Welcome to this week's edition of playoff probabilities, now complete with bonus graphics! As always, these numbers come courtesy of Chris Cox at NFL-forecast.com and are generated with the help of the NFL-Forecast software app, which uses the win probabilities generated by the team efficiency model to simulate the NFL season 5,000 times. And if you don't buy the game probabilities from Advanced NFL Stats, you can tweak them as much as you like to generate your own playoff projections. I encourage everyone to download the app and test out your own scenarios.
How 'bout them Giants? In the most exciting game of the year thus far, Eli Manning drove the Giants to victory over the Patriots, giving New York a two game lead over their nearest opponent in the NFC East. At #9, the Giants sit relatively high in the rankings, yet they're projected to win the East in only 55% of simulations—less often than both the Chargers and the Ravens, neither of whom are even in sole possession of first place in their divisions.
A lot of this comes down to the degree of difficulty of the Giants' upcoming games. Over the weekend, I heard a lot of sports chatter about how tough their remaining schedule is, and the team efficiency rankings bear this out. The chart below lists the average GWP of each team's remaining opponents:
As you can see, the conventional wisdom is right on this one: the Giants have the toughest schedule ahead of them of any team by far, with their remaining opponents averaging .601 GWP. As a result, the model expects them to win an average of just four more games over the rest of the season.
High-Leverage Games of the Week
Pittsburgh at Cincinnati | Sunday, November 13 | 1:00 pm
| Playoff Prob. | CIN Win | PIT Win |
 PIT | 78 | 96 |
 CIN | 60 | 28 |
If the playoffs started today, Cincinnati would be the #1 seed in the AFC, but the model is not yet convinced of their viability as a playoff contender. The Bengals have yet to play a team ranked in the top ten in GWP, but beginning with this Sunday's game against the Steelers, they embark on a very challenging stretch of games which should give us a better sense of their true potential.
Regardless of whether you consider the Bengals to be a legit contender, competition for the AFC North title is projected to be intense. As expressed in this nifty chart, presented here in a form too small to be read by human eyes (click to embiggen), we can use Brian's game probability model to estimate the joint probability of Baltimore and Pittsburgh each finishing with a certain number of wins:
Baltimore's number of wins are along the horizontal axis, Pittsburgh's along the vertical, and the middle contains the joint probability of each combination. The marginal probabilities of either team finishing with a certain number of wins are listed in bold in the bottom row and rightmost column, and at the very bottom in large numbers is the total probability of one team finishing ahead of the other. (Blank cells have probability zero; cells that contain "0.0" have a non-zero probability that was rounded down.)
So what do we learn? For one, that Cincinnati is going to have to perform very well over the rest of the season if they want to win the North—the model projects that either the Ravens or the Steelers will finish the season with 11+ wins 92% of the time.
That said, while a win on Sunday won't make Cincinnati the favorite to win the division (it would actually help the Ravens' chances most of all), it does have significant upside potential for their Bengals, raising their probability of a wild card berth to 45% and their overall playoff probability to 60%.
New England at New York Jets | Sunday, November 13 | 8:20 pm
| Playoff Prob. | NYJ Win | NE Win |
 NE | 66 | 91 |
 NYJ | 66 | 32 |
After back-to-back losses, the Patriots find themselves in a three-team tie atop the AFC East. And like last week's game between the Jets and the Bills, the outcome of this week's matchup will have large implications for the division race. There is a crowded wild card field in the AFC, with each of the three leaders in both the East and North having chances of greater than 20% at a wild card berth. Given that, neither team will want to lose ground here.
A New York victory would move the Jets into first place and turn the division race into a true toss-up between themselves, the Patriots, and the Bills, with each team having about a one-in-three chance of winning the division. A Patriot win on the other hand would put the Patriots back on top of the East, giving them a 66% chance to win the division. The Jets meanwhile would fall behind, with their chances of a division title dropping to only 6%.
News & Notes
- The model projects either the Texans or the Packers as the Super Bowl champion in over 48% of simulations. Place your bets now.
