As Week 11 has wrapped up in the NFL, two teams still remain undefeated (New England Patriots, Carolina Panthers) and a couple divisions have entered into gridlock for first place (AFC South, NFC East). Currently, the playoffs have shaped up to be the following:

• AFC Playoffs
  • #1 Seed: New England Patriots (10-0; East Leader)
  • #2 Seed: Cincinnati Bengals (8-2; North Leader)
  • #3 Seed: Denver Broncos (8-2; West Leader)
  • #4 Seed: Indianapolis Colts (5-5; South Leader)
  • #5 Seed: Pittsburgh Steelers (6-4)
  • #6 Seed: Kansas City Chiefs (5-5)
• NFC Playoffs
  • #1 Seed: Carolina Panthers (10-0; South Leader)
  • #2 Seed: Arizona Cardinals (8-2; West Leader)
  • #3 Seed: Green Bay Packers (7-3; North Leader)
  • #4 Seed: New York Giants (5-5; East Leader)
  • #5 Seed: Minnesota Vikings (7-3)
  • #6 Seed: Atlanta Falcons (6-4)

With six games to go for all teams, every team is still technically in the hunt for making the playoffs. Here we present our NFL power rankings and projected final standings. Similarly, since the projection is based on a beta-binomial distribution, we obtain probabilities for each team making the playoffs.

Power Rankings

First we take a look at the Power Rankings. We use a combination of a Binomial distribution (Bradley-Terry model) and a Beta scoring distribution to place a weight on winning a proposed match-up. The resulting r-square term is low, at 0.4036. This is indicated by the number of incorrectly fit games from the previous 160 NFL match-ups this season.

Beta regression fit (red) to the first 160 NFL games played (blue) during Week 1 through Week 11 of the 2015 NFL season.

For the 160 games played, our model improperly fits 33 games; primarily missing both Bengals losses, the Packers loss to the Lions at home, two Jets losses and two Bills losses. Most of the other losses are narrow margin losses and contained within the bounds of the model.

Using this scoring model, we use the predicted percentage of points as weights in each match-up in predicting the outcome of the game. This is through the Bradley-Terry model.

The rankings are as follows.

Rankings of the 32 NFL teams after Week 11 of the 2015 NFL Season (November 24th, 2015).

We see the Patriots and Panthers sitting atop the rankings, which is expected. With an unexpected slew of wins, the Packers and Bengals tumbled down  from similar spots, but manage to hold onto spots three and four, thanks to several other key teams losing. At the bottom of the rankings are the teams found near the basement of each division.

Predicting the Final Standings and Playoff Match-Ups

Using the rankings system, we can extract the probabilities of winning for each match-up and use a Markov-Chain Monte-Carlo (MCMC) process to simulate the remaining 96 games of the season. This will give us an expected final standings to the season.

Projected 2015 NFL Standings based on MCMC.

This gives us an expected playoffs for the AFC: Broncos – Steelers, Colts – Chiefs, Patriots and Bengals bye; NFC: Packers – Seahawks, Giants – Vikings, Cardinals and Panther bye. However, it does not give us probabilities for making the playoffs. Taking a look at the 100,000 simulations of the remaining 96 games, we obtain the following estimated probabilities of making the playoffs.

Projected NFL Standings with Probability of Making the Playoffs (PMP) after Week 11 of the 2015 NFL Season.

Here, the highest probabilities and expected wins suggest that the playoffs will be the following:

• AFC Playoffs
  • #1 Seed: New England Patriots (100.00%)
  • #2 Seed: Cincinnati Bengals (98.8458%)
  • #3 Seed: Denver Broncos (97.9140%)
  • #4 Seed: Indianapolis Colts (53.2156%)
  • #5 Seed: Pittsburgh Steelers (58.7271%)
  • #6 Seed: Buffalo Bills (49.7072%)
• NFC Playoffs
  • #1 Seed: Carolina Panthers (99.9968%)
  • #2 Seed: Arizona Cardinals (94.7989%)
  • #3 Seed: Green Bay Packers (96.0079%)
  • #4 Seed: New York Giants (49.2721%)
  • #5 Seed: Minnesota Vikings (75.3747%)
  • #6 Seed: Atlanta Falcons (51.4963%)