NFL Playoff Probabilities: Week 16 (Part One)

After an incredible shake-up in the Week 15 standings, and a monumental collapse of BOTH my fantasy football teams, we find the landscape of the NFL playoffs ever so tightening heading into Week 16. For instance…

Chiefs Take First from Raiders, Drop First to TITANS… 

succop

Ryan Succop celebrates Titans’ 19-17 win over the Chiefs. (Reed Hoffman / Getty Images)

A week after grabbing first place of the AFC West from the Oakland Raiders (11-3) in Week 14, the Kansas City Chiefs (10-4) lose to the Tennessee Titans (8-6) by a score of 19-17. The win keeps the Titans on pace with the Houston Texans (8-6) in the AFC South. The loss forces the Chiefs to wait for some outside help to regain first.

Redskins Move into Sixth… Lose Sixth hours later…

stewart

Jonathan Stewart stampeding for 130+ yards over the Redskins en route to a 26-15 Carolina win in Landover, MD. (Patrick Semansky / Associated Press)

A huge boost from a Dallas Cowboys (12-2) victory over the Tampa Bay Buccaneers (8-6) allowed for the Washington Redskins (7-5-1) to move into a half game lead for the sixth playoff spot. Within a day, the Redskins would lose that spot in a devastating 26-15 loss to the Carolina Panthers (6-8). This loss allowed the Green Bay Packers (8-6) to take control of the final Wild Card spot.

AFC Tightens, NFC Separates…

As the Denver Broncos (8-6) have fallen from sixth to ninth over the last two weeks, we find a log-jam for the sixth wild card spot. With the Miami Dolphins (9-5) holding on tight, there are three teams (Broncos, Ravens, Titans) hot on their heels at 8-6. Behind them, the 7-7 Colts and Bills are lurking.

In the NFC, teams teetering on the cusp of the sixth spot fell flat: Redskins lost to the Panthers, Minnesota Vikings (7-7) were obliterated by the Colts 34-6. Only four teams are effectively battling for the final spot instead of a potential five teams.

Who Is Eliminated? 

As of right now, any team with 8.5 or more losses are eliminated from the playoffs. This means that these teams are eliminated:

  • AFC
    1. Cincinnati Bengals (5-8-1)
    2. San Diego Chargers (5-9)
    3. New York Jets (4-10)
    4. Jacksonville Jaguars (2-12)
    5. Cleveland Browns (0-14)

 

  • NFC
    1.  Arizona Cardinals (5-8-1)
    2. Philadelphia Eagles (5-9)
    3. Los Angeles Rams (4-10)
    4. Chicago Bears (3-11)
    5. San Francisco 49ers (1-13)

 

This means there are eleven teams remaining in each conference that are vying for a playoff spot. So let’s take a look at which teams are in.

Who Is Already Guaranteed In?

The New England Patriots (12-2) have already clinched the AFC East. Similarly, the Seattle Seahawks (9-4-1) have clinched the NFC West. Despite these teams being the only to win their respective divisions so far; the Dallas Cowboys and the Oakland Raiders have clinched a playoff spot.

This leave six divisions up for grabs and eight playoff spots open. So let’s break down each division and find out the weighted probabilities for each team making the playoffs.

AFC NORTH: Predicted Winner… Pittsburgh Steelers.

This race ultimately comes down to the Pittsburgh Steelers (9-5) and the Baltimore Ravens (8-6). The Steelers remaining games are against at home against Baltimore on Christmas Day and against the Cleveland Browns. The Ravens final game is against the Bengals in Cincinnati.

This is where it gets interesting. The Ravens currently lead the series 1-0 over the Steelers. With a win on Christmas Day, the Steelers win the division outright. The Steelers have a probability of 0.527580 of winning this game.

If the Steelers lose this game, then the Steelers need the Ravens to lose the following week while beating the Browns. These probabilities (Bengals over Ravens; Steelers over Browns) are 0.591453 and 0.936850. This would suggest that the Steelers have an overall probability of 0.756103 of winning the AFC North. The Ravens? Only 0.243897.

