When doing fits to my playoff formula while excluding Super Bowl data, I noted the following:

./logistic_game.pl --nosb --start=2001 --end=2015
b[0]   = prev playoff experience
b[1]   = strength of schedule
b[2]   = constant
b_p[i] = probability the term could be a product of chance.


Start year    = 2001
Ending year   = 2015
Data points   = 150
Home team won = 94

2 = Years checked for playoff appearance.
complete results
D0	198.211779799779
Dm	181.040960409088
Dm_chisq	17.1708193906915
Dm_df	2
Dm_p	[0.00018681164]
b	[0.93247135 0.25819533 0.74094435]
b_chisq	[ 9.5962352   7.944765  15.099918]
b_p	[0.0019497672 0.0048226681 0.0001019677]
iter	6

There are 5 playoff games every year in the NFC, and 5 in the AFC, and over the last 10 years, the home team has won 94 of them. Nominally HFA is usually assigned to be a 3 point betting advantage, and nominally that advantage is approximately 60%. 94*100/150 is 62.66666 repeating, which rounds to 62.7 percent. That’s more than the nominal 60% and more than the average of the last five NFL seasons. To calculate, 2012-2016 home field wins are 146, 153, 145, 138, and 147 respectively. That totals to 729 wins over 5*256 games. The percentage calculates to be 56.95%. Expressed in logits, and then in points, these advantages then become:

Home Field Advantage
Type of HFA Win Percent Logit Prob Calculated Point Spread
Playoff HFA 62.7 0.518 3.8
Traditional HFA 60.0 0.405 3.0
Seasonal HFA 56.95 0.280 2.1
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I wasn’t around for week 15 because of the holidays, so I will be adding a couple weeks of data today.

So week 15 is below:

Global Statistics:
Games  Home Wins HwPct Winning_Score Losing_Score Margin
224       126     56.2      27.38        17.45      9.93

Calculated Pythagorean Exponent:  3.47


Rank  Team    Median  GP   W   L   T  Pct   Pred   SRS    MOV   SOS
------------------------------------------------------------------------
1     NE      12.0    14  12   2   0  85.7  82.6   7.28   9.43 -2.15
2     DAL      6.0    14  12   2   0  85.7  77.1   6.91   7.71 -0.80
3     OAK      3.0    14  11   3   0  78.6  59.9   4.43   2.93  1.50
4     KC       4.0    14  10   4   0  71.4  62.9   4.15   3.21  0.93
5     NYG      3.0    14  10   4   0  71.4  57.3   1.68   1.57  0.11
6     SEA      4.0    14   9   4   1  67.9  69.5   3.09   4.50 -1.41
7     PIT      7.5    14   9   5   0  64.3  67.6   4.97   4.64  0.33
8     ATL      7.0    14   9   5   0  64.3  71.9   8.08   7.93  0.15
9     MIA      3.5    14   9   5   0  64.3  50.3  -2.16   0.07 -2.23
10    DET      3.0    14   9   5   0  64.3  54.7  -0.09   1.14 -1.24
11    GB       3.5    14   8   6   0  57.1  55.9   2.14   1.71  0.43
12    TB       2.5    14   8   6   0  57.1  47.5   0.40  -0.64  1.04
13    HOU      2.0    14   8   6   0  57.1  36.3  -2.47  -3.14  0.68
14    TEN      1.5    14   8   6   0  57.1  54.4   0.58   1.21 -0.64
15    BAL      1.5    14   8   6   0  57.1  62.9   2.24   3.07 -0.83
16    DEN      1.5    14   8   6   0  57.1  62.5   4.45   2.93  1.52
17    WAS      1.0    14   7   6   1  53.6  50.5   1.32   0.14  1.18
18    IND      0.5    14   7   7   0  50.0  55.7   1.14   1.64 -0.50
19    BUF      0.5    14   7   7   0  50.0  61.2   1.55   3.14 -1.60
20    MIN      0.5    14   7   7   0  50.0  51.7   0.42   0.36  0.06
21    NO      -1.5    14   6   8   0  42.9  53.0   1.37   1.00  0.37
22    CAR     -2.0    14   6   8   0  42.9  46.2  -0.44  -1.07  0.64
23    ARI     -2.5    14   5   8   1  39.3  53.9  -0.48   1.07 -1.55
24    CIN     -2.5    14   5   8   1  39.3  48.5  -0.21  -0.36  0.15
25    SD      -3.0    14   5   9   0  35.7  50.0   1.59   0.00  1.59
26    PHI     -3.0    14   5   9   0  35.7  54.8   2.25   1.21  1.03
27    NYJ     -4.5    14   4  10   0  28.6  20.4  -9.28  -8.29 -0.99
28    LA      -5.5    14   4  10   0  28.6  14.5  -9.21  -9.36  0.14
29    CHI     -6.0    14   3  11   0  21.4  29.2  -5.37  -5.14 -0.23
30    JAX     -6.0    14   2  12   0  14.3  24.6  -6.19  -7.07  0.88
31    SF     -15.0    14   1  13   0   7.1  15.1 -12.05 -12.14  0.09
32    CLE    -14.0    14   0  14   0   0.0  10.5 -12.06 -13.43  1.37

and week 16 is here:

