NFL Monte Carlo Playoff Probabilities

By Nick Citrone

Heading into week 7 the NFL Season is nearing its midpoint and an early playoff picture has begun to appear.  The 2015 NFL campaign has been the most polarizing in recent memory, with an unusually high five undefeateds sitting on top and a majority of the league (18/32) having earned two or fewer wins through week 6.  In terms of playoff odds it means the top teams already hold firm grasps on their spot in the postseason while the rest of the league claws at each other for a wildcard spot (or the AFC South crown).  Below I have used two team efficiency ratings (Football Outsider’s DVOA Rankings and Pro Football Focus’ Team Ratings) and microsoft excel to generate playoff probabilities for every team in the NFL.

Methodology:  Monte Carlo probability distributions are generated through repeated random sampling.  I start by importing DVOA and PFFs team efficiency ratings.  These metrics are created by professionals and essentially grade every NFL team on their performance in every game.  Using these measures of team skill, I assign the probability of the home team winning for all remaining NFL games, taking into account home field advantage.  Then I simply use those probabilities to simulate hundreds of potential seasons, keeping track of which 12 teams make the postseason in each simulation.  Each teams probability percentage is simply the number of times they made the playoffs in the simulation divided by the number of simulations run.  The numbers below are all after simulating 500 seasons with the given probability calculator.

NFL Monte Carlo Playoff Probabilities:

AFC East:  All three models agree the Patriots are still the class of the AFC East, but the 4-1 Jets are also recognized as a probable playoff team: all three models give the Jets at least a ⅔ chance to play postseason football.  The 3-3 Bills, on the other hand, are likely to miss the postseason despite currently holding sole possession of 7th place.

Team W L DVOA PFF Coin-Flip
New England Patriots 5 0 95.6% 94.4% 79.2%
New York Jets 4 1 80.2% 66.2% 68.2%
Buffalo Bills 3 3 32.2% 30.2% 29.0%
Miami Dolphins 2 3 4.8% 12.2% 22.0%

AFC South:  Alongside the always wild NFC East, the AFC South is one of only two divisions with no team given a 70%+ chance to make the playoffs in all three models.  The low probability sums in each of the three models indicate the South is unlikely to capture one of the two wildcard spots in the AFC.

Team W L DVOA PFF Coin-Flip
Indianapolis Colts 3 3 66.0% 44.8% 57.0%
Houston Texans 2 4 12.2% 35.0% 29.2%
Tennessee Titans 1 4 14.8% 19.2% 14.4%
Jacksonville Jaguars 1 5 8.6% 5.2% 9.8%

AFC West:  The Broncos already enjoy a  3.5 game lead in their division, which translates to a 90%+ playoff probability even when we don’t consider their #1 ranked defense.  Pro Football Focus apparently isn’t impressed with the Chargers, placing them dead last in their team efficiency ratings.

Team W L DVOA PFF Coin-Flip
Denver Broncos 6 0 92.8% 97.6% 93.6%
Oakland Raiders 2 3 13.2% 18.8% 23.6%
San Diego Chargers 2 4 14.8% 1.6% 13.6%
Kansas City Chiefs 1 5 4.0% 8.0% 5.6%

AFC North:  Sorry Ravens fans, but the Coin-flip probability model says Baltimore is in the worst position of all 32 NFL Clubs heading into week 7.  Being 5 games back in the AFC North and 1-4 in the AFC has a lot to do with that.  Meanwhile, both the DVOA and PFF models predict Pittsburgh will overcome the injury to Roethlisberger and the threat of the 6-0 Bengals to make the postseason.

Team W L DVOA PFF Coin-Flip
Cincinnati Bengals 6 0 97.0% 98.0% 92.6%
Pittsburgh Steelers 4 2 58.0% 60.2% 49.8%
Cleveland Browns 2 4 3.4% 4.4% 9.2%
Baltimore Ravens 1 5 3.0% 3.4% 3.0%

NFC East:  Monday’s dominating performance by the Eagles convinced the PFF and DVOA metrics that the Eagles are the favorite to win the NFC East, but the coin-flip model is quick to point out the NFC East is still basically a tossup at this point.  All four teams are within a game of 1st place and all have already won within the division.

Team W L DVOA PFF Coin-Flip
Philadelphia Eagles 3 3 54.2% 65.2% 36.8%
New York Giants 3 3 38.0% 12.6% 36.0%
Dallas Cowboys 2 3 14.8% 29.0% 30.6%
Washington Redskins 2 4 20.8% 7.4% 22.2%

NFC South:  Despite Atlanta’s week 6 loss at the Saints, the PFF and DVOA models still disagree on who is more likely to come out on top in the NFC South.  DVOA favors the undefeated Panthers while PFF prefers Devonta Freeman and the Falcons.