AFC SOUTH: Predicted Winner… Houston Texans.

This division is a muddled mess. Only the Jacksonville Jaguars have been eliminated. Here, the Houston Texans and Tennessee Titans are gridlocked at 8-6 with the Indianapolis Colts sitting at 7-7. The remaining games are as follows:

  • Tennessee vs. Jacksonville (Tennessee 0.706916 chance of winning)
  • Indianapolis vs. Oakland (Indianapolis 0.404948 chance of winning)
  • Cincinnati vs. Houston (Houston 0.588723 chance of winning)
  • Jacksonville vs. Indianapolis (Indianapolis 0.688346 chance of winning)
  • Houston vs. Tennessee (Houston 0.502179 chance of winning)

Since the Texans play the Titans in the final game of the year, the Colts can only tie for the division lead. This means we head into tie-breakers across eight different scenarios!!!

Scenario One: Titans, Colts, Texans all finish 9-7… Texans win division

In this scenario, the Colts win both games played (0.278744 probability) and the winner of the Texans-Titans match-up loses their respective opposite game, as well as the loser of the match-up wins their opposite game.

If the Texans beat the Titans: Then the Texans lose to the Bengals and the Titans defeat the Jaguars. In this case, we go to head-to head match-ups. The records at this point would be Texans 4-0, Colts 2-2, Titans 0-4. In this case, the Titans are eliminated and we revert to a two-team format. In this case, the Texans win with a 2-0 match-up over the Colts.

If the Titans beat the Texans: Same result as above with the head-to-heads being Texans 3-1, Colts 2-2, Titans 1-3 leading to a Texans 2-0 win over the Colts. Hence if all teams finish 9-7; the Texans win the division.

The probability of a three team finish is .278744*(.085897 +.146003) = 0.064641; or a 6.4641 percent chance.

Scenario Two: Titans and Texans are tied alone… Texans win division

In this scenario, we remove the Colts tying scenario and follow through the Texans-Titans game. However, in the case of the Titans beating the Texans, the head-to-head is no longer a deciding factor as the records would be 1-1. The secondary tie-breaker is the division win-loss record. In this case, the Titans win and finish at a 9-7 tie would require the Titans to lose to Jacksonville. At this point, the Texans would hold a 5-1 division record to the Titans 2-4 division record. Hence the Texans win the division in either case.

The probability that the Titans and Texans finish tied for first (alone) in the division is (1-.278744)*(.085897 + .146003) = 0.167259; or a 16.7259 percent chance. 

Scenario Three: Titans sweep last two games… Titans win division.

If the Titans sweep, they finish 10-6 and in sole possession of first place. In this case, only two games matter; both Titans games. This has a 0.351918; or a 35.1918 percent chance of happening.

Scenario Four: Texans sweep last two games… Texans win division.

This scenario mirrors the Titans sweep and has a 0.295644; or a 29.5644 percent chance of happening. 

Scenario Five: Colts tie with Titans; Texans out… Colts win division.

In this case, the Colts win out, the Texans lose out and the Titans lose to Jacksonville. In this case, the Colts and Titans finish 9-7 while the Texans finish 8-8. In this case, the Colts own a 2-0 head-to-head tie-breaker over the Colts.

This can only happen one way and has a 0.016727; or a 1.6727 percent chance of happening.

Scenario Six: Colts tie with Texans; Titans out… Texans win division

In this scenario, the Texans beat the Titans but lose to Cincinnati. Couple that with an Indianapolis sweep of Oakland and Jacksonville combined with a Titans collapse against the Jaguars; and we find that the Texans win the division based on a 2-0 head-to-head tie breaker over the Colts.

This can only happen one way and has a 0.017062; or a 1.7062 percent chance of happening. 

