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Week 14, 2022—Issue 198

Estimating Work: the Coastline Paradox, Orders of Approximation, and Agile Scoping

Photo by Louis Hansel on Unsplash

Each week: three ideas to help us create better organizations. This week: three ideas on estimation and scoping. (This story was first published in the WorkMatters newsletter on April 8, 2022).

British polymath Lewis Fry Richardson made a surprising discovery in 1950: the larger the unit of measurement, the smaller that measurement becomes.

Richardson made his discovery while estimating the lengths of various borders and coastlines. He realized that larger units (e.g., 100 km as opposed to 50 km) invariably resulted in smaller estimates:

Successive estimations of Britain’s coastline using smaller and smaller units of measurement.

I would argue that the same applies to all types of estimates.

Let’s explore.

1. The Coastline Paradox

Richardson never went on to popularize his discovery. That task fell to another polymath — Benoit Mandelbrot — who, in the 1960s, published a paper called How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. In the paper, Mandelbrot provided a mathematical explanation of Richardson’s discovery, explaining why the length of a coastline depends on the scale and detail of the map used in the measurement* — a fact that has since become known as the Coastline Paradox.

2. Orders of Approximation

Mandelbrot’s paper made clear that it’s all but impossible to answer the how-long question without first agreeing on a unit of measurement. Precision takes time which is why a trade-off needs to be made regarding the level of confidence needed and the time and resources required for the measurement. In this regard, scientists often talk about Orders of Approximation with Zeroth Order being the first and most rudimentary estimate, followed by 1st, 2nd, and 3rd Order estimates with increasing levels of precision and confidence.

3. Agile Scoping

The idea of labeling estimates according to an agreed-upon standard strikes me as rather clever — especially given the fact that we now know rough estimates tend to skew small. There are some obvious implications here, not least for the Agile community who, like Mandelbrot and science more generally, approach scoping as a series of approximations, starting with Initiatives that break into Epics that break into User Stories that break into Acceptance Criteria, etcetera.

Personal experience suggests that Richardson’s discovery is true and that it’s applicable not just to coastlines but to all manners of estimation — Agile software projects included.

Rough estimates do tend to skew small, and they do tend to miss the mark by an order of magnitude similar to those that Mandelbrot found in his coastline approximations.

That’s not to say that coastlines and software projects are the same or even similar. They’re obviously not. But I do find the idea quite instructive all the same.

When estimating work, we should always make clear what unit of measurement (e.g., 100km, User Stories) is required. And we should always be aware that the larger the unit, the smaller the estimate.

That’s all for this week.
Until next time: Make it matter.


*The answer lies in the fact that coastlines are crinkly and self-similar, meaning that the same general configuration repeats at different scales — from bays and inlets on the one hand, to individual grains of sand on the other. It’s all a bit above my head, to be honest, but the general predicament is clear enough; as Mandelbrot explains: “coastline length turns out to be an elusive notion that slips between the fingers of those who want to grasp it”.

Did you know? WorkMatters is a weekly newsletter that explores new and better ways of working. New issues drop Fridays at 10 AM ICT and subscription is free. Back-issues are published to Medium after three months.



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