Dan TM's Blog
You may want to check my Previous Natural Power Rankings posts if you haven't read these before.

I believe I may have made my final tweak to the Natural Power Rankings.  I've removed the last bit of the system that wasn't purely mathematical, and figured out a mathematical way to resolve it.  Here's how I rank the teams now:

*keep in mind, I only use the past 4 weeks for reasons mentioned in my earlier blogs*

1) If A beat B, A is higher than B.  This gets me a nice long string or two of teams whose order cannot be changed.

2) If A has not played B, I look at degrees of separation, finding the common team(s) at the nearest point in the "network" of opponents.  I add up strength-of-victory points according to the system I came up with last week.  I resolve all first-degree situations first, and progress through the degrees until everything is worked out.

That's it.  But part 2 deserves further explanation.

What do I mean by "degrees of separation" and "network"?  The opponents a team has faced are the first degree.  The opponents those teams have faced are the second degree, and so on.  And of course, teams go in the closest applicable degree-Oakland has San Diego, Kansas City, and Miami in its first degree.  Kansas City has also played San Diego, Jacksonville, and Cincinnati.  San Diego is not in the second degree, since they're already in the first.

However, for the purposes of this, I only factor in chains of wins or chains of losses.  So Cincinnati actually wouldn't show up in Oakland's network - Oakland lost to Kansas City, who beat Cincinnati; a L-W chain.  However Jacksonville is - Oakland lost to Kansas City, who lost to Jacksonville; a L-L chain.  Indianapolis is in the third degree, a L-L-L chain, thanks to last night's win over Jacksonville.

How do I use this?  Well, at the first degree, it's simple, and it's the same process I used before.  Kansas City's strength-of-victory (SOV) score over Cincinnati was 2.61; over San Diego it was 5.34.  Thus, Cincinnati fared better against a common opponent, and is ranked higher than San Diego. 

It's the same principle, but with more numbers for further degrees.  New England-New York Giants' closest common opponent was the Jets; who were 2 degrees away from the Patriots, and 1 from the Giants.  The Giants beat the Jets with a SOV score of 5.5.  The Patriots beat the Bengals with a SOV score of 8.28; and the Bengals beat the Jets with a SOV score of 2.54.  8.28+2.54>5.5, so the Patriots get ranked higher.

One important thing to keep in mind - it's still impossible to rank the NFC Central + Washington in these rules; they're a big mess that I went into last week.  The way I deal with them is that I treat them all as essentially equal; with only the slightest edge based on SOV over each other.  But since Minnesota lost to Dallas, they are all considered worse than Dallas.  Since Washington beat Arizona, they are all considered better than Arizona.  It makes no common sense, but it makes perfect mathematical sense.

With that in mind, here's how I resolved the #1 position, which was very complicated.  The nearest common opponent was Arizona.  New England beat Dallas with a POV of 7.22.  Dallas beat Minnesota with a POV of 4.29.  Minnesota and Washington are equal; Washington beat Arizona with a POV of .78.  Total = 12.28.  Indianapolis beat Tampa Bay with a POV of 7.36.  Tampa Bay beat Carolina with a POV of 6.22.  Carolina beat Arizona with a POV of 6.39.  Total = 19.97.  Thus, Indianapolis is #1.

And here are the rest of the rankings, with their record over the past 4 weeks in parentheses:

  • 1) Indianapolis (3-0)
  • 2) New England (4-0)
  • 3) NY Giants (4-0)
  • 4) Jacksonville (2-1)
  • 5) Kansas City (3-1)
  • 6) Cleveland (2-1)
  • 7) Dallas (3-1)
  • 8) Cincinnati (1-2)
  • 9) San Diego (2-1)
  • 10) Buffalo (2-1)
  • 11) Washington (2-1)
  • 12) Chicago (2-2)
  • 13) Green Bay (2-1)
  • 14) Minnesota (1-2)
  • 15) Detroit (2-1)
  • 16) Oakland (1-2)
  • 17) Tampa Bay (2-2)
  • 18) Philadelphia (1-2)
  • 19) Tennessee (2-1)
  • 20) NY Jets (0-4)
  • 21) Carolina (1-2)
  • 22) New Orleans (2-1)
  • 23) Arizona (2-2)
  • 24) Denver (1-2)
  • 25) Pittsburgh (1-2)
  • 26) Atlanta (1-3)
  • 27) Seattle (2-2)
  • 28) Houston (1-3)
  • 29) Miami (0-4)
  • 30) Baltimore (2-2)
  • 31) San Francisco (0-3)
  • 32) St. Louis (0-4)

And therefore, here are this week's NPR predictions.  They went 10-4 last week after going 9-4 the previous.  Way better than my personal record, so I'm still doing this.  Not many surprises this week, which probably means I won't do so well.

Cleveland beats St. Louis

Chicago beats Detroit

Indianapolis beats Carolina

NY Giants beat Miami

Oakland beats Tennessee

Minnesota beats Philadelphia

Cincinnati beats Pittsburgh

Buffalo beats NY Jets

San Diego beats Houston

Jacksonville beats Tampa Bay

New Orleans beats San Francisco

New England beats Washington

Green Bay beats Denver


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