Conference Finals

Using the power rankings that excluded the meaningless games (in my opinion), which are listed in last week's post, the probability of each of the remaining teams winning their conference and the Super Bowl, respectively, are listed below. I have a gut feeling I just butchered the grammer in the last sentence. Oh well . . . I'm a statistician - not a writer.

Probability win Conference / Prob win Super Bowl / Team
0.95647837 / 0.450289880 / Phi
0.04352163 / 0.002488641 / Atl
0.77729986 / 0.463053397 / Pit
0.22270014 / 0.084168082 / NE


The results from the Bradley-Terry logistic regression model are in log odds ratios. Basically, this means that the outcome of a game can be put into probability terms based on the performance of each team throughout the season, and the home-field advantage effect. The probability of each team winning the Super Bowl depends on the probability of winning their conference, as well as the conditional probabilities of beating either team in the other conference:

Probability the Patriots win the Super Bowl (P=probability):
P(Patriots beat Steelers in Pittsburgh)*P(Eagles beat Falcons in Philly)*P(Patriots beat Eagles)+P(Patriots beat Steelers in Pittsburgh)*P(Falcons beat Eagles in Philly)*P(Patriots beat Falcons)

It is assumed that there is no home-field advantage effect for the Super Bowl.

Divisional Playoffs - before

Based on the regular season results, excluding obvious "junk" games involving Philadelphia, Pittsburgh, Atlanta, and Indianapolis at the end of the season, the probability of one team beating another can be estimated. The following table gives the probabilities of each team winning their next game and the probability of each team winning their conference.

NFC

1. 0.97833173 0.941106882 Phi
2. 0.81153267 0.047580083 Atl
3. 0.18846733 0.004631178 StL
4. 0.02166827 0.006681857 Min

AFC

1. 0.95166237 0.76512765 Pit
2. 0.78751316 0.20066513 NE
3. 0.21248684 0.02730017 Ind
4. 0.04833763 0.00690705 NYJ

Here are the rankings without the "junk" games. More specifically: Philadelphia vs St. Louis in week 16, Pittsburgh vs Buffalo, Philadelphia vs Cincinnati, Indianapolis vs Denver, and Atlanta vs Seattle in week 17.

1. 3.51 / 14 - 1 / Pittsburgh Steelers
2. 3.19 / 13 - 1 / Philadelphia Eagles
3. 2.59 / 14 - 2 / New England Patriots
4. 1.61 / 12 - 3 / Indianapolis Colts
5. 1.12 / 12 - 4 / San Diego Chargers
6. 0.92 / 9 - 7 / Baltimore Ravens
7. 0.86 / 10 - 6 / New York Jets
8. 0.50 / 9 - 6 / Buffalo Bills
9. 0.47 / 9 - 7 / Jacksonville Jaguars
10. 0.43 / 11 - 4 / Atlanta Falcons
11. 0.26 / 9 - 6 / Denver Broncos
12. 0.24 / 10 - 6 / Green Bay Packers
13. 0.10 / 7 - 8 / Cincinnati Bengals
14. -0.10 / 7 - 9 / Kansas City Chiefs
15. -0.25 / 7 - 9 / Houston Texans
16. -0.29 / 8 - 8 / Minnesota Vikings
17. -0.53 / 8 - 8 / New Orleans Saints
18. -0.55 / 8 - 7 / Seattle Seahawks
19. -0.60 / 6 - 10 / New York Giants
20. -0.62 / 6 - 10 / Dallas Cowboys
21. -0.66 / 7 - 9 / Carolina Panthers
22. -0.67 / 4 - 12 / Cleveland Browns
23. -0.70 / 7 - 8 / St Louis Rams
24. -0.72 / 5 - 11 / Oakland Raiders
25. -0.75 / 6 - 10 / Detroit Lions
26. -0.82 / 6 - 10 / Washington Redskins
27. -0.87 / 5 - 11 / Tennessee Titans
28. -1.20 / 6 - 10 / Arizona Cardinals
29. -1.21 / 4 - 12 / Miami Dolphins
30. -1.22 / 5 - 11 / Chicago Bears
31. -1.40 / 5 - 11 / Tampa Bay Buccaneers
32. -2.65 / 2 - 14 / San Francisco 49ers

Home-field Advantage = 0.33

Week 17 Power Ranking - 2005

As I said last week, there is clearly a flaw in any ranking system that gives equal weight to games toward the end of the season that include teams that have clinched a specific seed. The Eagles, Colts, and Falcons had absolutely nothing to gain with a victory, and thus used their stars sparingly. The Steelers also sat Roethlisberger and Burress, and didn't give Staley or Ward much action. Even though they won, their last game should have little impact on their rankings because there was nothing on the line.

