ACC Power Ratings - Games Through 1/13/98

ACC Power Ratings - Games Through 1/13/98

Post by George W. Harr » Thu, 15 Jan 1998 04:00:00

        What follows are power ratings for ACC men's
basketball teams based solely on the results of games
among conference members through Saturday, January
10th 1998.  Following the ratings will be a brief
explanation of methodology.

Team           Rating      Record       Previous
                       Conf    Total

1)Duke          84.81   4-0     14-1    1)85.79
2)UNC           77.61   4-0     17-0    2)77.30
3)Clemson       73.74   2-2     11-5    5)67.96
4)***ia      67.89   1-2      9-7    3)69.07
5)FSU           66.71   1-4     12-4    4)68.89
6)Maryland      65.63   2-2      9-5    6)65.22
7)NC State      62.50   1-3      9-5    8)63.48
8)Wake          61.75   1-2      8-5    7)64.61
9)Ga Tech       61.12   1-2     11-4    9)62.30

Recent Games:

Tuesday, 1/13/98

        FSU at Clemson
                Prediction: Clemson by ~1
                Result:     Clemson by 21

Predictions, immediate & cumulative: 1-0, 6-3

Upcoming Games:

Wednesday, 1/14/98

        Duke at Wake Forest
                Prediction: Duke by ~15
        UNC at Maryland
                Prediction: UNC by ~4

Methodology:

        These ratings are derived by finding a least-
squares approximation of a set of linear equations of the
form TeamA-TeamB=AdjMargin.  One finds the minimum
solution (expressed by eight equations of the form
TeamA-TeamH=Margin for TeamA through TeamG, with
TeamH fixed) of the sum of (TeamA-TeamB-AdjMargin)^2
over all games for the variables TeamA through TeamH.  
This is done by taking the derivative and then gathering
the terms containing each variable, setting those sums of
terms equal to zero, and finding the solution of *that* set
of equations.

        Fortunately in practice this can be done fairly
mechanically.  Since the solution will invariably have at
least one dimension, one can actually set up a matrix
with only eight, rather than nine, rows and columns, set
the value for the ninth variable arbitrarily, and then treat
the resultant single solution for the other eight variables
as their offset from the ninth.

        The matrix looks like this:

-                     - -           -
| m_A_A m_A_B...m_A_G | |AdjMargSumA|
| m_B_A m_B_B...m_B_G | |AdjMargSumB|
|       .         .   | |     .     |
|       .    ...  .   | |     .     |
|       .         .   | |     .     |
| m_G_A m_G_B...m_G_G | |AdjMargSumG|
-                     - -           -

        where m_A_A equals the total games played by
A, m_A_B = -n where n equals the total games played
between A and B (so m_A_B=m_B_A), and
AdjMargSumA is the sum of the adjusted margins of all
games (including games against TeamH) played by A;
for this rating, the margin is adjusted for a blowout factor,
so points between ten and twenty are worth .75, points
between twenty and thirty are worth .5, points between
thirty and forty are worth .25, and points above forty are
discarded; then the margin is adjusted for home-court
advantage, which is set at 4.5 (based on a study of ACC
games over the last four years) and then four points are
added [subtracted] for a win [loss].  Thus, three one-point
wins would be worth +15, while one five-point win and
two one-point losses, while having the same point
differential, would be worth -1.  Solving this matrix gives
values for TeamA through TeamG which is their
difference from TeamH; I arbitrarily set the average of the
nine power ratings to seventy.

        One can use this method to predict the outcome
of future games by taking the difference in the power
ratings, adjusting for home-court advantage, and then, if
the difference is greater than four, taking the team with
the higher value and a margin (adjusted back up for the
blowout factor if desired) of the difference minus four; if
the difference is less than four, then the team with the
higher value with a margin of one (the game is really too
close to call).

        The accuracy of such predictions has not been
tested, but will be presented over the course of this
season.  Presumably as more games are played, the
ratings will become more accurate.

--
Real men don't need macho posturing to bolster their egos.

George W. Harris  For actual email address, replace each 'u' with an 'i'.