It’s funny how random things stick in your head a couple of decades later. I don’t even remember which class in IIMB this was. It surely wasn’t an accounting or a finance class. But it was one in which we learnt about some financial ratios.

I don’t even remember what exactly we had learnt that day (possibly return on invested capital?). I think it was three different financial metrics that can be read off a financial statement, and which then telescope very nicely together to give a fourth metric. I’ve forgotten the details, but I remember the basic concepts.

A decade ago, I used to lecture frequently on how NOT to do data analytics. I had this standard lecture that I called “smelling bullshit” that dealt with common statistical fallacies. Things like correlation-causation, or reasoning with small samples, or selection bias. Or stocks and flows.

One set of slides in that lecture was about not comparing stocks and flows. Most people don’t internalise it. It even seems like you can**not** get a job as a journalist if you understand the distinction between stocks and flows. Every other week you see comparisons of someone’s net worth to some country’s GDP, for example. Journalists make a living out of this.

In any case, whenever I would come to these slides, there would always be someone in the audience with a training in finance who would ask “but what about financial ratios? Don’t we constantly divide stocks and flows there?”

And then I would go off into how we would divide a stock by a flow (typically) in finance, but we never compared a stock to a flow. For example, you can think of working capital as a ratio – you take the total receivables on the balance sheet and divide it by the sales in a given period from the income statement, to get “days of working capital”. Note that you are only dividing, not comparing the sales to the receivables. And then you take this ratio (which has dimension “days”) and then compare it across companies or across regions to do your financial analysis.

If you look at financial ratios, a lot of them have dimensions, though sometimes you don’t really notice it (I sometimes say “dimensional analysis is among the most powerful tools in data science”). Asset turnover, for example, is sales in a period divided by assets and has the dimension of inverse time. Inventory (total inventory on BS divided by sales in a period) has a dimension of time. Likewise working capital. Profit margins, however, are dimensionless.

In any case, the other day at work I was trying to come up with a ratio for something. I kept doing gymnastics with numbers on an excel sheet, but without luck. And I had given up.

Nowadays I have started taking afternoon walks at office (whenever I go there), just after I eat lunch (I carry a box of lunch which I eat at my desk, and then go for a walk). And on today’s walk (or was it Tuesday’s?) I realised the shortcomings in my attempts to come up with a metric for whatever I was trying to measure.

I was basically trying too hard to come up with a dimensionless metric and kept coming up with some nonsense or the other. Somewhere during my walk, I thought of finance, and financial metrics. Light bulb lit up.

My mistake had been that I had been trying to come up with something dimensionless. The moment I realised that this metric needs to involve both stocks and flows, I had it. To be honest, I haven’t yet come up with the perfect metric (this is for those colleagues who are reading this and wondering what new metric I’ve come up with), but I’m on my way there.

Since both a stock and a flow need to be measured, the metric is going to be a ratio of both. And it is necessarily going to have dimensions (most likely either time or inverse time).

And if I think about it (again I won’t be able to give specific examples), a lot of metrics in life will follow this pattern – where you take a stock and a flow and divide one by the other. Not just in finance, not just in logistics, not just in data science, it is useful to think of metrics that have dimensions, and express them using those dimensions.

Some product manager (I have a lot of friends in that profession) once told me that a major job of being a product manager is to define metrics. Now I’ll say that dimensional analysis is the most fundamental tool for a product manager.