random…

this would be a pretty easy problem.

1. At the end of the season, identify the division winners and consider the remaining twelve teams in the conference.
2. The top remaining team grabs the first wild card spot and decides the division going for the wild card sweep.
3. The chances one of the two remaining teams in that division has the best record of the remaining eleven teams is 2/11.
4. The chances the final division team has the best record of the remaining ten teams is 1/10.
5. There are two conferences, so the probability of seeing the wild card sweep in a given year is double that of a single conference.
6. 2/11 * 1/10 * 2 = 4/110 = 1/27.5

The chances in a given season would be 3.6% and you’d expect to see it happen once a generation or so.

But NFL records are very much not independent.

NFL Standings Are a Zero-Sum Game

This may sound elementary, but for a team to win, it must make its opponent lose.

There are 256 games in every NFL season. Each game has a winner and a loser. The combined records of the NFL at the end of the season will always be 256-256. (I am not dealing with ties. They complicate things tremendously and have a negligible impact.)

This is further complicated by the NFL schedule. Each team plays their division rivals twice each (six total games), all four teams from a division in-conference, all four teams from a division from the opposite conference, and the two teams in their conference not in the division they’re already scheduled to play who finished at the same division standing as them the previous year.

Simple enough, right? Not exactly. Because we have to account for this win-loss dynamic, instead of just taking the binomial distribution for 16 teams and calling it a day, we have 256 games we have to consider.

The number of different ways an NFL season can play out is 2²⁵⁶, or more than a trillion trillion trillion trillion trillion trillion. The number has 78 digits. Cannot stress enough that that’s a big number.

Among these are weird edge cases, like a season where the fourth team in a division goes 13-3 and misses the playoffs, or another where the fourth team goes 4-12 and makes it.

Trying to reach a rigorous mathematical answer on this is giving me fits, so a different approach is required:

Simulating an NFL Season in Excel

How Though?

1. Create a 32 x 32 grid with each team laid out along the rows and columns
2. If the column team and row team are designated to play against each other per the NFL scheduling rules, we randomly generate a 0 or 1. For in-division matchups, we generate two 0-or-1’s and add them to account for two games.
3. If it’s a 1, row team wins. 0, row team loses.
4. When the row and column team flip positions, just take 1 minus the result of their first meeting. So if the first matchup had a 0, this one has a 1. (For in-division, we take 2 minus…) This creates a reflection along the diagonal axis where the opposite result is recorded. We’re trying to avoid both teams taking credit for winning the same game.
5. At the end of each row, sum the results of the games.
6. Add a random number from 0-1 as a tiebreaker. (I know this isn’t tiebreak procedure, but the nested IF statements necessary to make it work are the stuff of nightmares. It helps as often as it hurts, so I’m just going to leave it be.)
7. Mark all division winners with a “Z”.
8. Then mark the top wild card team in each conference with a “Y”.
9. Then the next wild card team with a “X”.
10. And the final wild card team with a “W”.
11. If all teams in a division make the playoffs, put a 1. If not, put a 0.

Below you’ll see a simulated season where all four teams from Division A make the playoffs.

Limitations

One of the major limitations of this approach is that it assumes all games have exactly 50/50 odds. I appreciate the Any Given Sunday-esque sentiment, but this simulation does not account for the simple fact that some teams are better than others.

Now if we were trying to capture the odds a team would go 16-0, 50/50 odds would tell you it’ll happen once every 2,000 years or so. (The above image shows every single team finishing between 5-11 and 11-5.) But as luck would have it, we’re trying to identify weirdness in the middle of the pack. These teams are average and genuinely do have close to 50/50 odds against other average opponents, so that alone isn’t too big of a concern. Sure some games it might be 70/30 and others 30/70, but when trying to identify which 7-9 team ends up 9-7, it’s a somewhat moot point.

What actually does have an effect is strength of schedule. The team fighting for the final wild card spot from fourth in its own division has to play every other superior team in its division twice. It would be rather lucky to escape that 3-3, whereas the other fringe playoff team only has to play one better team in-division and could be sitting at a healthy 5-1 division record. That two game hole is a chasm in a 16-game season and would be very tough to overcome.

However, strength of schedule cuts both ways. Division rivals share eight out-of-division opponents each season. The clearest path for a whole division to make the playoffs together is if the eight teams they face are below average, but this sim doesn’t provide that opportunity.

So we’ve got our gameplan, how do we figure out the odds of it happening in a given season?

Simulating One Million NFL Seasons in Excel

A million? With copy-pasting and VBA Do While Loops, anything is possible.

Essentially, we copied our sim down a hundred times and summed the last column. Then we took that sum, added it to X, regenerated random numbers, and repeated 10,000 times. Tidy stuff.

So what were the results?

After 1,000,000 NFL seasons, the number of times a division sent all of its teams to the postseason was 40,606.

Meaning that in a given season, you have about a 4.06% chance of seeing one division lock up all three wild card spots.

The expectation would be that you’d see one about every 25 years or so, but 154 of the centuries we simmed didn’t have any, so no guarantees. We also had 98 centuries where it happened ten or more times, so maybe we’ll get lucky.

Or maybe the NFC West does it this year.