### Statistics

Summary: with some calculations based on adjusted yards per attempt, Matt Ryan’s value as a passer in the 2016 season can be shown to be almost 9 points a game more than the average QB.

Mark Zinno is a host on a sports talk show, 92.9 the Game, in the 7pm ET time slot. Often booted out of the slot by Atlanta Hawks games, he nonetheless has been a dogged supporter of Matt Ryan. This isn’t new, btw. Even in years where Matt Ryan wasn’t at his best, he would doggedly argue that Matt Ryan was an elite quarterback, and said repeatedly that compared to an average NFL team, that Atlanta was blessed.

So, we’re dedicating this blog post to Mark Zinno.

It’s hard to understand the scope of what Matt Ryan has done until you look at his adjusted yards per attempt in 2016. Pro Football Reference lists it as 10.1, which is one of the highest I’ve seen, and comparable to Peyton Manning’s 2004 season, where PM’s AYA was 10.2. Looking a little further, you can see that PFR ranks this the 4th best performance in history. Aaron Rogers is in the top 4, and for some reason, so is Nick Foles.

The value in using AYA is that you can build an expected points curve that satisfies all the requirements of the AYA function, and then use the slope of that curve to relate yards to points. Don’t worry, I did that long ago, and the result is documented here. The simple take home is the magic conversion 2.25, which converts AYA from yards to “expected points generated per 30 passes”.

Then, using the 2016 annual data from Pro Football Reference, you can calculate  what the average QB did, by calculating an AYA using the overall season’s statistics.  So the formula is:

(123639 yards + 20*786 TD – 45*415 Ints)/  18295 attempts

(123639 yards + 15720 “TD” yards – 18675 “Int” yards) / 18295 attempts

120684 yards / 18295 attempts

6.60 AYA to 3 significant digits.

Now things become simpler. Matt Ryan generated 10.1*2.25 = 22.7 points per 30 attempts, while Joe QB generated 14.8 points per 30 attempts. The difference, rounded to a whole number, suggests that Matt Ryan was worth about 8 more points in 30 attempts than the average NFL QB this season.

That doesn’t entirely encompass his per game value. Matt threw 534 attempts  this season for an average of 33.4 passes per game. So his per game value, to the nearest tenth of a point, was more like 8.8 points a game more than the average quarterback.

But if the numbers baffle you, then the simple take home is that Matt’s statistical efficiency in 2016 is comparable to the best single season Peyton Manning ever had.

The teams in the 2016 Championship are Atlanta and New England, and my system this year slightly favors Atlanta, given the same assumptions that we used initially. Atlanta is selected as the “home team”, though no home team is used in any of the final calculations.

Odds are presented from the home team’s point of view:

NFL Championship Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Atlanta Falcons New England Patriots 0.092 0.523 0.6

We present a series of alternate calculations below. They are based on — what if Atlanta should be treated as a team with playoff experience, then median point spread, then Pythagoreans, and then the Simple Ranking system.

ATL – NE Alternate Calculations
Odds Method Score Diff Win Prob Est. Point Spread
ATL has playoff experience 0.839 0.698 6.2
Median Point Spread -0.68 0.34 -5.0
Pythagoreans -0.92 0.29 -6.8
Simple Ranking -0.11 0.47 -0.8

There is nothing consistent in any of the ratings methods. Median point spreads, when pumped into a logistic regression, have less correlation than Pythagorean, though in both cases, the confidence intervals are on the order of 0.15, as opposed to less than 0.05. Medians and Pythagoreans suggest New England has a large advantage, Simple Rankings say the game will be close, too close to bet. So two claim close games, toss ups more or less, one suggests an easy Atlanta victory, and the others suggest a substantial Patriots margin.

Last week was not the best for the “system”. That said, a system that wins all the time probably isn’t a system at all, but merely wishful thinking.

For the third week of the 2016 playoffs, odds are presented from the home team’s point of view:

Conference Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Atlenta Falcons Green Bay Packers -0.079 0.480 -0.6
New England Patriots Pittsburgh Steelers -0.219 0.445 -1.6

The odds in Atlanta -GB are too close to call. My system would not suggest betting that game. My system favors Pittsburgh. As stated previously, New England played a weak schedule and that’s a major factor in our rankings. Both games are seen as close.