- The Colts' chances of winning the Andrew Luck Sweepstakes are up to 82%. My chances of making it through the season without using the phrase "the Andrew Luck Sweepstakes" have dropped to 0%.
| AFC EAST | ||||
| Team | 1st | 2nd | 3rd | 4th |
| NE | 56 | 29 | 15 | 0 |
| NYJ | 23 | 38 | 39 | 1 |
 BUF | 21 | 33 | 45 | 1 |
 MIA | 0 | 0 | 2 | 98 |
| AFC NORTH | ||||
| Team | 1st | 2nd | 3rd | 4th |
 BAL | 61 | 29 | 9 | 1 |
| PIT | 32 | 53 | 14 | 1 |
| CIN | 7 | 17 | 69 | 7 |
 CLE | 0 | 1 | 7 | 92 |
| AFC SOUTH | ||||
| Team | 1st | 2nd | 3rd | 4th |
 HOU | 99 | 1 | 0 | 0 |
 TEN | 1 | 72 | 27 | 0 |
 JAC | 0 | 27 | 70 | 3 |
 IND | 0 | 0 | 3 | 97 |
| AFC WEST | ||||
| Team | 1st | 2nd | 3rd | 4th |
 SD | 65 | 22 | 10 | 2 |
 OAK | 21 | 31 | 31 | 17 |
 KC | 10 | 30 | 32 | 28 |
 DEN | 4 | 16 | 27 | 52 |
| NFC EAST | ||||
| Team | 1st | 2nd | 3rd | 4th |
 NYG | 55 | 28 | 14 | 3 |
 DAL | 31 | 35 | 27 | 7 |
 PHI | 13 | 31 | 43 | 13 |
 WAS | 1 | 5 | 17 | 76 |
| NFC NORTH | ||||
| Team | 1st | 2nd | 3rd | 4th |
 GB | 90 | 9 | 1 | 0 |
 DET | 9 | 65 | 27 | 0 |
 CHI | 1 | 27 | 71 | 1 |
 MIN | 0 | 0 | 1 | 99 |
| NFC SOUTH | ||||
| Team | 1st | 2nd | 3rd | 4th |
 NO | 80 | 18 | 2 | 0 |
 ATL | 18 | 62 | 17 | 4 |
 TB | 1 | 14 | 49 | 36 |
 CAR | 0 | 7 | 32 | 61 |
| NFC WEST | ||||
| Team | 1st | 2nd | 3rd | 4th |
 SF | 100 | 0 | 0 | 0 |
 SEA | 0 | 38 | 32 | 30 |
 ARI | 0 | 29 | 36 | 35 |
 STL | 0 | 32 | 32 | 35 |
| AFC Percent Probability Playoff Seeding | |||||||
| Team | 1st | 2nd | 3rd | 4th | 5th | 6th | Total |
| HOU | 32 | 36 | 26 | 4 | 0 | 0 | 99 |
| BAL | 36 | 16 | 8 | 1 | 22 | 9 | 92 |
| PIT | 14 | 13 | 5 | 0 | 46 | 12 | 90 |
| NE | 10 | 18 | 26 | 2 | 6 | 16 | 79 |
| SD | 1 | 2 | 7 | 56 | 0 | 1 | 66 |
| NYJ | 2 | 6 | 14 | 2 | 6 | 19 | 48 |
| BUF | 2 | 6 | 11 | 2 | 6 | 15 | 42 |
| CIN | 2 | 3 | 2 | 0 | 12 | 19 | 39 |
| OAK | 0 | 0 | 2 | 18 | 0 | 1 | 22 |
| KC | 0 | 0 | 0 | 9 | 0 | 1 | 10 |
| TEN | 0 | 0 | 1 | 0 | 1 | 5 | 7 |
| DEN | 0 | 0 | 0 | 4 | 0 | 0 | 5 |
| JAC | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| CLE | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| MIA | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| IND | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| NFC Percent Probability Playoff Seeding | |||||||
| Team | 1st | 2nd | 3rd | 4th | 5th | 6th | Total |
| GB | 78 | 12 | 1 | 0 | 9 | 1 | 100 |
| SF | 14 | 47 | 23 | 15 | 0 | 0 | 100 |
| NO | 1 | 16 | 32 | 32 | 2 | 4 | 86 |
| DET | 4 | 3 | 1 | 0 | 53 | 19 | 80 |
| NYG | 3 | 13 | 18 | 20 | 3 | 9 | 67 |
| CHI | 0 | 0 | 0 | 0 | 23 | 35 | 60 |
| DAL | 0 | 6 | 12 | 12 | 3 | 12 | 46 |
| ATL | 0 | 2 | 8 | 8 | 6 | 12 | 36 |
| PHI | 0 | 0 | 3 | 9 | 1 | 6 | 19 |
| WAS | 0 | 0 | 0 | 1 | 0 | 1 | 2 |
| TB | 0 | 0 | 0 | 1 | 0 | 1 | 2 |
| CAR | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| SEA | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| ARI | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| MIN | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| STL | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Considering how likely it is that Green Bay will get the #1 seed and San Fransisco the #2 seed in the NFC, that makes a significant impact on the other playoff teams' postseason success depending upon seeding pairings.
