Statistics

The competitors are Denver and Seattle, and as stated previously, my model favors Seattle substantially.

Super Bowl
NFC Champion AFC Champion Score Diff Win Prob Est. Point Spread
Seattle Seahawks Denver Broncos 1.041 0.739 7.7

Of course by this point my model has been reduced to a single factor, as there is no home field advantage in the Super Bowl and both teams are playoff experienced. Since every season 8 of the 11 games are before the Conference chanpionships and Super Bowl, the model works best for those first eight games. Still, it’s always interesting to see what the model calculates.

At least as interesting is the Peyton Manning factor, a player having the second best season of his career (as measured by adjusted yards per attempt). I thought it would be interesting to try and figure out how much of the value above average of the potent Denver Broncos attack that Peyton Manning was responsible for. We’ll start by looking at the simple ranking of the team, divided into the offensive and defensive components. Simple rankings help adapt for the quality of opposition, which for Denver was below league average.

Denver Broncos Simple Ranking Stats
Margin of Victory Strength of Schedule Simple Ranking Defensive Simple Ranking Offensive Simple Ranking
12.47 -1.12 11.35 -3.31 14.65

Narrowed down to the essentials, how much of the 14.65 points of Denver offense (above average) was Peyton Manning’s doing? With some pretty simple stats, we can come up with some decent estimates of the Manning contribution to Denver’s value above average.

We’ll start by calculating Peyton’s adjusted yards per attempt, and do so for the league as a whole. We’ll use the Pro Football Reference formula. Later, we’ll use the known conversion factors for AYA to turn that contribution to points, and the subtract the league average from that contribution.

Passing Stats, 2013
Player(s) Completions Attempts Yards Touchdowns Interceptions AYA
Peyton Manning 450 659 5477 55 10 9.3
All NFL passing 11102 18136 120626 804 502 6.3

The difference between Peyton Manning’s AYA and the league average is 3 points. Peyton Manning threw 659 times, averaging about 41.2 passes per game. This compares to the average team passing about 35.4 times a game. To convert an AYA into points per 40 passes, the conversion factor is 3.0. This is math people can do in their head. 3 times 3 equals 9 points. In a game situation, in 2013, where Peyton Manning throws 40 passes, he’ll generate 9 points more offense than the average NFL quarterback. So, of the 14.65 points above average that the Denver Broncos generated, Peyton Manning is at least responsible for 61% of that.

Notes:

There is a 0.5 point difference between the AYA reported by Pro Football Reference and the one I calculated for all NFL teams. I suspect PFR came to theirs by taking an average of the AYA of all 32 teams as opposed to calculating the number for all teams. To be sure, we’ll grind the number out step by step.

The yards term: 120626
The TD term: 20 x 804 = 16080
The Int term: 45 x 502 = 22590

120626 + 16080 – 22590 = 114116

Numerator over denominator is:

114116 / 18136 = 6.29223… to two significant digits is 6.3.

My system went 3-0-1 last weekend (Or 3-1 if you consider my prediction in the Bengals – Chargers game a loss, as opposed to “too close to pick”), so time to present playoff odds for the second round of the playoffs.

Divisional Round Playoff Odds
Home Team Visiting Team Score Diff Win Prob Est. Point Spread
Seattle Seahawks New Orleans Saints 0.676 0.663 5.0
Carolina Panthers SF 49ers -0.157 0.461 -1.2
Denver Broncos San Diego Chargers 0.411 0.601 3.0
New England Patriots Indianapolis Colts -0.060 0.485 -0.4

Odds that differ by less than a point in estimated point spread are probably not significant, and from my POV, a suggestion that you don’t bet that particular game.

The regular season has ended and the playoffs have begun. It would be useful to have a set of playoff grade data to do playoff probabilities, and though I’ve been down and out this season (no job at times, foot stress fracture at times, and a bad right shoulder), I currently have some time off my new job, a new laptop, and enough time to grind through some playoff numbers.

