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I am trying to create a formula that will determine the percent to goal between an actual value and the goal value for a call metric for a call center. The metric that I am examining is Repeat Rate (RR), which is essentially out of X calls the customer called back Y number of times.

Ex) Agent John Smith has a RR of: 25%. His Repeat Goal (RG) is 30%. He is exceeding his goal, but by how much? The fewer repeat calls then the better, so an agent with 0% RR should have the highest percent to goal (RtG), whereas an agent with 100% RR should have the lowest percent to goal (RtG).

Should the formula be:

 1. f(x) = RG / RR
 2. f(x) = (1-RR) / (1-RG)?


Formula 1:

 1. RR: 100%; RG: 30%; RtoG: 30%   
 2. RR: 50%; RG: 30%; RtG: 60%
 3. RR: 20%; RG: 30%; RtG: 150%
 4. RR: 0%; RG: 30%; RtG: #DIV/0!


Formula 2:

 1. RR: 100%; RG: 30%; RtG: 0%   
 2. RR: 50%; RG: 30%; RtG: 71.43%
 3. RR: 20%; RG: 30%; RtG: 114.29%
 4. RR: 0%; RG: 30%; RtG: 125%

Or should it be none of the above?

share|improve this question
What it should be is not really a mathematical question -- mathematics can determine the objective properties of each formula, but not which of them will be most useful to you for whatever eventual purpose you have in computing the number. Informally, though the second approach seems to be saner -- it doesn't really seem useful to assign a nonzero productivity measure if you just tell every customer that you know nothing and suggest that he try again later, does it? –  Henning Makholm Sep 13 '11 at 20:22
Thank you for your response. What prompted this question was the fact that the organization I currently work for uses the first approach, which does not seem correct to me. After having a conversation with my co-worker, I was advised that the first approach made sense and not the second approach, which was my proposed solution. I turned to this forum because of successful experience with the Stack Exchange network and I didn't know where else to go to get meaningful assistance. –  Curious Sep 13 '11 at 20:49
Well, does your organization use the scores for something where the difference between the two formulas actually matters at the end of the day? For example, if all you do is compare percentages, then they lead to the same results anyway. –  Henning Makholm Sep 13 '11 at 21:01
The scores are used for determining agent performance for the desired metric. A higher percentage to goal signifies better performing agents, whereas a lower percentage to goal signifies poorer performing agents. A percentage is used because an agents rate and goal will vary based off of the call mix that they take. –  Curious Sep 13 '11 at 21:37
You could compare worker A with a 50% goal and an actual rate of 100%, to worker B with a 25% goal and an actual rate of 60%. According to the first formula, the A (who for all we know is providing no value at all) will be considered "better performing" than B (who is at least trying). –  Henning Makholm Sep 13 '11 at 22:42

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