Miscellaneous Facts about Daniel 2 Ratings

Why Daniel 2 only ranks Division I-A Teams

Here are the Top 25 rankings with all NCAA and NAIA teams included, October 7, 2000 (excepting certain teams that don't connect with everyone else):

   1.  Nebraska                  2802
   2.  Ohio State                2726
   3.  Delaware                  2720
   4.  Northwestern              2687
   5.  Florida State             2673
   6.  Carson-Newman             2660
   7.  Clemson                   2643
   8.  South Carolina            2536
   9.  Miami (FL)                2527
  10.  Washington                2523
  11.  Virginia Tech             2485
  12.  North Dakota State        2470
  13.  Mississippi State         2460
  14.  West Georgia              2417
  15.  NW Missouri St            2378
  16.  Portland State            2366
  17.  Drake                     2340
  18.  Iowa State                2249
  19.  Toledo                    2225
  20.  Southern Miss             2204
  21.  Florida                   2176
  22.  Oregon                    2167
  23.  Western Kentucky          2167
  24.  Louisville                2167
  25.  Kansas State              2145

Make your own decision.

Also, see my discussion of flaws with this system.

Why Daniel 2 multiplies the rating by 100 before printing

Astute readers may have noticed that teams have ratings that are way too high than what I described in the detail on how the system works. The reason for this is that they've been multiplied by 100. Why is that?

The reason is that, because the numbers were on the order of 20, I figured there would be people dumb enough to use the ratings as predicted point differences. The ratings are not related to point differentials AT ALL, so I multiplied by 100 to take it out of the typical point differential range.

Now, I'm sure there's still people dumb enough to use the ratings as point differentials....

Inspiration for Daniel 2 Ratings

The Daniel 2 ratings were inspired mainly from my time in the rec.sport.football.college newsgroup. In that chatro^H^H^H^H^H^H newsgroup, it is common to taunt fans of perennially strong teams with something like this when they lose a game:

Buffalo > Bowling Green > Central Michigan > Akron > Ohio > Minnesota > Penn State > Purdue > Michigan > Wisconsin > Oregon > Washington > Miami > Florida State,
therefore Buffalo >>>>>>> Florida State

Of course, that is absurd, and it became clear to me from this type of post that a very long path was rather meaningless.

There was an influential post by Steve Casburn which noted that it was better to have a short transitive path than a long one, and gave an example. I don't remember exactly what the example was.

Finally, a lot of inspiration came from Robert Gretta's transitivity poll. In his system, there was not relative transitivity. In other words, Buffalo got just as many points as Miami for being "better" than Florida State. By seasons end, just about everyone with at least one win and one loss had the same rating. The Daniel 2 ratings system is the result of my thoughts on how to improve upon that system.

Arbitrariness in Daniel 2

Many ranking systems have quite a few arbitrary parameters. Arbitrariness is considered a bad thing, because it increases the subjectivity of the rating system.

I feel that Daniel 2 does quite well in regards to arbitrariness. There are a few arbitrary decisions in system:

That long transitive paths of are less worth than short paths. This is something I feel most would agree with.
That we should only consider the shortest transitive path when determining a team's rating.
That we should only rank Division I-A teams, but still consider paths going through non-Division-I-A teams.

The transitive power function (i.e., that which tells us how many rating points a certain transitive path is worth) is arbitrary also. It is a negative exponential to base 2. My use of an exponential function has a mathematical justification, and so I feel it is not arbitrary. The justification is that the number of possible transitive paths increases exponentially with path length. For example, there are about about 11 paths of length 1, 11^2=121 paths of length 2, etc. Thus, a corresponding exponential decrease in value of the path.

However, the use of base 2 is very arbitrary. It seems to be a parameter that weighs the ratings between strength-of-schedule and wins-losses. The higher the base, the lower the strength-of-schedule weight. I would say the base 2 appears to weight SOS a little higher than most systems.

Despite the aribitrary features of this system, I think it does do better than most rating systems in this regard.

Why I named it Daniel 2

Daniel 2 is actually a Biblical reference, to the Book of Daniel, Chapter 2, specifically Daniel 2:36-45. This is the story of King Nebuchadnezzar's dream about the statue of four metals. The gold head represented the Chaldean empire of Nebuchadnezzar. The silver chest represented the Persian empire, who conquered the Chaldeans. The bronze belly and thighs represented the empire of Alexander the Great, who conquered the Persians. The iron legs represent the empire of Alexander's generals, who outlasted Alexander. The iron and tile feet were the divided empire, namely the Selucid and Ptolemaic empires. And the stone that destroyed the statue is, of course, God.

Thus, can we say God > Selucids and Ptolemaics > Alexander the Great > Persians > Chaldeans. There's transitivity in the post-exilic period for you.

(Parenthetically, I disagreed with the footnotes from the New American Bible, who had Alexander the Great as the iron legs, even though the bronze belly was a kingdom "who shall rule over the whole earth." Now, this is a reasonable hyperbole for Alexander the Great's kingdom, but not the Persians, which is why I have Alexander as the bronze.)

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