My system scored 4-0 in terms of predicting wins, but at this point the teams are better and the games are closer. Detroit, I believe, would have been a closer game had Matthew Stafford not been injured. His receiver dropped balls and Seattle was the beneficiary of some incredible pass receptions. That said, we’re into the second round and so will present the second round odds, as determined by the 2 year PPX formula. 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
Dallas Cowboys Green Bay Packers 0.569 0.639 4.2
Atlanta Falcons Seattle Seahawks 0.475 0.617 3.5
New England Patriots Houston Texans -0.247 0.439 -1.8
Kansas City Chiefs Pittsburgh Steelers 0.806 0.691 6.0

I will note that this system does not favor the New England Patriots, because their -2.65 point Strength of Schedule weighs against them. Both Kansas City or Pittsburgh would be favored in the next round, should New England win. But it’s not a large difference, and Tom Brady is having a magical season. We’ll see.

It is certainly reasonable to argue that Dallas only has playoff experience to 2014 and Green Bay has 2015 experience, and thus the 1 Year PPX formula should be used. We did calculate those odds, as well as odds generated by a median point spread and also Pythagorean expectations and the Simple Ranking System. In all three cases we used the stock 3 point home field advantage.

Dallas Green Bay Alternate Calculations
Odds Method Score Diff Win Prob Est. Point Spread
New 1 Year PPX Formula -0.113 0.47 -0.8
Median Point Spread 0.47 0.62 3.5
Pythagoreans 1.1 0.75 8.1
Simple Ranking 0.96 0.72 7.1

Using a 1 year formula, Dallas-GB would be too close to call. All other formulas favor Dallas. Medians would have given essentially the same odds as the two year PPX, had we chosen to honor a 3.8 point HFA, as is calculated for playoff teams. Both Pythagoreans and SRS give Dallas about a touchdown advantage.

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:

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

The playoffs are here, and it’s time to work on the Code and Football playoff formula. The one used the past five years has been this one, and it has served the author well.

(PX within 1 year) Logit P = 0.668 + 0.348(SOS) + 0.434(PPX)

Where P is probability of winning, SOS is Strength of Schedule, as measured by the Simple Ranking System, PX is playoff experience, and PPX is previous playoff experience. But with the advantage of time, and also the question of whether Dallas’s playoff experience in 2014 is significant, we added five more years of data and calculated the following three formula, for which all coefficients were statistically significant to better than 95%.

(PX within 1 year) Logit P = 0.594 + 0.288(SOS) + 0.621(PPX)
(PX within 2 years) Logit P = 0.660 + 0.304(SOS) + 0.747(PPX)
(PX within 3 years) Logit P = 0.699 + 0.323(SOS) + 0.895(PPX)

With the original 11 year data set (2001-2011), the 2 year and 3 year formulas were not significant, but with the larger data set (2001-2015), they are. You can also derive significant formulas for playoff experience within 1 year, 2 years, or 3 years using just the last 11 years of data (2005-2015). So the outlier appears to be that original 11 years of NFL data.

Since the only teams where the difference might be significant would be Dallas-Seattle, Dallas-GB, or Dallas-AFC matchups (and we can deal with those on a case-by-case basis), we will now work our spreadsheet out using the 2 year formulas this year.

2016 NFL Playoff Teams, C&F Worksheet.
NFC
Rank Name Home Field Adv Playoff Experience SOS Total Score
1 Dallas Cowboys 0.660 0.747 -0.067 1.34
2 Atlanta Falcons 0.660 0.000 0.033 0.693
3 Seattle Seahawks 0.660 0.747 -0.529 0.878
4 Green Bay Packers 0.660 0.747 0.024 1.431
5 New York Giants 0.0 0.0 0.152 0.152
6 Detroit Lions 0.0 0.747 -0.198 0.549
AFC
1 New England Patriots 0.660 0.747 -0.806 0.601
2 Kansas City Chiefs 0.660 0.747 0.219 1.626
3 Pittsburgh Steelers 0.660 0.747 0.073 1.480
4 Houston Texans 0.660 0.747 0.131 1.508
5 Oakland Raiders 0.0 0.0 0.404 0.404
6 Miami Dolphins 0.0 0.0 -0.407 -0.407

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.

All that said, a couple more notes about the playoff formulas. Note that the PPX coefficient grows larger as the PPX gap grows larger. I’m not so sure that a team with playoff experience three years ago is all that much advantaged, as the sum of all teams that lack playoff experience over three years or more are disadvantaged. Teams that come to mind are Oakland and Miami and Detroit this year, who haven’t been in the playoffs in many years. The Giants also, have not been in the playoffs in a fairly long time, and that factors into the survivability of their team in the playoffs.

