How to properly define the score function from prediction of GLM

Question

I am reading a book, which states how to calculate the Score function from the prediction of the glm() function of R.

The statement goes as below -

Our aim is to define a new scale with anchor set at 660 points and log-odds doubling each 40 points. A 72:1 odds ratio is identified in line with credit bureau common practice.

And finally they define the score function as -

scaled_score <- function(logit, odds, offset = 500, pdo = 20)
{
b = pdo/log(2)
a = offset - b*log(odds)
round(a + b*log((1-logit)/logit))
}

It appears that :

logit -> the prediction from the glm() function in R using predict() function

odds -> 72 (hard-coded)

I failed to understand what is the exact purpose of this scaled_score() function? Why they define the scaled_score() in the above way i.e. what do the variables a,b etc. signify?

Any insight will be very appreciated.

Answer 1

The terms $a$ and $b$ are derived by solving a system of equations. For example, if 20 points doubles the odds and the base score is 660, then you can set up two equations. See this question.