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It is quite common to cast a multi-objective problem of, for example, several KPIs as a weighted sum to define an UberKPI as described here:

https://marketingland.com/5-simple-steps-defining-multi-objective-uber-kpis-93516

One thing I have noticed is, that the KPIs are not normalize. Should one not normalize the KPIs (e.g. by dividing them by the maximum)?

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The reason to normalise our variables before their use in a technical analysis is to ensure that their importance appears similar in our context-agnostic procedure. An optimisation procedure does not know if Sales from channel A have a higher return-on-investement than Sales from channel B.

Therefore normalising our KPIs wholly depends on how are these KPIs evaluated internally. If KPI_1, KPI_2 and KPI_3 are three different revenue streams, measured using the same monetary unit, then normalising them is probably unnecessary and potentially misleading. If KPI_1, KPI_2 and KPI_3 account for number of clients, number of purchases, and average cost per purchase respectively, then these KPIs are incompatible and makes little sense to simply sum them together; normalising them (by dividing by their max as you describe) or scaling them (such that they have mean $0$ and variance $1$), it probably more relevant.

In the page linked, the worked example actually scaled the KPIs by their average value. It a slightly non-standard way to make sure that the KPIs scale independent (min-max scaling and normalisation to Gaussian are more common) but the idea is similar.

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  • $\begingroup$ thanks. in my case some KPIs are in currency, whereas others are in days or percentage. all have to be minimized. would you recommend min max over z-scoring? $\endgroup$ – cs0815 Jan 20 at 15:53
  • $\begingroup$ I am glad I can help. I would suggest z-scoring because: 1. the transformation is straightforward to interpreter (as the min-max) but does not put hard thresholds in the values our data might take (like the min-max). 2. It is more directly relatable for hypothesis testing. 3. Above/below average performances can be easily inspected just by looking at the sign. $\endgroup$ – usεr11852 says Reinstate Monic Jan 20 at 17:01

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