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Understanding the Massey Matrix

For our WNBA Massey Matrix model, some adjustments need to be made for a solution to our rating problem to exist and be unique.

This is because the matrix \(M\), with R output

1  33 -4 -2 -3 -3 -3 -3 -3 -3 -3 -3 -3
2  -4 33 -3 -3 -3 -3 -2 -3 -3 -3 -3 -3
3  -2 -3 34 -3 -3 -3 -3 -4 -4 -3 -3 -3
4  -3 -3 -3 34 -3 -4 -3 -3 -2 -3 -3 -4
5  -3 -3 -3 -3 33 -3 -3 -3 -3 -3 -2 -4
6  -3 -3 -3 -4 -3 41 -8 -3 -6 -3 -2 -3
7  -3 -2 -3 -3 -3 -8 41 -3 -4 -3 -3 -6
8  -3 -3 -4 -3 -3 -3 -3 34 -3 -2 -3 -4
9  -3 -3 -4 -2 -3 -6 -4 -3 38 -3 -4 -3
10 -3 -3 -3 -3 -3 -3 -3 -2 -3 32 -4 -2
11 -3 -3 -3 -3 -2 -2 -3 -3 -4 -4 33 -3
12 -3 -3 -3 -4 -4 -3 -6 -4 -3 -2 -3 38

usually does not (computationally) have an inverse, as shown by the error produced from running solve(M) in a previous exercise.

One way we can change this is to add a row of 1's on the bottom of the matrix \(M\), a column of -1's to the far right of \(M\), and a 0 to the bottom of the vector of point differentials \(\vec{f}\).

What does that row of 1's represent in the setting of rating teams? In other words, what does the final equation stipulate?

This exercise is part of the course

Linear Algebra for Data Science in R

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