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I have a really simple problem and no idea on how to solve it. I work at a large news website, and we want to implement a way of tracking how efficient our employers are.

Figures we are playing with are (1) Number of user interactions with one journalist's articles and (2) Interval of days referent to the measuring.

So, for example, we can have a journalist whose articles were read 500.000 over a 1 month of time, and another whose articles were read 1.000.000 times over 2 months time. Those two journalists should have same Index of Efficiency.

Also, this is going to be implemented in a computer-programmed environment, so have that in mind.

Any ideas are appreciated. Thanks in advance

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    I don't know the answer but I think a "large news website" could *pay* somebody for this service...2012-09-26

2 Answers 2

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Let $Z = \frac{\text{#user interactions}}{\text{months}}.$

Clearly $Z$ is a number that ranges from $0$ to $+\infty$, with $0$ being the worst. Hence we want to map the non-negative reals $\mathbb{R}_+$ to $[1,10].$

For example, you can achieve this by taking $R(Z) := 10 - \frac{9}{1+Z}$, where $R$ denotes the rating of the journalist. It is easy to see that $R$ is strictly increasing in $Z$. Moreover, $R(0) = 1$ (the lowest possible rating) and $\lim_{R\rightarrow \infty}=10$ (the highest possible rating). Hope this helps!

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    Edit: obviously, if all ratings are too close to 10, you can easily rescale $Z$. E.g., you can measure "user interactions" in 100,000 users (so 550,200 user interactions would be 5.502).2012-09-26
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1 + 9 / (1 + exp(-(mega articles per month) ) )

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    It always returns 10.0?2012-09-26