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 {r} 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?

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