NFL stats at the end of the regular season:

To explain the columns above, Median is a median point spread, and can be used to get a feel for how good a team is without overly weighting a blowout win or blowout loss. HS is Brian Burke’s Homemade Sagarin, as implemented in Maggie Xiong’s PDL::Stats. Pred is the predicted Pythagorean expectation. The exponent for this measure is fitted to the data set itself. SOS, SRS, and MOV are the simple ranking components, analyzed via this Perl implementation. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

Playoff Odds are calculated according to this model:

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

The results are given below, as a “score” in logits:

2013 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 0.494 1.334
2 Carolina Panthers 0.406 0.0 0.484 0.889
3 Philadelphia Eagles 0.406 0.0 -0.661 -0.256
4 Green Bay Packers 0.406 0.434 -0.842 -0.003
5 San Francisco 49ers 0.0 0.434 0.612 1.046
6 New Orleans Saints 0.0 0.0 0.658 0.658
AFC
1 Denver Broncos 0.406 0.434 -0.546 0.293
2 NE Patriots 0.406 0.434 -0.258 0.582
3 Cancinnati Bengals 0.406 0.434 -0.856 -0.017
4 Indianapolis Colts 0.406 0.434 0.209 1.048
5 Kansas City Chiefs 0.0 0.0 -0.602 -0.602
6 San Diego Chargers 0.0 0.0 -0.118 -0.118

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 first week of the 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
Philadelphia Eagles New Orleans Saints -0.914 0.286 -6.8
Green Bay Packers SF 49ers -1.049 0.259 -7.8
Cincinnati Bengals San Diego Chargers 0.101 0.525 0.7
Indianapolis Colts Kansas City Chiefs 1.650 0.839 12.2

Some general conclusions from the data above: the teams my model favors most are the Seattle Seahawks, the Indianapolis Colts, the 49ers, the Carolina Panthers, and then the New Orleans Saints, mostly NFC teams. Since the Super Bowl itself does not have a home team, the odds change once you actually reach the Super Bowl. The sum of the SOS column and the Previous Playoff Experience column can be used to estimate odds of winning “the big one”. The strongest team in a Super Bowl setting would be the San Francisco 49ers, with a total score, less HFA, of 1.049. The Indianapolis Colts, with a total score of 0.643 less HFA, would be the strongest possible AFC contender.

A point I’d like the reader to consider is this question: should the New Orleans Saints be granted an exception to the previous playoff experience rule of “last year only counts” and given the 0.434 advantage of a playoff team? 2012 was an aberration as the coach was suspended. I’m not calculating this variation into the formula at this point, but I’ll note that this is an issue that you, the reader, need to resolve for yourself.

The road to the playoffs is not easy, a topic that can be studied by trying to calculate the path to the playoffs of the Indianapolis colts, a team that would be favored in every matchup along the way. Let’s calculate the odds of Indianapolis actually winning all three games.

Odds of Indianapolis reaching the Super Bowl
WP versus Kansas City WP versus Denver Broncos WP versus NE Pats Cume Probability
0.839 0.586 0.515 0.253

Three teams from the NFC would be favored over any possible AFC contender. Those are San Francisco, Seattle, and the New Orleans Saints. Carolina would be favored over any AFC contender except the Indianapolis Colts.

Sorry about any delays in publication. I was between jobs at the time.

Week 13 NFL Stats:

To explain the columns above, Median is a median point spread, and can be used to get a feel for how good a team is without overly weighting a blowout win or blowout loss. HS is Brian Burke’s Homemade Sagarin, as implemented in Maggie Xiong’s PDL::Stats. Pred is the predicted Pythagorean expectation. The exponent for this measure is fitted to the data set itself. SOS, SRS, and MOV are the simple ranking components, analyzed via this Perl implementation. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

OSRS and DSRS stats look like this:

The two most impressive teams so far, IMO, are Seattle and Carolina. New Orleans may win the division but right now Carolina is something of a statistical darling.

If the NFL were to stop playing altogether, and judge teams on their current records, and assign division winners, the playoff rankings in the AFC and NFC would look something like the table below. The teams’ associated playoff stats, according to my playoff model, are also presented.

Playoff Teams, if NFL playoffs were started 10/30/2103.
NFC
Rank Name Wins Losses Home Field Advantage Prev. Playoff Experience Strength of Schedule
1 Seattle Seahawks 7 1 Yes, throughout. Yes 0.31
2 New Orleans Saints 6 1 Yes, 1 game. No (?) -2.28
3 Green Bay Packers 5 2 Yes, 1 game. Yes 0.30
4 Dallas Cowboys 4 4 Yes, 1 game. No 0.42
5 San Francisco 49ers 6 2 No Yes 0.47
6 Detroit Lions 5 3 No No 0.42
AFC
1 Kansas City Chiefs 8 0 Yes, throughout. No -4.34
2 Cinncinnati Bengals 6 2 Yes, 1 game. Yes -1.37
3 New England Patriots 6 2 Yes, 1 game. Yes -3.06
4 Indianapolis Colts 5 2 Yes, 1 game. Yes 2.03
5 Denver Broncos 7 1 No Yes -2.63
6 San Diego Chargers 4 3 No No -2.01

The first thing that pops out in this chart is the remarkable strength of schedule advantage Indianapolis has so far. Given their remaining schedule (games with the Texans, Titans, Rams and Jaguars), that advantage is likely to evaporate over the next 8 games, but it leads to the interesting assertion that Indianapolis would be favored by some 14 points over Kansas City should Indianapolis play KC in a second round playoff game, right now.

