What follows are power ratings for ACC men's

basketball teams based solely on the results of games

among conference members through Thursday, January

15th 1998. Following the ratings will be a brief

explanation of methodology.

Team Rating Record Previous

Conf Total

1)Duke 85.30 5-0 15-1 1)86.31

2)UNC 74.77 4-1 17-1 2)74.81

3)Clemson 73.28 2-2 11-5 3)73.35

4)Maryland 68.46 3-2 10-5 4)68.43

5)FSU 67.13 1-4 12-4 5)67.10

6)Ga Tech 65.67 2-2 12-4 8t)59.83

7)NC State 64.58 1-3 10-5 7)63.36

8)***ia 60.81 1-3 9-8 6)66.81

9)Wake 59.52 1-3 8-6 8t)59.83

Recent Games:

Thursday, 1/15/98

Georgia Tech at ***ia

Prediction: ***ia by ~7

Result: Tech by 18

Predictions, immediate & cumulative: 0-1, 7-5

Upcoming Games:

Saturday, 1/17/98

Clemson at Duke

Prediction: Duke by ~13

Maryland at Wake Forest

Prediction: Maryland by ~1

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'.