Scenario Seven: Titans beat Texans, everyone loses… Titans win division

In this case, the Titans beat the Texans but they lose to Jacksonville. In order to finish alone on top of the division, the Texans must lose to Cincinnati and the Colts must lose at least one game. The probability of the Colts losing at least one game is 1 – .278744; or 0.721256.

The probability of the other three fixed results occurring is 0.043280; or 4.3280 percent.

Scenario Eight: Texans beat Titans, everyone loses… Texans win division

In this scenario, everything holds in the previous scenario except that the Texans win the final game of the year. In this case, the Texans are alone atop the standings with a 9-7 record with the Titans at 8-8 and the Colts at 7-9 or 8-8; either doesn’t matter as long as it is not 9-7.

The probability of this occurring is 0.043659; or 4.3659 percent.

Put these probabilities together and we find that the Texans have a 58.8265 percent chance of winning the division. Follow this up with a Titans 39.5198 percent chance and a Colts 1.6727 percent chance; and we should find the best bet for the Texans to win the division. Note: Adding this probabilities will give you 100.019. This is merely rounding error compounded across 5 games over 8 scenarios.

AFC WEST: Predicted Winner… Oakland Raiders.

The AFC West is a little tighter than the AFC North but nowhere as muddled as the AFC South. Currently the 11-3 Oakland Raiders hold a single game lead over the 10-4 Kansas City Chiefs. Kansas City owns the head-to-head over the Raiders with a 2-0 record, so this means in order to win the division, they must either finish 2-0 with a Raiders 1-1 or worse finish; or 1-1 with a Raiders 0-2 finish. So let’s walk through those scenarios. The remaining games for these two teams are:

  • Indianapolis vs. Oakland (Oakland 0.595052 chance of winning)
  • Denver vs. Kansas City (Kansas City 0.539724 chance of winning)
  • Oakland vs. Denver (Oakland 0.559225 chance of winning)
  • Kansas City vs. San Diego (Kansas City 0.595540 chance of winning)

Scenario One: Kansas City ties Oakland or wins outright… Chiefs wins division

In this case, the Chiefs win via the head-to-head and can do this one of two ways. Either the Chiefs win out; or the Chiefs win one while the Raiders lose both. In the former, the Chiefs have a 0.321427 chance of winning out while the Raiders have a 1 – 0.332768 = 0.667232 chance of losing at least one game. In this case, the Chiefs have a 21.4466 chance of winning the division.

Scenario Two: Raiders finishes atop alone… Raiders win division

In the other case, the Raiders win as many or more games than the Chiefs. This ensures the Raiders avoid a tie and clinches the division. There are four ways this can happen, but all point to a 78.5534 percent chance of winning the division.

NFC EAST: Predicted Winner… Dallas Cowboys.

The team with the best record in the NFC can’t seem to clinch just yet. Why? The pesky New York Giants. Despite the Giants being two games out with a 10-4 record, they are still able to snag the NFC East if the 12-2 Dallas Cowboys lose their final two games. This is due to the entire list of Cowboy losses being the New York Giants.

Unfortunately, this happens only one way. The Cowboys must lose to the Lions at home and to the Eagles on the road. While possible, it still requires the Giants to pick up two more wins over the Eagles in Philadelphia and the Redskins in Washington.

In this case, the probability of this occurring is relatively small:

  • Cowboys vs. Lions (Cowboys 0.403597 chance of loss)
  • Cowboys vs. Eagles (Cowboys 0.355108 chance of loss)
  • Giants vs. Eagles (Giants 0.603555 chance of win)
  • Giants vs. Redskins (Giants 0.538437 chance of win)

Hence the probability of the Giants winning the NFC East is 4.6576 percent. For the Cowboys winning the NFC East, it is then 95.3424 percent.

NFC NORTH: Predicted Winner… Detroit Lions.