Specifically, the #3 seed is vastly more desirable than the #4 seed, and the #5 more than the #6 (as the #6 is locked to play GB if they advance, whereas #5 has a chance to avoid GB). Obviously this is the way the seedings are intended to be, but I think this year it has the potential to be a much more significant difference than normal.
Man, that heat graph really takes me back! Check out this one from the 2006 season.
Fantastic post. I was just scribbling together a post about CIN and Josh just did all the hard work for me.
An interesting thing about the PIT-BAL race is that they've both won a strenth-of-schedule game so far (BAL over NYJ, PIT over NE), but despite being in 1st place last year, PIT draws KC and BAL draws SD. I think SD is the much better team despite the fluky loss to KC.
Why average OppGWP instead of median? Average makes sense for normalizing stats that might scale more smoothly with opponent strength (YPA, SR%, etc.) but for # of games won, a game against a particularly strong team can lose you at most 1 game, regardless of how strong they are (and vice versa for particularly weak teams.)
A quick spreadsheet to show the difference: https://docs.google.com/spreadsheet/ccc?key=0At2xGu_ne0lcdGZjZjBlN0pLNTkwakJLMHNGa3NFS0E
James: That's a great point. I hadn't realized how often San Francisco makes it in as the #2 seed.
Brian: Nice! I must have seen that graph at some point in the long, long ago and filed it away for inspiration to strike.
Anon: As for mean vs. median (though to be honest, I didn't give it that much thought beforehand), while it's true that as you say, a game against a strong team can lose you at most 1 game, you are much more likely to lose that game, so it has a greater impact on a your expected wins.
For example, if Team A plays teams with GWPs of .450, .500, and .900, their number of expected wins is going to be much lower than Team B playing teams with GWPs of .450, .500, and .550 (even though the medians are identical).
good point anonymous...
I can see the merits of both sides. Median will basically tell you how many games are "tough opponents" vs "easy opponents".
On the other hand the Mean gives you and average of how good or how bad each team is... obviously a GWP team of .9 is a much tougher matchup than one at 0.6, and your chances of winning that individual game are much less, but then looking at the average it skews the rest of the games.
I think you probably need both pieces of information to get the real answer.
Mistake! Sorry guys, I realized the OppGWP chart erroneously included the games from Week 9... Chart now updated to reflect the real values.
OAK now jumps ahead of SD with their win last night. Total chance of making playoffs: OAK: 46%, SD: 39%.
This is fun stuff; thanks.
Can you please start putting some information in on draft position? Those of us who are fans of also-ran teams (I'm looking at you, Seahawks) would love to see some data on what the draft's likely to look like.
Stuff on #1 pick probabilities is fun, but maybe a little deeper look (top 3? top 5?) would be informative and fun, too.
Thanks much!
robbbbbb --
You should run my software. It's easy and free.
Here are odds fro the worst 5 teams and the first 5 picks:
Indy: 82%, 11%, 4%, 2%, 1%
Miami: 7%, 25%, 17%, 12%, 9%
Arizona: 4%, 18%, 16%, 13%, 11%
Seattle: 2%, 12%, 13%, 11% 10%
St. Louis 1%, 9%, 10%, 10%. 9%
Tangentially related question that arose on Niners Nation. Some posters were quite insistent that it's bad practice in statistical analysis to round up probabilities to 100%. Someone even claimed it's in the first chapter of any Intro to Stats textbook.
Yet I've never, ever heard this before. Anyone else?
bigmouth: I've never heard that before either, and it's certainly not in the first chapter of my Intro to Stats book.
That said, I suppose I could understand the argument if you're in a situation, as here, where a team could feasibly have a 100% probability and you want to differentiate between them and a team having a probability of less than 100% but greater than 99.5. Likewise for differentiating between a 0% probability and non-zero probabilities that have been rounded down.
For the record, neither Green Bay nor San Francisco has clinched a berth yet, and the playoffs remain a mathematical possibility for every team (yes, even the Colts).
If you know, or if it's not too much trouble to run it, how does the Bears-Lions game look in terms of leverage?