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Teachers' Lounge Discussion: A project on matrices

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From: Garry Lockwood <garry.lockwood@unisa.edu.au>
To: Teacher2Teacher Public Discussion
Date: 1999100801:35:00
Subject: Matrices project

I tried predicting Basketball results using dominance matrices. I
don't have a reference for this topic, but you should be able to find
one. Basically, for teams 1 to n, set up an nxn matrix L. Set all
entries to 0.  When team i plays team j, if team i wins increase the
value of L(i,j) by 1. It was interesting to deal with the fact that
the teams do not all play the same number of games each week. So to
predict the results of the matches, which in Australia occur only on
weekends, I had to divide every row by the number of games that team
had played, to get matrix M. Then I used the power matrix P = M +
0.5M^2. Form the row sums and rank the teams in order of the row sums.
Tip the team with the higher ranking.

The first week of the season proved a problem, so I just tipped
according to their results from the previous season. Expansion teams
are a problem, and my results for the first week were terrible. But
they soon improved. It might be interesting to compare predictions
with predictions made by a panel, some sort of Delphi approach. I did
also try ranking according to row sums of P = M + 0.5M^2 + 1/3M^3, but
after two rounds there was no difference between this and the previous
P, in ranking. In cases where the teams are tied for ranking, tip the
home team.

There are all sorts of extensions possible, including estimating the
value of the home court advantage. Try increasing the ranking of the
home team by, say, 5% and see if that makes the tips more accurate.

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