How to predict Service Level based on Call Abandon Rates

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How to predict Service Level based on Call Abandon Rates
Our client has been predicting SL based on Call Abandon Rates for a long time as below formula.
But, I don't know the logical of this formula of SL% forecast.

Could you kindly tell me what are “10.176” , “5.066”, “10.0136” and calculation logical of them?

A site SL outlook = 10.176 x AR% x AR% - 5.066 x AR% + 1.0136
B site SL outlook = 8.102 x AR% x AR% - 0.159 x AR% + 0.933


Call Centre Helper

This looks like a formula by observation
There is no easy formula that links Service Level to Abandon Rate. The closest mathematical way to model this is to use the Erlang A formula.
We include both Service Level and Abandon Rates in the Erlang Calculator - which is a hybrid of Erlang C for Service Level and Erlang A for Abandon rates. But both of these are outputs and not inputs.

Both of your formulas follow the quadratic equation - y = ax² + bx + c
Where a b and c are constants.
So in your case SL = a AR² + b AR + c
So a = 10.176, b=5.066, c=10.0136

What I suspect has happened is that they have plotted service level against abandon rate and done a quadratic regression to get the "curve of best fit" between them. So this would then give values of a, b and c.

But propensity to abandon changes over time. Increasingly people become more impatient and so the values of a, b and c will be wrong.

The only way to test this would be to do another plot of abandoned call rate against service level and make your own curve.

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