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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