Three Blind Dice: Three Ways to Organize Your Weekly Power Rankings

As we hit the bye week, the league picture is finally forming, and fans (and analysts) finally can get a read on the quality in the NFL—even if they know things will change.

It's easy to look up Power Rankings on CBS, ESPN or NFL.com to see where your favorite team is ranked by the "experts"—and it's no surprise to most of us to see any particular team have rankings far apart from each other, especially because most sports writers don't have the ability to watch every game. Subjective rankings can be useful (and perhaps even accurate), but they always leave fans wanting more—or at the very least, shouting "bias" at the top of their lungs.

Here at the Daily Norseman, there have been a few readers who have tried their hand at creating objective power rankings based on specific sets of data that meet their criteria. It's difficult to construct "objective" power rankings, however.

What data you choose says a lot about what you think matters.

To that end, I've constructed three separate power rankings and two separate methods for organizing the data in order to accomplish different goals. In addition, I've created a strength-of-schedule adjustment based on an iterative function that not only takes a team's opponents into account, but their opponents' opponents and those opponents' opponents into account and so on.

For example, the Denver Broncos and the Kansas City Chiefs have both done very well to grab 4-0 records, but have done them against weak opponents (the Broncos have played against teams that have gone 4-12, while the Chiefs have played against teams that put up 3 wins to 13 losses), but the Broncos' opponents achieved that record against slightly tougher opponents than the Chiefs'.

The first way of organizing the data is "blind." It doesn't know if Vince Wilfork is injured or when Von Miller is coming back. It won't be able to figure out that a quarterback change and a running back trade may have saved the Browns, nor will it use injury reports to see if Percy Harvin is finally coming back. It merely uses all of the data to construct it's ranking.

The second way is not "blind" although it is "dumb" in that it doesn't take any of the above into account, but does capture trends in data by weighting the most recent games the most ("What Have You Done For Me Lately?"). Many times the trends are driven by long-term injuries or a coaching revelation (which is sustainable and predictive) or by a home stretch or a two-game injury from a major player (which is neither).

Who Would Win in a Fight?

The first set of ranks grabs data from common efficiency metrics historically designed to predict future wins. There are some serious sins in terms of gathering and weighting the data (the two biggest of which are: 1. The sample size is too small, and 2. Assuming the variable are independent when the assuredly are not) but for the most part is generally predictive in terms of figuring out who will win.

In this particular adjustment, we use 1) Net yards per attempt (passing yards minus sack yards lost divided by sacks and attempts), a strongly predictive statistic; 2) Run success rate (which looks at how often a runner is "successful"); 3) Turnover rate, 4) Touchdown rate, 5) Yards per carry.

Run success rate uses a particular definition of success that fits what Bob Carroll, Pete Palmer and John Thorn came up with in the Hidden Game of Football, a book that in some ways helped begin the advanced statistics movement in football. A run on first down that goes for 40% of the required yardage necessary to create a new set of downs (or grabs a touchdown) is successful, as is a run on second down that goes for 60% of required yardage or a run on third or fourth down that goes for 100% of required yardage.

This is different than what Football Outsiders uses, because they did actual research on the predictive power on success rate, but it is not too far off:

  • In general, a play counts as a "hit" if it gains 40% of yards on first down, 60% of yards on second down, and 100% of yards on third down.
  • If the team is behind by more than a touchdown in the fourth quarter, the benchmarks switch to 50%/65%/100%.
  • If the team is ahead by any amount in the fourth quarter, the benchmarks switch to 30%/50%/100%.

Advanced NFL stats uses a different definition altogether, which is to use a linearized expected points model (that is, how many points can you expect from a particular down and distance at a specific position on the field) and count a run as a "success" if the running back added to the expected points total.

They come up with some different conclusions about the success rate of runners (2012 top five from FO: Willis McGahee, Knowshon Moreno, C.J. Spiller, Stevan Ridley and DeMarco Murray; 2012 top five from ANS: Mike Tolbert, Danny Woodhead, Cedric Peerman, Mike Goodson and Andre Brown—Moreno, McGahee and Spiller are just outside their top five), but both generally do a decent job of adding to team success, oddly enough.

