# Simulating the NFL: Week 12

As week 12 completed on Thanksgiving day, we finally hit the 164 game mark of the 256 game NFL season. With almost two-thirds of the season being completed, we take a quick look at our power rankings, a combination of win-loss total by team-vs-team match-ups and points scored versus points allowed by team-by-team match-ups. Currently the season standings as of this morning on NFL.com are:

If the playoffs ended today, we would see the following playoff positions:

• AFC
1. Raiders
2. Patriots
3. Texans
4. Steelers
5. Chiefs
6. Broncos
• NFC
1. Cowboys
2. Seahawks
3. Lions
4. Falcons
5. Giants
6. Redskins

However, there are some tight races and still 4-5 games left for each team. So instead of a “let’s assume the season ended today” post, which is meaningless, let’s take a look at simulating the remaining games and estimate the probabilities for each team winning their divisions and making the playoffs.

In this case, we must identify a probability structure. To do this, we use a conglomeration of multiple measurements that directly compare teams. First, we use the Bradley-Terry model with number of days between games, distance traveled from previous game, and home/away as extra factors for determining a win. Next, we prepare a beta regression based on the diminishing returns on the number of points scored in a game. Third, we perform a Colley decomposition, which only takes into account wins and losses of teams using a joint Bayesian multinomial process. Using these three scores, we build a cumulative distribution function for each score and then combine the three measurements using a partial preference system using those CDF’s. Cool, right? If you didn’t follow, that’s OK.

## NFL Power Rankings: November 25, 2016

Running our models, we find that the most dominant teams are (no surprise) the Dallas Cowboys and the New England Patriots. What is interesting is that the 6-4-1 Washington Redskins are listed as 5th overall in the league. To those following the Redskins, this should come as no surprise as they have played well this season, putting up strong numbers. Their four losses have come against the Steelers (AFC North leader; week 1 by 22 at home), Cowboys (at home; week 2 by 4), Lions (NFC North leader; week 7 by 3 at Detroit), and Dallas again (at Dallas; week 12 by 5). Their key wins have come against the Giants (in New York), the Ravens (in Baltimore) and the Vikings (before their imminent slide down the standings). Due to the small number of games played, this makes the Redskins look like a fighting team, but a couple looming match ups may reshuffle their rankings: at Arizona, home against Carolina and the Giants.

Here we see that the current playoff teams indeed cover the Top 12 spots, with exception of the 5-5 Philadelphia Eagles. The reason this team is so high despite the mediocre record is that the NFC East is hands down the top division in the league at the moment. Their losses are to the Cowboys, Giants, Seahawks, Redskins, and Lions. Not a single weak team. Their wins include the Steelers, Vikings, and Falcons (discount the Browns and Bears). So the Eagles too are propped up higher because of their losses as opposed to their wins. This too will change depending on the remaining 6 games of the season.

So using these rankings, we can then ask, who is most likely to win the division? Who is most likely to make the playoffs? To answer this, we simulate the season one million times and calculate the number of times a team wins the division and wild card. This Markov process helps us estimate each team’s probability of making the playoffs.

MCMC simulations for predicted number of wins, losses and ties. PWD = Probability of Winning Division, PWC = Probability of Wild Card, PMP = Probability of Making the Playoffs

Here, we find that the Dallas Cowboys are expected to finish the season 13-3. This means they are expected to lose 2 of their final 6 games. Similarly, we anticipate the Steelers to win the AFC North, but with a paltry 9-7 record. The playoffs are simulated to be:

• AFC
1. Patriots
2. Raiders
3. Texans
4. Steelers
5. Broncos
6. Chiefs
• NFC
1. Cowboys
2. Seahawks
3. Falcons
4. Lions
5. Giants
6. Redskins

This would also suggest that the Miami Dolphins could win 10 games and not make the playoffs, despite a 9-7 team sneaking in. Similarly, we are anticipating the season to become tight between the Minnesota Vikings and Washington Redskins. The variation on each team is large enough to suggest they tie at 9-7. This would then favor the Redskins due to the head-to-head match-up win for Washington in Week 10.

Our simulations have also effectively eliminated four teams: Cleveland Browns, Jacksonville Jaguars, Chicago Bears, and San Francisco 49ers.

So what do you think? Who are your top 12 teams to make the playoffs?

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