Team W L DVOA PFF Coin-Flip
Carolina Panthers 5 0 90.4% 93.8% 82.4%
Atlanta Falcons 5 1 85.6% 95.0% 77.4%
Tampa Bay Buccaneers 2 3 12.4% 3.0% 22.0%
New Orleans Saints 2 4 9.8% 6.8% 10.0%

NFC West:  How the mighty have fallen.  DVOA still believes the Seahawks are the 9th best team in Football, but it appears likely that won’t be enough to pull them out of the hole four 4th-quarter collapses have left them in.  DVOA is much less forgiving to the 49ers, rating them the worst team in Football through six weeks.

Team W L DVOA PFF Coin-Flip
Arizona Cardinals 4 2 88.8% 72.6% 62.8%
St. Louis Rams 2 3 29.8% 53.0% 31.2%
Seattle Seahawks 2 4 21.2% 12.6% 18.8%
San Francisco 49ers 2 4 3.0% 1.8% 17.4%

NFC North:  500 times the PFF model simulated the remainder of the NFL season.  500 times those seasons led to a postseason slate without the Lions.  PFF has the Lions as the 28th best team in the NFL, but spots 29-32 are filled with teams that have mustered at least two wins.  Green Bay might be the league's most injured team, but postseason football still seems to be a lock in Title Town.

Team W L DVOA PFF Coin-Flip
Green Bay Packers 6 0 98.6% 94.2% 91.2%
Minnesota Vikings 3 2 22.6% 47.8% 43.2%
Chicago Bears 2 4 7.2% 3.8% 10.2%
Detroit Lions 1 5 2.2% 0.0% 6.6%

Why Flipping Coins is Useful:  Using team skill ratings to weight win probabilities is without question more accurate than picking at random: the DVOA and PFF models have correctly predicted 68% and 70% of NFL games so far (although they were trained on the data set).  Why, then, is simulating weeks 7 through 17 with a 50% chance for each team in every game useful?  The answer is, surprisingly, because it tells us nothing about strength of schedule, offense, defense, special teams, quarterback play, etc.  Instead, blindly throwing darts at the future allows us an unprecedented look at the current standings.  In today’s fervorous rush to follow all 32 teams at once we use W/L record as a placeholder for current standings, but it is only the tip of the iceberg.  

To demonstrate this, let's take two teams with the a very similar record but very different coin-flip playoff probability: the 4-2 Pittsburgh Steelers and the 4-1 New York Jets.  The Jets are only ½ a game ahead of Pittsburgh, but, according to the model, are much more likely to make the playoffs (68.2% vs. 49.8%).  The ½ game is only one of many reasons for the 18% difference.  Pittsburgh is 2 games behind Cincinnati in the division; the Jets are only ½ a game behind New England for the lead in the AFC East.  The Jets are 1-0 within their division, the Steelers are 0-1.  Finally, the Jets are 3-0 in the AFC while the Steelers are 1-2.  The coin-flip probability model highlights these differences which are often hidden in weighted probability simulations.  

The probability gives a concise snapshot of the team's current standing.  You can compare the position of two teams across conferences simply by looking at their coin-flip playoff probability.  That is why flipping coins is useful.

Week 7 Predictions:

As a bonus, here are the probabilities assigned to each game using the two team efficiency ratings mentioned above.  Note my predictions are less bold than Cortana and other computer algorithms, this is intentional.  The team efficiency ratings I use are far from perfect (as evidenced by how much they disagree this week) and applying them too forcefully would skew my playoff probabilities.  It would be more reflective of the ratings than of current standings and future schedule.

Game DVOA Pick % PFF Pick %
Seahawks @ 49ers Seahawks 62% Seahawks 59%
Bills @ Jaguars* Bills 58% Bills 56%
Vikings @ Lions Lions 52% Vikings 62%
Jets @ Patriots Patriots 60% Patriots 63%
Falcons @ Titans Titans 50% Falcons 57%
Steelers @ Chiefs Steelers 54% Steelers 54%
Texans @ Dolphins Dolphins 59% Texans 54%
Buccaneers @ Redskins Redskins 61% Redskins 60%
Saints @ Colts Colts 57% Colts 56%
Browns @ Rams Rams 55% Rams 63%
Raiders @ Chargers Chargers 52% Raiders 64%
Cowboys @ Giants Giants 60% Cowboys 56%
Eagles @ Panthers Panthers 52% Panthers 57%
Ravens @ Cardinals Cardinals 69% Cardinals 62%

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