Yards per carry is very weak in predicting wins, and it may be swallowed up entirely by run success rate (that's the issue with not having independent data), but I figured yards were yards and used a generic win correlation found on a few sites as the weight for the statistic.

A few caveats: there is good research that indicates that you can expect different degrees of variability in efficiency from an offensive and defensive perspective. That is, sometimes it is more important to look at offensive data for some statistics (say, turnover rate) and defensive data for other statistics (like run success rate). I did not do the work to weight things differently for offenses and defenses, so there is equal weight given to a defense that has a good touchdown rate as there is for an offense with a poor one.

Modifying the data so that there was an appropriate weight for its importance as well as making sure the distribution of all the data was similar (the modified data all have the same mean value and standard deviation) probably screwed everything up, but I went with it anyway. Here are the efficiency ranks, organized with no recency bias:

Click the header of a column to sort it.

Rank Team
1 Seattle
2 Carolina
3 New Orleans
4 Kansas City
5 Buffalo
6 Tennessee
7 New England
8 Denver
9 Houston
10 Detroit
11 Tampa Bay
12 Indianapolis
13 Dallas
14 Philadelphia
15 New York Jets
16 San Diego
17 Arizona
18 Atlanta
19 Cleveland
20 San Francisco
21 Chicago
22 Washington
23 Baltimore
24 New York Giants
25 Miami
26 Minnesota
27 Green Bay
28 Cincinnati
29 St. Louis
30 Oakland
31 Jacksonville
32 Pittsburgh

The strength-of-schedule adjustments were significant, and the team most affected by it was Cincinnati, who would have been a middling team in these rankings otherwise. On the other hand, Tampa Bay had a pretty mediocre rank until the strength-of-schedule adjustment boosted them up the rankings somewhat significantly.

Here are the "What Have You Done For Me Lately" rankings:

Click the header of a column to sort it.

Rank Team
1 Seattle
2 Carolina
3 New Orleans
4 Buffalo
5 New England
6 Tennessee
7 Kansas City
8 Houston
9 Detroit
10 Denver
11 Tampa Bay
12 Indianapolis
13 New York Jets
14 San Diego
15 Arizona
16 Dallas
17 Philadelphia
18 Atlanta
19 Cleveland
20 Chicago
21 San Francisco
22 Minnesota
23 Washington
24 Baltimore
25 Green Bay
26 Cincinnati
27 New York Giants
28 Miami
29 Oakland
30 St. Louis
31 Jacksonville
32 Pittsburgh

The biggest change is Minnesota, who moved up four rankings. A number of teams dropped three rankings (Dallas, Kansas City, Philadelphia, the New York Giants and the Miami Dolphins.

Put Them On the Board

The only rankings here are the ones that deal with the scoreboard. Points allowed vs. points scored, with no other frills (besides a points-oriented strength-of-schedule adjustment). It doesn't matter how you got your points (special teams touchdowns or eight field goals), because team quality ultimately played a part.

Generally speaking, point differential does a decent job predicting wins and is a great estimate of how well a team has done in the past. It is functionally a balance between those who care more about what football teams actually try to accomplish (winning, by putting points on the board) and those who care about metrics designed to predict performance.

Point differential ranking, adjusted for strength-of-schedule with no recency bias:

Click the header of a column to sort it.

Rank Team
1 Denver
2 Seattle
3 Carolina
4 New Orleans
5 New England
6 Indianapolis
7 Baltimore
8 Kansas
9 Buffalo
10 Tennessee
11 Miami
12 Houston
13 San Diego
14 Dallas
15 Atlanta
16 New York Jets
17 Detroit
18 Cleveland
19 Green Bay
20 Chicago
21 San Francisco
22 Tampa Bay
23 Cincinnati
24 Philadelphi
25 Oakland
26 Minnesota
27 Arizona
28 Washington
29 New York Giants
30 Pittsburgh
31 St. Louis
32 Jacksonville

I imagine no one is surprised to see Denver take the top spot despite the strength-of-schedule and relatively weak defensive efficiency. Adjusted for recency:

Click the header of a column to sort it.