Global Statistics:
Games  Home Wins HwPct Winning_Score Losing_Score Margin
240       137     57.1      27.67        17.61     10.06

Calculated Pythagorean Exponent:  3.30


Rank  Team    Median  GP   W   L   T  Pct   Pred   SRS    MOV   SOS
------------------------------------------------------------------------
1     NE      13.0    15  13   2   0  86.7  85.7   8.65  11.33 -2.69
2     DAL      6.0    15  13   2   0  86.7  77.8   8.01   8.60 -0.59
3     OAK      3.0    15  12   3   0  80.0  60.3   4.52   3.27  1.26
4     KC       5.0    15  11   4   0  73.3  67.0   5.26   4.53  0.72
5     ATL      7.0    15  10   5   0  66.7  72.5   8.47   8.53 -0.06
6     PIT      7.0    15  10   5   0  66.7  66.3   5.46   4.60  0.86
7     MIA      3.0    15  10   5   0  66.7  51.0  -1.82   0.27 -2.09
8     NYG      3.0    15  10   5   0  66.7  54.9   1.67   1.13  0.54
9     SEA      2.0    15   9   5   1  63.3  66.0   2.76   4.00 -1.24
10    GB       4.0    15   9   6   0  60.0  57.9   2.69   2.47  0.23
11    DET      3.0    15   9   6   0  60.0  48.7  -1.14  -0.33 -0.80
12    HOU      2.0    15   9   6   0  60.0  38.0  -2.40  -2.80  0.40
13    WAS      2.0    15   8   6   1  56.7  54.8   2.42   1.47  0.95
14    TB       2.0    15   8   7   0  53.3  46.2  -0.07  -1.07  1.00
15    TEN      1.0    15   8   7   0  53.3  49.1  -1.35  -0.27 -1.08
16    BAL      1.0    15   8   7   0  53.3  60.1   2.71   2.60  0.11
17    DEN      1.0    15   8   7   0  53.3  54.9   2.85   1.20  1.65
18    NO      -1.0    15   7   8   0  46.7  54.1   1.48   1.40  0.08
19    MIN     -2.0    15   7   8   0  46.7  47.8  -0.38  -0.53  0.16
20    BUF     -3.0    15   7   8   0  46.7  59.1   1.51   2.73 -1.22
21    IND     -3.0    15   7   8   0  46.7  53.3   0.38   1.00 -0.62
22    ARI     -2.0    15   6   8   1  43.3  54.1  -0.04   1.20 -1.24
23    PHI     -1.0    15   6   9   0  40.0  55.5   2.77   1.47  1.30
24    CAR     -3.0    15   6   9   0  40.0  42.9  -1.05  -2.13  1.08
25    CIN     -2.0    15   5   9   1  36.7  48.1  -0.11  -0.47  0.36
26    SD      -3.0    15   5  10   0  33.3  49.4   0.33  -0.20  0.53
27    LA      -4.0    15   4  11   0  26.7  17.3  -9.51  -8.80 -0.71
28    NYJ     -5.0    15   4  11   0  26.7  16.7 -10.30 -10.27 -0.04
29    JAX     -5.0    15   3  12   0  20.0  31.7  -4.87  -5.20  0.33
30    CHI     -6.0    15   3  12   0  20.0  27.5  -6.30  -6.13 -0.17
31    SF     -13.0    15   2  13   0  13.3  17.8 -11.78 -11.27 -0.52
32    CLE    -14.0    15   1  14   0   6.7  13.2 -10.83 -12.33  1.50

Playoff slots by now are almost all determined. AFC playoff contenders are set. NFC playoff contenders are set but for one wild card slot and one division champion (NFC North). Pittsburgh beat Baltimore in a thrilling game. Kansas City played the heaviest QB in my memory. Two good QBs broke legs and the loss of Carr could have a serious impact on Oakland’s playoff success.

The odds that teams like Oakland and Dallas make the playoffs are getting larger, but what can’t be predicted is where in the ranking (1-6) they will be. At this point, Washington could still win the NFC East. Philadelphia could tie, I guess, though the absence of 3 good receivers really does hamper them.

It’s hard to understand Oakland’s success until you split the season in two. The first half was luck. The last half has been offensive dominance, OSRS over 11, best in league over that period of time.

Given that Dallas has playoff experience in 2014 and not in 2015, I have new formulas for playoff odds, based on adding four more years of data. Those will be published in the near future.

