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Teachers' Lounge Discussion: A project on matrices

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From: Garry Lockwood

To: Teacher2Teacher Public Discussion
Date: 1999100802:38:18
Subject: Re: Project on Matrices

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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