Rank Team
1 Denver
2 Seattle
3 Carolina
4 New Orleands
5 Indianapolis
6 Baltimore
7 New England
8 Tennessee
9 Buffalo
10 Kansas City
11 Houston
12 Miami
13 San Diego
14 Cleveland
15 Detroit
16 Atlanta
17 San Franscisco
18 Dallas
19 Chicago
20 New York Jets
21 Green Bay
22 Cincinnati
23 Minnesota
24 Tampa Bay
25 Oakland
26 Arizona
27 Philadelphia
28 Washington
29 Pittsburgh
30 New York Giants
31 St. Louis
32 Jacksonville

Not too many surprises in terms of who moves around as a result of recency—it's functionally similar to what happened with the previous efficiency rankings.

It's Not Everything, It's the Only Thing

What's the stat that matters most? Winning. Football teams do not care how they win, they just want to add to their standings, hopefully to get the Super Bowl ring.

While wins are unsurprisingly a terrible predictor for future performance, efficiency doesn't get you into the playoffs: wins do.

But ranking teams by wins is no fun; we already know everyone's record. Instead, adjusting for the strength of schedule allows you to determine if a teams' wins were "quality" and if a team's losses were "bad". There is a BCS-style of logic at play: if you only have one loss on your schedule, but it's to the top-ranked team in the country, you could still be the second-best team in the country if the rest of your wins were "good".

Without a recency weight:

Click the header of a column to sort it.

Rank Team Record
1 New Orleans 1.000
2 New England 1.000
3 Miami 0.750
4 Seattle 1.000
5 Denver 1.000
6 New York Jets 0.500
7 Buffalo 0.500
8 Kansas City 1.000
9 Houston 0.500
10 Tennessee 0.750
11 Indianapolis 0.750
12 Baltimore 0.500
13 Atlanta 0.250
14 Arizona 0.500
15 San Diego 0.500
16 Detroit 0.750
17 San Francisco 0.500
18 Cleveland 0.500
19 Carolina 0.333
20 Tampa Bay 0.000
21 Chicago 0.750
22 Dallas 0.500
23 St. Louis 0.250
24 Philadelphia 0.250
25 Cincinnati 0.500
26 Oakland 0.250
27 Jacksonville 0.000
28 New York Giants 0.000
29 Green Bay 0.333
30 Minnesota 0.250
31 Washington 0.250
32 Pittsburgh 0.000

Maybe Ben Roethlisberger was right about being the worst team in the league.

But what have you done for me lately?

Click the header of a column to sort it.

Rank Team Record
1 New Orleans 1.000
2 New England 1.000
3 Miami 0.750
4 Seattle 1.000
5 Buffalo 0.500
6 Denver 1.000
7 New York Jets 0.500
8 Tennessee 0.750
9 Baltimore 0.500
10 Indianapolis 0.750
11 Kansas City 1.000
12 Houston 0.500
13 Arizona 0.500
14 Cleveland 0.500
15 Detroit 0.750
16 Atlanta 0.250
17 San Diego 0.500
18 Carolina 0.333
19 San Francisco 0.500
20 Chicago 0.750
21 Tampa Bay 0.000
22 Dallas 0.500
23 Cincinnati 0.500
24 Philadelphia 0.250
25 St. Louis 0.250
26 Minnesota 0.250
27 Oakland 0.250
28 Green Bay 0.333
29 Jacksonville 0.000
30 Washington 0.250
31 New York Giants 0.000
32 Pittsburgh 0.000

Not much else, evidently.

Let's Combine Them!

Here are the combined rankings, with the recency bias removed first:

Click the header of a column to sort it.