Global Statistics:
Games  Home Wins HwPct Winning_Score Losing_Score Margin
177       101     57.1      27.48        18.02      9.46

Calculated Pythagorean Exponent:  3.45

Rank  Team    Median  GP   W   L   T  Pct   Pred   SRS    MOV   SOS
------------------------------------------------------------------------
1     DAL      7.0    11  10   1   0  90.9  79.6   7.74   9.36 -1.63
2     NE      11.0    11   9   2   0  81.8  79.7   7.10   8.73 -1.62
3     OAK      3.0    11   9   2   0  81.8  59.4   3.86   2.91  0.95
4     KC       5.0    11   8   3   0  72.7  63.7   3.42   3.45 -0.03
5     NYG      3.0    11   8   3   0  72.7  57.0   0.75   1.64 -0.88
6     SEA      2.0    11   7   3   1  68.2  65.1   3.72   3.36  0.35
7     ATL      7.0    11   7   4   0  63.6  64.3   7.27   5.09  2.18
8     MIA      4.0    11   7   4   0  63.6  53.2  -0.59   0.82 -1.40
9     DET      3.0    11   7   4   0  63.6  53.2  -1.28   0.82 -2.10
10    DEN      2.0    11   7   4   0  63.6  66.2   5.72   4.27  1.44
11    WAS      2.0    11   6   4   1  59.1  55.1   2.38   1.45  0.92
12    PIT      8.0    11   6   5   0  54.5  65.1   4.09   4.00  0.09
13    BUF      4.0    11   6   5   0  54.5  64.6   2.95   4.09 -1.15
14    MIN      3.0    11   6   5   0  54.5  60.8   1.60   2.36 -0.77
15    HOU      3.0    11   6   5   0  54.5  33.7  -3.64  -3.82  0.18
16    TB       2.0    11   6   5   0  54.5  45.0  -0.48  -1.36  0.88
17    BAL      2.0    11   6   5   0  54.5  57.0  -0.02   1.55 -1.56
18    TEN     -3.0    12   6   6   0  50.0  53.4  -1.77   1.00 -2.77
19    NO      -1.0    11   5   6   0  45.5  57.2   3.78   2.45  1.33
20    SD      -1.0    11   5   6   0  45.5  56.3   3.12   2.00  1.12
21    GB      -1.0    11   5   6   0  45.5  45.4  -1.27  -1.36  0.10
22    PHI     -1.0    11   5   6   0  45.5  64.7   4.19   3.73  0.46
23    IND     -3.0    11   5   6   0  45.5  40.7  -3.68  -2.82 -0.86
24    ARI     -2.0    11   4   6   1  40.9  56.2   0.92   1.55 -0.63
25    CAR     -3.0    11   4   7   0  36.4  48.5   0.89  -0.45  1.35
26    LA      -3.0    11   4   7   0  36.4  24.4  -6.38  -6.00 -0.38
27    CIN     -4.0    11   3   7   1  31.8  38.2  -1.79  -2.91  1.12
28    NYJ     -4.0    11   3   8   0  27.3  25.9  -6.20  -6.36  0.17
29    JAX     -5.0    11   2   9   0  18.2  25.3  -7.79  -7.18 -0.60
30    CHI     -6.0    11   2   9   0  18.2  20.4  -8.33  -7.82 -0.51
31    SF     -13.0    11   1  10   0   9.1  19.5  -8.68 -10.55  1.87
32    CLE    -14.0    12   0  12   0   0.0  11.9 -11.59 -12.92  1.32

Odds for the 2015 NFL playoff final, presented from the AFC team’s point of view:

SuperBowl Playoff Odds
Prediction Method AFC Team NFC Team Score Diff Win Prob Est. Point Spread
C&F Playoff Model Denver Broncos Carolina Panthers 2.097 0.891 15.5
Pythagorean Expectations Denver Broncos Carolina Panthers -0.173 0.295 -6.4
Simple Ranking Denver Broncos Carolina Panthers -2.3 0.423 -2.3
Median Point Spread Denver Broncos Carolina Panthers -5.0 0.337 -5.0

 

Last week the system went 1-1, for a total record of 6-4. The system favors Denver more than any other team, and does not like Carolina at all. Understand, when a team makes it to the Super Bowl easily, and a predictive system gave them about a 3% chance to get there in the first place, it’s reasonable to assume that in that instance, the system really isn’t working.

So we’re going to modify our table a little bit and give some other predictions and predictive methods. The first is the good old Pythagorean formula. We best fit the Pythagorean exponent to the data for the year, so there is good reason to believe that it is more accurate than the old 2.37. It favors Carolina by a little more than six points. SRS directly gives point spread, which can be back calculated into a 57.7% chance of Carolina winning. Likewise, using median point spreads to predict the Denver-Carolina game gives Carolina a 66.3% chance of winning.