Score / Change from Last Week / W - L / Team

1. 3.32 / 0.10 / 15 - 1 / Pittsburgh Steelers
2. 2.64 / 0.01 / 14 - 2 / New England Patriots
3. 1.43 / -0.50 / 13 - 3 / Philadelphia Eagles
4. 1.32 / -0.37 / 12 - 4 / Indianapolis Colts
5. 1.17 / 0.00 / 12 - 4 / San Diego Chargers
6. 0.99 / -0.22 / 10 - 6 / New York Jets
7. 0.89 / 0.11 / 9 - 7 / Baltimore Ravens
8. 0.62 / 0.06 / 9 - 7 / Buffalo Bills
9. 0.53 / 0.17 / 10 - 6 / Denver Broncos
10. 0.47 / -0.01 / 9 - 7 / Jacksonville Jaguars
11. 0.45 / 0.44 / 8 - 8 / Cincinnati Bengals
12. 0.34 / -0.19 / 11 - 5 / Atlanta Falcons
13. 0.19 / -0.03 / 10 - 6 / Green Bay Packers
14. -0.05 / -0.11 / 7 - 9 / Kansas City Chiefs
15. -0.20 / 0.25 / 9 - 7 / Seattle Seahawks
16. -0.24 / -0.31 / 7 - 9 / Houston Texans
17. -0.27 / 0.32 / 8 - 8 / St Louis Rams
18. -0.33 / -0.26 / 8 - 8 / Minnesota Vikings
19. -0.42 / 0.14 / 8 - 8 / New Orleans Saints
20. -0.57 / -0.18 / 7 - 9 / Carolina Panthers
21. -0.65 / 0.42 / 4 - 12 / Cleveland Browns
22. -0.65 / -0.16 / 5 - 11 / Oakland Raiders
23. -0.66 / -0.08 / 6 - 10 / Dallas Cowboys
24. -0.67 / 0.18 / 6 - 10 / New York Giants
25. -0.82 / -0.24 / 6 - 10 / Detroit Lions
26. -0.84 / 0.08 / 5 - 11 / Tennessee Titans
27. -0.87 / 0.22 / 6 - 10 / Washington Redskins
28. -1.03 / 0.24 / 6 - 10 / Arizona Cardinals
29. -1.04 / 0.13 / 4 - 12 / Miami Dolphins
30. -1.26 / -0.18 / 5 - 11 / Chicago Bears
31. -1.29 / -0.11 / 5 - 11 / Tampa Bay Buccaneers
32. -2.50 / 0.10 / 2 - 14 / San Francisco 49ers

Home-field Advantage = 0.35

Week 16 Power Ranking - 2005

No longer will I defend the Cleveland Browns. Earlier in the season, the Browns were ranked very high and I defended their ranking due to their early victory against the Ravens and difficult schedule. Their recent losses to mediocre teams has dropped them very quickly. This week also shows an obvious flaw in equally weighting all games. There comes a point with some teams where games just don't matter anymore. The Eagles had locked home-field advantage for the playoffs, leaving nothing to play for and no reason to risk injury, so they didn't play their regular starters against the Rams. This game should have little to no effect on the rankings, however, since every game is treated equally, the Eagles fall and the Rams rise. Despite this flaw, I have made no adjustment to the weight of the Rams/Eagles game so that the rankings remain objective - perhaps next season I'll decide on a weighting strategy based on game importance. A weighting stragety, however, would add an element of subjectivity to the rankings.

Score / Change from Last Week / W - L / Team

1. 3.22 / -0.21 / 14 - 1 / Pittsburgh Steelers
2. 2.63 / 0.24 / 13 - 2 / New England Patriots
3. 1.93 / -1.22 / 13 - 2 / Philadelphia Eagles
4. 1.69 / 0.17 / 12 - 3 / Indianapolis Colts
5. 1.21 / -0.08 / 10 - 5 / New York Jets
6. 1.17 / -0.12 / 11 - 4 / San Diego Chargers
7. 0.78 / -0.11 / 8 - 7 / Baltimore Ravens
8. 0.56 / 0.09 / 9 - 6 / Buffalo Bills
9. 0.53 / -0.22 / 11 - 4 / Atlanta Falcons
10. 0.48 / -0.19 / 8 - 7 / Jacksonville Jaguars
11. 0.36 / 0.13 / 9 - 6 / Denver Broncos
12. 0.22 / 0.17 / 9 - 6 / Green Bay Packers
13. 0.07 / 0.23 / 7 - 8 / Houston Texans
14. 0.06 / 0.15 / 7 - 8 / Kansas City Chiefs
15. 0.01 / 0.04 / 7 - 8 / Cincinnati Bengals
16. -0.07 / -0.16 / 8 - 7 / Minnesota Vikings
17. -0.39 / 0.24 / 7 - 8 / Carolina Panthers
18. -0.45 / 0.30 / 8 - 7 / Seattle Seahawks
19. -0.49 / -0.04 / 5 - 10 / Oakland Raiders
20. -0.56 / 0.33 / 7 - 8 / New Orleans Saints
21. -0.58 / 0.05 / 6 - 9 / Dallas Cowboys
22. -0.58 / 0.05 / 6 - 9 / Detroit Lions
23. -0.59 / 0.54 / 7 - 8 / St Louis Rams
24. -0.85 / -0.23 / 5 - 10 / New York Giants
25. -0.92 / -0.06 / 4 - 11 / Tennessee Titans
26. -1.07 / -0.33 / 3 - 12 / Cleveland Browns
27. -1.08 / -0.17 / 5 - 10 / Chicago Bears
28. -1.09 / -0.22 / 5 - 10 / Washington Redskins
29. -1.17 / 0.39 / 4 - 11 / Miami Dolphins
30. -1.18 / -0.04 / 5 - 10 / Tampa Bay Buccaneers
31. -1.27 / 0.11 / 5 - 10 / Arizona Cardinals
32. -2.60 / 0.14 / 2 - 13 / San Francisco 49ers

Home-field Advantage = 0.32