Team Efficiency Points Wins Average Ranked Average
Seattle 1 2 4 2.33 1
New Orleans 3 4 1 2.66 2
New England 7 5 2 4.66 3
Denver 8 1 6 5 4
Buffalo 5 9 5 6.33 5
Carolina 2 3 18 7.66 6
Kansas 4 8 11 7.66 6
Tennessee 6 10 8 8 8
Indianapolis 12 6 10 9.33 9
Houston 9 12 12 11 10
New York Jets 15 16 7 12.66 11
Baltimore 23 7 9 13 12
Miami 25 11 3 13 12
Detroit 10 17 15 14 14
San Diego 16 13 17 15.33 15
Dallas 13 14 22 16.33 16
Atlanta 18 15 16 16.33 16
Cleveland 19 18 14 17 18
Tampa Bay 11 22 21 18 19
Arizona 17 27 13 19 20
San Francisco 20 21 19 20 21
Chicago 21 20 20 20.33 22
Philadelphia 14 24 24 20.66 23
Green Bay 27 19 28 24.66 24
Cincinnati 28 23 23 24.66 24
Minnesota 26 26 26 26 26
Washington 22 28 30 26.66 27
Oakland 30 25 27 27.33 28
New York Giants 24 29 31 28 29
St. Louis Rams 29 31 25 28.33 30
Jacksonville 31 32 29 30.66 31
Pittsburgh 32 30 32 31.33 32

And of course, with the "What Have You Done For Me Lately" adjustment:

Click the header of a column to sort it.

Team Efficiency Points Wins Average Ranked Average
Seattle 1 2 4 2.33 1
New Orleans 3 4 1 2.67 2
New England 7 5 2 4.67 3
Denver 8 1 6 5.00 4
Buffalo 5 9 5 6.33 5
Carolina 2 3 18 7.67 6
Kansas City 4 8 11 7.67 6
Tennessee 6 10 8 8.00 8
Indianapolis 12 6 10 9.33 9
Houston 9 12 12 11.00 10
New York Jets 15 16 7 12.67 11
Baltimore 23 7 9 13.00 12
Miami 25 11 3 13.00 12
Detroit 10 17 15 14.00 14
San Diego 16 13 17 15.33 15
Dallas 13 14 22 16.33 16
Atlanta 18 15 16 16.33 16
Cleveland 19 18 14 17.00 18
Tampa Bay 11 22 21 18.00 19
Arizona 17 27 13 19.00 20
San Francisco 20 21 19 20.00 21
Chicago 21 20 20 20.33 22
Philadelphia 14 24 24 20.67 23
Green Bay 27 19 28 24.67 24
Cincinnati 28 23 23 24.67 24
Minnesota 26 26 26 26.00 26
Washington 22 28 30 26.67 27
Oakland 30 25 27 27.33 28
New York Giants 24 29 31 28.00 29
St. Louis 29 31 25 28.33 30
Jacksonville 31 32 29 30.67 31
Pittsburgh 32 30 32 31.33 32

And who has had the hardest go of it? The strength of schedule ranks:

Click the header of a column to sort it.

Team Efficiency SOS Points SOS Wins SOS Average Ranked SOS Average
New York Jets 2 8 4 4.67 1
Tampa Bay 4 9 1 4.67 1
New York Giants 1 1 13 5.00 3
Houston 7 2 6 5.00 3
Buffalo 9 3 3 5.00 3
Baltimore 8 4 7 6.33 6
Jacksonville 6 5 10 7.00 7
Carolina 3 10 11 8.00 8
Miami 13 7 5 8.33 9
Atlanta 14 11 2 9.00 10
Philadelphia 10 6 15 10.33 11
New England 11 14 9 11.33 12
San Diego 5 12 18 11.67 13
Arizona 12 20 12 14.67 14
New Orleans 19 18 8 15.00 15
San Francisco 16 13 17 15.33 16
Seattle 15 17 20 17.33 17
St. Louis 17 22 16 18.33 18
Oakland 20 16 22 19.33 19
Cleveland 29 15 14 19.33 19
Tennessee 21 19 19 19.67 21
Pittsburgh 24 21 23 22.67 22
Dallas 18 26 25 23.00 23
Washington 22 24 29 25.00 24
Denver 26 23 27 25.33 25
Minnesota 27 25 24 25.33 25
Indianapolis 31 29 21 27.00 27
Detroit 25 31 26 27.33 28
Green Bay 28 28 28 28.00 29
Kansas 23 32 32 29.00 30
Cincinnati 32 27 30 29.67 31
Chicago 30 30 31 30.33 32

Miami's 3-1 record is even more interesting here, but Cincinnati's 2-2 record is a bit disappointing, to say the least.

There you go! The best team in the league is clearly *cough*.

We'll use this to predict games for the rest of the season and see who comes out ahead (with no home-field adjustment or reference to the Vegas spread).

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