The home field advantage these formulas give is larger than the historic playoff gap. Playoff teams over the 15 year period win games by 62.7%, corresponding to a logit coefficient of 0.518. Note this is still a bigger advantage than regular season home field advantage (57-58%) but not as much as predicted by the raw formulas.

The team this system favors best is the Kansas City Chiefs. But if Oakland had not lost Carr in the 16th week of the season, would they have had home field advantage and a bye? I’m not sure about that.

Because the sheet above can be hard to decipher, for the first week of the 2016 playoffs, I’ve done all this for you, in the table below. Odds are presented from the home team’s point of view:

First Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Seattle Seahawks Detroit Lions 0.349 0.586 2.4
Green Bay Packers New York Giants 1.279 0.782 9.5
Pittsburgh Steelers Miami Dolphins 1.887 0.868 14.0
Houston Texans Oakland Raiders 1.104 0.751 8.2

None of the games are judged as close. The dominant factor is the lack of playoff experience on the part of the visiting teams.

Update: forgot that Detroit was in the playoffs in 2014, which changes odds in Seattle-Detroit significantly.

Finally! The 2016 season is over and we can figure out playoff formulas.

```Global Statistics:
Games  Home Wins HwPct Winning_Score Losing_Score Margin
256       147     57.4      27.76        17.53     10.23

Calculated Pythagorean Exponent:  3.24

Rank  Team    Median  GP   W   L   T  Pct   Pred   SRS    MOV   SOS
------------------------------------------------------------------------
1     NE      13.0    16  14   2   0  87.5  86.3   9.29  11.94 -2.65
2     DAL      6.0    16  13   3   0  81.2  73.8   6.97   7.19 -0.22
3     KC       5.5    16  12   4   0  75.0  67.4   5.60   4.88  0.72
4     OAK      3.0    16  12   4   0  75.0  56.2   3.26   1.94  1.33
5     ATL      7.0    16  11   5   0  68.8  71.6   8.48   8.38  0.11
6     PIT      5.5    16  11   5   0  68.8  65.6   4.74   4.50  0.24
7     NYG      3.0    16  11   5   0  68.8  57.1   2.13   1.62  0.50
8     SEA      2.0    16  10   5   1  65.6  65.1   2.13   3.88 -1.74
9     GB       5.5    16  10   6   0  62.5  58.6   2.83   2.75  0.08
10    MIA      3.0    16  10   6   0  62.5  46.3  -2.40  -1.06 -1.34
11    DET      2.0    16   9   7   0  56.2  47.2  -1.40  -0.75 -0.65
12    TEN      1.5    16   9   7   0  56.2  50.6  -1.01   0.19 -1.19
13    TB       1.5    16   9   7   0  56.2  46.6  -0.19  -0.94  0.74
14    DEN      1.5    16   9   7   0  56.2  59.2   4.05   2.25  1.80
15    HOU      1.5    16   9   7   0  56.2  37.2  -2.63  -3.06  0.43
16    WAS      1.0    16   8   7   1  53.1  52.7   1.97   0.81  1.16
17    IND      0.5    16   8   8   0  50.0  53.8   0.37   1.19 -0.82
18    MIN      0.5    16   8   8   0  50.0  55.1   0.94   1.25 -0.31
19    BAL      0.0    16   8   8   0  50.0  55.4   1.54   1.38  0.16
20    ARI     -1.0    16   7   8   1  46.9  61.5   1.59   3.50 -1.91
21    PHI     -1.0    16   7   9   0  43.8  58.3   3.80   2.25  1.55
22    NO      -1.5    16   7   9   0  43.8  52.6   1.54   0.94  0.61
23    BUF     -3.0    16   7   9   0  43.8  54.4  -0.33   1.31 -1.64
24    CIN     -1.5    16   6   9   1  40.6  52.5   1.04   0.62  0.42
25    CAR     -2.0    16   6  10   0  37.5  43.1  -1.00  -2.06  1.06
26    SD      -3.0    16   5  11   0  31.2  47.5   0.06  -0.81  0.87
27    NYJ     -4.5    16   5  11   0  31.2  21.6  -8.52  -8.38 -0.14
28    LA      -5.5    16   4  12   0  25.0  13.8 -11.09 -10.62 -0.46
29    JAX     -4.5    16   3  13   0  18.8  32.2  -4.97  -5.12  0.16
30    CHI     -6.0    16   3  13   0  18.8  23.9  -7.50  -7.50 -0.00
31    SF     -12.5    16   2  14   0  12.5  19.3 -11.21 -10.69 -0.52
32    CLE    -13.5    16   1  15   0   6.2  14.9 -10.09 -11.75  1.66
```

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