In Agile Fibonacci numbers are the latest rage. But it's just that the latest rage. The reason for using the Fibonacci sequence is to reflect the inherent uncertainty in estimating larger items. What this means is the larger the size of the card (in the planning poker paradigm)
There of course is no evidence the uncertainty of a Fibonacci large number is any more uncertain than the uncertainty of a Geometric series large number, of 1, 2, 4, 8, 16, 32, ... compared to Fibonacci's series 1, 1, 2, 3, 5, 8, 13, 21, ...
The Geometric series is below.
But there is a very interesting relationship between Fibonacci and Geometric series. The connection is ɸ (Phi). Phi is an irrational number in connection with a classical problem of the division of a line segment to mean and extreme ratio
Phi is the common ratio between geometric series and the Fibonacci series.
Both the Fibonacci series and the Geometric series can be used to assess the differences between items like difficulty, cost, durations - or any Ordinal comparisons. The Fibonacci series is just is clever approach with no actual differentiation from the Geometric.
Now for the Point
If agile is using Fibonacci numbers or Geometric numbers as RELATIVE comparisons of work, complexity, or anything, this is seriously flawed, since these numbers are not calibrated - they are relative. Relative is not Bad per se, but they are also not Good. Because the business is very unlikely to carry Fibonacci numbers of Story Points in the general ledger.
What needs to happen is to estimate work in Cardinal units. Measures that have been calibrated in a credible manner. Sampling 20 or so past sprints without consideration of their variance, changes in risk, future changes is all the variables that will impact the project is naive at best and bad math at worse.
So while it may sound cool to be tossing around Fibonacci numbers in those planning session, you might as well be making up any progress separation series and use it because to outcome is the same. This notion is simply a marketing ploy that somehow entered the vocabulary of agilest. Both Fibonacci and series and Geometric series provide a simple way to separate adjacent Ordinal measures so they don't appear related.
