# Calculating Abandoned Calls in the light of the Ofcom 2008 Statement

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5 Referring to the table, we know that O = D L + F C. From the table we can see that we cannot measure either D L or F C directly, so we need to arrive at a method of calculating them both. Firstly, to arrive at a way of stating D L. The effect of false negatives is twofold it will connect calls that were answered by answering machines to agents, but it also impacts the live dropped predictive call rate because some of the calls dropped by the predictive dialler will have been false negatives. The proportion of predictively dropped calls that are live will be the same as the proportion of calls transferred to agents that are live. So we can write that the proportion of genuinely live calls, P L, is: (2) Thus D L, the number of calls dropped as a result of predictive dialling that were actually answered by live individuals is: Substituting P L from equation (2), we get: (3) (4) Next, we have to consider the false positive count, F C. From our definition, we know that. We also know that. Substituting our formula for F C in our definition of L, we get: (5) Subtracting from both sides, we get: (6) Which can be re-arranged as: 1 (7) Which we can use to express L as: (8) Substituting our equation for D L from (4), we can show this as: (9) The false positive count, F C, can then be written as: (10) all of which, with the exception of F R which is measured by experiment, can be taken directly from the dialler s statistics. We can now start applying some of this work back into our original equation (1) to determine the abandoned call rate. Firstly, we will express O, the number of calls abandoned according to Ofcom s definition, as a function of statistics that can be taken from the dialler. We know from our definitions in the table that O is made up of calls abandoned + false positives or D L + F C. From our definition of D L in equation (4) and F C in equation (10), we can write that: (11) We also have a definition of L, factoring in false positives, from equation (8). So we can re-state equation (1) using our formula for O from (11) and our formula for L from (8) as: (12) DMA Contact Centres & Telemarketing Council Page 5 of 6 Ofcom s September 2008 Statement

6 This would be a truly awkward formula to work with. Fortunately, it simplifies quite well. Firstly, multiply the top and bottom of equation (12) by 1 and we get: (13) Expanding the right hand side of the numerator in equation (13), we can re-state it as: (14) Multiplying the top and bottom of equation (14) by, we get: (15) For which the numerator can be further simplified and written as: (16) te that if AMD is not being used, the false positive rate will be zero. Thus the equation simplifies to: (17) which is the same as the formula derived when we went through the case without AMD. DMA Contact Centres & Telemarketing Council Page 6 of 6 Ofcom s September 2008 Statement

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