The NFC North is just as ugly as the AFC South. In this case, the Lions are currently 9-5, the Green Bay Packers are 8-6, and the Minnesota Vikings are 7-7. The remaining games scheduled are:

  • Minnesota vs. Green Bay (Packers 0.530760 chance of win)
  • Detroit vs. Dallas (Lions 0.403597 chance of win)
  • Minnesota vs. Chicago (Vikings 0.657802 chance of win)
  • Detroit vs. Green Bay (Packers 0.511394 chance of win)

Due to the Lions – Packers game at the end of the season, the Vikings chances are very slim. So slim, that the need the Packers to beat the Lions in order to look at tie-breakers. Let’s break down the NFC North Scenarios…

Scenario One: Green Bay Controls the Division… Packers win division.

Believe it or not, but the Packers control this division. If they win their final two games, they win the division. They will either be alone with a 10-6 record, or the Lions will be tied with the Packers with a 10-6 record. Either way, the Packers will own the head-to-head record over the Lions and win the division. The Packers have a 27.1427 percent chance of winning the final two games of the season. 

Scenario Two: Detroit Controls the Division with One Game… Lions win division

The Lions also control the division but not by winning out. All they need to do is beat the Packers in Week 17. With this, the Lions have 10 wins and the Packers have 7 losses. In this case, the Lions have a 48.8606 chance of winning the division.

Scenario Three: Green Bay beats Detroit but Loses to Minnesota… Mixed Results

 

Now if the Packers beat the Lions but do not win out, we run into some other tie-breaking procedures. The probability of Green Bay beating the Lions and losing to the Vikings is 23.9967 percent. At this point, the Lions are 9-6, Packers are 9-7 and Vikings are 8-7.

Scenario Three – A: Cowboys and Vikings win… Packers win division.

In this case, we have a three-way tie at 9-7. The first tie breaker gives us a 2-2 record across the board for each team, forcing us to move into the divisional record tie-breaker. In this case, the Packers would be 4-2 as the Lions and Vikings would both be 3-3. In this case the Packers in. The probability of this happening is 9.4143 percent. 

Scenario Three – B: Lions win… Lions win division.

If the Lions beat the Cowboys, they will finish with a 10-6 record, giving them sole possession of first place. In this case, the Lions have a 9.6850 percent chance of winning the division.

Scenario Three – C: Cowboys win and Vikings lose… Packers win division.

In this last scenario, the Lions are 9-7 with the Packers at 9-7. The Packers will own the 2-0 head-to-head and therefore win the division. This has a 4.8974 percent chance of happening.

Hence the Packers have a 41.4544 percent chance on winning the division, while the Lions have a 58.5456 of winning the NFC North. Sorry, Minnesota… you’re mathematically eliminated from repeating the NFC North championship.

NFC SOUTH: Predicted Winner… Atlanta Falcons.

For the final division diagnosis, we find the NFC South to be a two team race between the Atlanta Falcons and the Tampa Bay Buccaneers. The 9-5 Falcons  and 8-6 Buccaneers both play the Carolina Panthers and the New Orleans Saints (both 6-8) to finish the year.

Atlanta and Tampa Bay split their regular season match-ups, so a division tie will head to a division records comparison. In this case, a tie will favor Tampa Bay as it will require the Buccaneers to have a 5-1 to 4-2 comparison, or a 4-2 to 3-3 comparison. Hence, there are really two scenarios to look at.

Scenario One: Atlanta wins out the division… Falcons win division.

In this scenario, the Falcons win out or Tampa Bay loses out (or both). In this case, we have that the Falcons have .573351 and .565706 chances of winning over the Panthers and Saints, respectively. Similarly, the Buccaneers have 0.553453 and 0.545733 chance of winning over the Panthers and Saints, respectively.

Atlanta has a probability of 0.324348 of winning out and clinching the division.

Scenario Two: Tampa Bay Mimics Atlanta… Falcons win division.