Kansas City, by contrast, is an exceptionally weak #1 team in terms of playoff experience and strength of schedule. The Chiefs do start playing some tougher teams in the second half, but just a few.

In the NFC, all the possible playoff teams have had about the same strength of schedule except for the Saints, whose schedule has been a lot easier than most. The one factor an analyst will have to decide for themselves is whether the Saints are a team with previous playoff experience, despite the formal definition of the term, in my formula, as experience in last year’s playoffs. I’ve done that in the past, for the 2011 New York Giants.

Conversation around Atlanta is that the Falcons are effectively out of the playoff hunt, as they would need to go 8-1 to be back in it. Personally, I don’t see how they can become a better team than Carolina at this point, much less New Orleans.

Week 8 NFL Stats:

To explain the columns above, Median is a median point spread, and can be used to get a feel for how good a team is without overly weighting a blowout win or blowout loss. HS is Brian Burke’s Homemade Sagarin, as implemented in Maggie Xiong’s PDL::Stats. Pred is the predicted Pythagorean expectation. The exponent for this measure is fitted to the data set itself. SOS, SRS, and MOV are the simple ranking components, analyzed via this Perl implementation. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

OSRS and DSRS stats look like this:

I’m very tempted to start figuring out who would win playoffs if results were frozen and teams were to go into rounds of games at this time. That’s something for a future post, though.

Detroit for me is a puzzling team, I suspect in part it is because casual fans watching football in Georgia expected Matthew Stafford to mature into a leading NFL quarterback. That he’s become a good quarterback is given, but I guess the hope he would be a modern day Bobby Layne hasn’t left those of us living in the Southeast.

Detroit Lions 2005-2013
Year Team W L T SRS OSRS DSRS MOV SOS
2005 DET 5 11 0 -6.70 -5.75 -0.95 -5.69 -1.01
2006 DET 3 13 0 -6.35 -1.82 -4.53 -5.81 -0.54
2007 DET 7 9 0 -3.55 1.14 -4.69 -6.12 2.57
2008 DET 0 16 0 -13.11 -2.81 -10.30 -15.56 2.45
2009 DET 2 14 0 -14.38 -4.97 -9.41 -14.50 0.12
2010 DET 6 10 0 1.91 0.72 1.19 -0.44 2.35
2011 DET 10 6 0 6.07 8.07 -2.01 5.44 0.63
2012 DET 4 12 0 -2.31 0.59 -2.89 -4.06 1.76
2013 DET 4 3 0 0.75 3.54 -2.79 2.71 -1.96

Detroit hosts Dallas this weekend and not at all surprisingly, for two teams fairly closely matched, the three predictive systems yield three different results. Pythagoreans have Dallas and Detroit as essentially even. Simple rankings would suggest that Dallas has a slight edge. Medians suggest the opposite, that Detroit will win by about 5 points.

Odds of Detroit Winning and Predicted Point Spread.
Pythagorean Expectation Simple Ranking System Median Analysis
Pct Points Pct Points Pct Points
0.49 -0.3 0.40 -3.0 0.66 5

As #1 teams go, Kansas City has had an exceptionally weak set of opponents and as a #1, Kansas City looks to be had. The schedule doesn’t give them very many hard opponents. Denver looms in week 11 and 13, and Indianapolis in week 16, but otherwise the schedule favors this team — until the playoffs.

Week 7 NFL Stats:

To explain the columns above, Median is a median point spread, and can be used to get a feel for how good a team is without overly weighting a blowout win or blowout loss. HS is Brian Burke’s Homemade Sagarin, as implemented in Maggie Xiong’s PDL::Stats. Pred is the predicted Pythagorean expectation. The exponent for this measure is fitted to the data set itself. SOS, SRS, and MOV are the simple ranking components, analyzed via this Perl implementation. MOV is margin of victory, or point spread divided by games played. SOS is strength of schedule. SRS is the simple ranking.