Note that none of these systems predicted the outcome of the Carolina – Arizona game. Arizona played a tougher schedule and was more of a regular season statistical powerhouse than Carolina. Arizona, however, began to lose poise as it worked its way through the playoffs. And it lost a lot of poise in the NFC championship game.

Odds for the third week of the 2015 playoffs, presented from the home team’s point of view:

Conference Championship Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Carolina Panthers Arizona Cardinals -1.40 0.198 -10.4
Denver Broncos New England Patriots 1.972 0.879 14.6

 

Last week the system went 2-2, for a total record of 5-3. The system favors Arizona markedly, and Denver by an even larger margin. That said, the teams my system does not like have already won one game. There have been years when a team my system didn’t like much won anyway. That was the case in 2009, when my system favored the Colts over the Saints. The system isn’t perfect, and the system is static. It does not take into account critical injuries, morale, better coaching, etc.

Odds for the second week of the 2015 playoffs, presented from the home team’s point of view:

Second Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Carolina Panthers Seattle Seahawks -1.713 0.153 -12.7
Arizona Cardinals Green Bay Packers -0.001 0.500 0.0
Denver Broncos Pittsburgh Steelers 0.437 0.608 3.2
New England Patriots Kansas City Chiefs -0.563 0.363 -4.2

 

Last week the system went 3-1 and perhaps would have gone 4-0 if after the Burflict interception, Cincinnati had just killed three plays and kicked a field goal.

The system currently gives Seattle a massive advantage in the playoffs. It says that Green Bay/Arizona is effectively an even match up, and that both the AFC games are pretty close. It favors Denver in their matchup, and the Chiefs in theirs.

One last comment about last week’s games. The Cincinnati-Pitt game was the most depressing playoff game I’ve seen in a long time, both for the dirty play on both sides of the ball, and the end being decided by stupid play on Cincinnati’s part.  It took away from the good parts of the game, the tough defense when people weren’t pushing the edges of the rules, and the gritty play on the part of McCarron and Roethlisberger. There was some heroic play on both their parts, in pouring rain.

But for me, watching Ryan Shazier leading with the crown of his helmet and then listening to officials explain away what is obvious on video more or less took the cake. If in any way shape or form, this kind of hit is legal, then the NFL rules system is busted.

To start, a summary of the 2014 regular season data:

2014-regular-season-stats

This gives us the basis to generate playoff values based on my playoff formula. Playoff Odds are calculated according to this model:

logit P = 0.668 + 0.348*(delta SOS) + 0.434*(delta Playoff Experience)

and the results are:

2014 NFL Playoff Teams, C&F Playoff Model Worksheet.
NFC
Rank Name Home Field Advantage Prev. Playoff Experience Strength of Schedule Total Score
1 Seattle Seahawks 0.406 0.434 0.275 1.115
2 Green Bay Packers 0.406 0.434 -0.118 0.722
3 Dallas Cowboys 0.406 0.0 -0.630 -0.224
4 Carolina Panthers 0.406 0.434 -0.292 0.548
5 Arizona Cardinals 0.0 0.0 0.449 0.449
6 Detroit Lions 0.0 0.0 -0.132 -0.132
AFC
1 NE Patriots 0.406 0.434 0.438 1.278
2 Denver Broncos 0.406 0.434 0.550 1.390
3 Pittsburgh Steelers 0.406 0.0 -0.703 -0.297
4 Indianapolis Colts 0.406 0.434 -0.393 0.447
5 Cinncinnati Bengals 0.0 0.434 -0.202 -0.602
6 Baltimore Ravens 0.0 0.0 -0.724 -0.724

 

The total score of a particular team is used as a base. Subtract the score of the opponent and the result is the logit of the win probability for that game. You can use the inverse logit (see Wolfram Alpha to do this easily) to get the probability, and you can multiply the logit of the win probability by 7.4 to get the estimated point spread.

For the second week of the 2014 playoffs, I’ve done all this for you, in the table below. Odds are presented from the home team’s point of view.

Second Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Seattle Seahawks Carolina Panthers 0.567 0.638 4.2
Green Bay Packers Dallas Cowboys 1.352 0.795 10.0
New England Patriots Baltimore Ravens 2.002 0.881 14.8
Denver Broncos Indianapolis Colts 1.349 0.794 10.0

 

Baltimore is not given much of a chance by these techniques, but an interesting analysis by Benjamin Morris of Skeptical Sports (featured now on fivethirtyeight.com) is worth paying attention to. Though the divisional round is hard on teams without a bye, those that survive appear to have a superior chance to go forward in the playoffs. Benjamin has always struck me as an incisive analyst, so he’s absolutely worth paying attention to.