But if Atlanta loses, they need Tampa Bay to lose as well. The probability of Atlanta losing one game is 0.490361. Combine this with Tampa Bay losing one or more game being 1- .302038 = 0.697962, the Falcons have a probability of 0.342121 of winning the division. 

Finally, if the Falcons lose out, they need the Buccaneers to lose out. In this case, the probability of this happening is 0.037587.

This shows that the Atlanta Falcons have a 70.4056 chance of winning the division. The Buccaneers? Much less chance at 29.5944 percent.

WILDCARD RACES…

Seeing that a couple divisions are in complete bedlam with three-team races, the Wild Card races are much more crazy. For instance, the 10-4 Giants (second best record in the NFC) is at risk of not making the playoffs. The 11-3 Raiders and 10-4 Chiefs have no idea who may end with up the bye…

To give insight on the complexity of the playoffs… Of the remaining 32 games, 15 have AFC Wild Card implications on the line. That’s 32,768 possible combinations. On the NFC side? there are only 12 games that have wild card implications. This give us only 4,096 possible scenarios. In our next segment, tomorrow (in attempt to race the New York Giants versus Philadelphia Eagles game) we will break down the probabilities for each team making the wild card spots.

 

To do this analysis, we must condition on the division leaders and use that to key off the remaining teams. For the AFC, we have the following breakdown:

  1. Patriots, Steelers, Texans, Raiders
    • Probability: 34.9397
  2. Patriots, Steelers, Texans, Chiefs
    • Probability: 9.5392
  3. Patriots, Steelers, Titans, Raiders
    • Probability: 23.4726
  4. Patriots, Steelers, Titans, Chiefs
    • Probability: 6.4085
  5. Patriots, Steelers, Colts, Raiders
    • Probability: 0.9935
  6. Patriots, Steelers, Colts, Chiefs
    • Probability: 0.2712
  7. Patriots, Ravens, Texans, Raiders
    • Probability: 11.2705
  8. Patriots, Ravens, Texans, Chiefs
    • Probability: 3.0771
  9. Patriots, Ravens, Titans, Raiders
    • Probability: 7.5716
  10. Patriots, Ravens, Titans, Chiefs
    • Probability: 2.0672
  11. Patriots, Ravens, Colts, Raiders
    • Probability: 0.3205
  12. Patriots, Ravens, Colts, Chiefs
    • Probability: 0.0875

Note that the sum of the probabilities are 100.0191. This again is due to rounding.

Similarly, for the NFC Teams, we have the following breakdown:

  1. Seahawks, Cowboys, Lions, Falcons
    • Probability: 39.2995
  2. Seahawks, Cowboys, Lions, Buccaneers
    • Probability: 16.5192
  3. Seahawks, Cowboys, Packers, Falcons
    • Probability: 27.8268
  4. Seahawks, Cowboys, Packers, Buccaneers
    • Probability: 11.6968
  5. Seahawks, Giants, Lions, Falcons
    • Probability: 1.9198
  6. Seahawks, Giants, Lions, Buccaneers
    • Probability: 0.8070
  7. Seahawks, Giants, Packers, Falcons
    • Probability: 1.3594
  8. Seahawks, Giants, Packers, Buccaneers
    • Probability: 0.5714

So far we have worked out the 96 different possible division winner scenarios for the NFL playoffs, along with their respective probabilities based off our MCMC models. Instead of sampling, we decided to break out all possible scenarios in grueling detail.

Tomorrow, we aim to work through the Wild Card scenarios to identify the probability each of the remaining 7 teams in each cases have at nabbing a wild card spot. Some may be as lucky as in the divisional cases as  the Indianapolis Colts, and have an actual chance… some may be like the Minnesota Vikings and be mathematically left out in the cold.

Advertisements

One thought on “NFL Playoff Probabilities: Week 16 (Part One)

  1. Pingback: NFC Wild Card Playoff Probabilities: Week 16 (Part Two) | Squared Statistics: Analyzing Crime, Sports, and People

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s