OSRS and DSRS stats look like this:

The OSRS and SDSR stats are calculated as described here. The top 5 teams in OSRS turn out to be Denver, Chicago, Indianapolis, Dallas, and Green Bay. The top 5 teams in DSRS are Carolina, Kansas City, Seattle, San Francisco, and New Orleans. Carolina’s stats in general are notable, as they have the second best Pythagorean in the league.

Enough data has been published previously on Denver and Indianapolis to do a direct comparison, but what do they look like historically?

Denver’s data set looks like this:

Denver Broncos 2005-2013
Year Team W L T SRS OSRS DSRS MOV SOS
2005 DEN 13 3 0 10.79 6.30 4.49 8.56 2.23
2006 DEN 9 7 0 1.32 -0.72 2.04 0.88 0.44
2007 DEN 7 9 0 -3.95 -1.57 -2.38 -5.56 1.61
2008 DEN 8 8 0 -5.79 1.15 -6.94 -4.88 -0.91
2009 DEN 8 8 0 0.32 -1.09 1.41 0.12 0.20
2010 DEN 4 12 0 -8.91 -0.54 -8.37 -7.94 -0.97
2011 DEN 8 8 0 -5.30 -2.87 -2.43 -5.06 -0.23
2012 DEN 13 3 0 10.10 7.08 3.02 12.00 -1.90
2013 DEN 6 0 0 13.95 21.22 -7.26 17.83 -3.88

And Indianapolis’s data set looks like this:

Indianapolis Colts 2005-2013
Year Team W L T SRS OSRS DSRS MOV SOS
2005 IND 14 2 0 10.80 6.82 3.98 12.00 -1.20
2006 IND 12 4 0 5.88 7.31 -1.43 4.19 1.69
2007 IND 13 3 0 12.01 6.44 5.57 11.75 0.26
2008 IND 12 4 0 6.49 1.58 4.91 4.94 1.55
2009 IND 14 2 0 5.93 3.65 2.28 6.81 -0.88
2010 IND 10 6 0 2.88 5.15 -2.27 2.94 -0.06
2011 IND 2 14 0 -11.28 -6.99 -4.29 -11.69 0.40
2012 IND 11 5 0 -4.71 -2.39 -2.32 -1.88 -2.84
2013 IND 4 2 0 8.89 1.72 7.18 8.33 0.56

Using SRS, you would say that Denver has a slight advantage. Let’s look at three different predictive techniques and what they say about point spread and odds of winning the game. (1) These three, for the Denver-Indianapolis game, yield very different results.

Odds of Denver Winning and Predicted Point Spread
Pythagorean Expectation Simple Ranking System Median Analysis
Pct Points Pct Points Pct Points
0.48 -0.6 0.57 2.1 0.77 9

The two techniques I trust more, Pythagoreans and SRS, yield different results for the winner but both say the game will be decided by less than three points. With games this close, small factors – a single turnover, a great punt return – can decide the results. I add the median prediction largely as a comparison. I don’t trust it as much as the other two methods in terms of predicting results.

All three predictions include a home field advantage effect.

Notes:

1. For a simple relationship between point spreads and winning percentages, look here. A different approach is given in the book “Mathletics“, worth reading if you’re into betting football.

I haven’t followed this team closely, but some people I associate with are huge Pittsburgh Steelers fans. So for them, we’ll drop this set of SRS quick hits.

Pittsburgh Steelers 2004-2013
Year Team W L T SRS OSRS DSRS MOV SOS
2004 PIT 15 1 0 9.00 1.77 7.23 7.56 1.44
2005 PIT 11 5 0 7.81 3.32 4.49 8.19 -0.37
2006 PIT 8 8 0 3.42 1.40 2.01 2.38 1.04
2007 PIT 10 6 0 5.21 2.46 2.75 7.75 -2.54
2008 PIT 12 4 0 9.80 -0.29 10.09 7.75 2.05
2009 PIT 9 7 0 1.69 0.70 0.99 2.75 -1.06
2010 PIT 12 4 0 10.22 1.40 8.82 8.94 1.28
2011 PIT 12 4 0 5.29 -2.71 7.99 6.12 -0.84
2012 PIT 8 8 0 -0.65 -2.16 1.51 1.38 -2.03
2013 PIT 1 4 0 -8.30 -8.05 -0.25 -5.60 -2.70

The bigger loss of productivity on the Steelers, so far, has been on the offensive side. They won their last game, so perhaps the doldrums will begin to abate, and the team will begin to score more consistently. If they had as rock ribbed a defense as in 2008, then they would likely be in the playoff hunt despite the poor offensive showing (see the 2005 Chicago Bears as an example), but the defense is just ordinary at this point.

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