# No Single Metric – Proof By Contradiction

There is significant interest among businesses – enterprises and startups alike – to look for a single metric, one magic number that will point to overall success, profitability etc. When a metric is pitched, if it is reasonably popular, seemingly rigorous yet very simple to understand and comes from a firm or person with a pedigree or position, the metric will find almost religious acceptance.

Can there really be one metric that predicts profitability? I used statistical biases to explain why there cannot be just one metric, now let me make another attempt with Proof by Contradiction.

Let us assume there is indeed a single metric, let us call it X. If by a logical sequence of arguments, I  show you that there  is in fact one more metric  it will be  a contradiction to the assumption, proving it is false.

If X is a predictor of profitability, then improving it is good for the business.  There are three cases:

1. There are no  levers to move X
2. There is exactly one lever that businesses can pull to move X
3. There are more than one levers to pull

The first case is not possible, after all no one will pitch a metric that cannot be controlled and managed. Granted, this is not really part of proof by contradiction but I am simply eliminating this branch of the decision tree.

In the second case, if there is exactly one lever that businesses can pull to move the metric, then by extension that becomes the predictor of profitability and not X.  This is a contradiction.

In the third case, if there are more than one lever to pull, that means the whole set of those affect profitability and not X. This is again a contradiction of the assumption that there is a single metric.

What do you say?