# Why Do We Use Fibonacci Series for Estimation

Why Do We Use Fibonacci Series for Estimation

In this article, my focus is on sharing my experience as a Trainer/Mentor/Coach to Agile teams with respect to Agile estimations; and on using the Fibonacci sequence as scale to size the Story.

Agile practitioners mostly use Story points as a measure for estimation, typically using the Fibonacci scale. In this article we are going to understand the top reasons why we use the Fibonacci series for estimation, and how it works in practice.

Before we get to the details, let us try to understand some of the fundamentals.

Estimates help the project team to:

Some software developers fear to provide effort estimates as they are accountable to complete their work within the time.  Hence, they take so much time to get into the details to make sure they have enough information to provide the estimates. This sometimes may not be possible during the beginning of the project as the team may not have enough information on hand to provide the effort estimates for all the tasks to be performed. Hence the order of magnitude (ROM, Budget or Definitive) will be applied at various stages during the project based on the available information to predict the effort needed to complete the activities.

Typically, in traditional project management, effort estimations may or may not be agreed upon by the entire team. Estimates may either be given by the Project Manager/Tech Lead to the team or the developers/testers may estimate for the piece of work that they have been assigned. This way of estimating a project does not provide an opportunity for the team to collaborate. There may be a difference of opinion with the team members in the effort that need to be spent on an activity.

The way the estimations are done within an Agile team is little different. It is just not about the measure used to estimate the effort (for example Story Points), but ensures that the team collaborate among themselves, thus providing an opportunity for knowledge sharing. This helps the accuracy of the estimates when compared to doing individual vs group estimates as the team members come from different backgrounds and roles (developers, testers, quality analysts, business analysts).

An Agile team effort estimate focuses on relative sizing of user stories and does not focus on the duration; hence it is faster. The team learns to size the story relatively and accurately over a period of few iterations (sprints), thus improving the predictability (arrived through establishing consistent velocity over a period of few iterations) as well.

Planning Poker is commonly used as the planning exercise for the team to collaborate and size the stories. Planning Poker uses Fibonacci sequence to assign a value to the epic/feature/story.

According to Oxford dictionary, Fibonacci Series is :

“ a series of numbers in which each number ( Fibonacci number ) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc

The formula to arrive at a Fibonacci sequence is:

Xn = Xn-1 + Xn-2

This sequence will be slightly modified when used in Agile estimations: typically, it will not have values beyond 100 and may have 0, ½, 1, 2, 3, 5,8, 13, 20, 40, 100. Some teams limit the highest value as 21 and use 0, 1/2, 1, 2, 3, 5, 8, 13, 21.

“The Weber–Fechner law refers to two related hypotheses in the field of psychophysics, known as Weber’s law and Fechner’s law. Both laws relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell”

Applying the law to Numerical Cognition,

Psychological studies show that it becomes increasingly difficult to discriminate between two numbers as the difference between them decreases. This is called the distance effect. This is important in areas of magnitude estimation, such as dealing with large scales and estimating distances. It may also play a role in explaining why consumers neglect to shop around to save a small percentage on a large purchase, but will shop around to save a large percentage on a small purchase which represents a much smaller absolute dollar amount”

The Fibonacci sequence very well corresponds to Weber’s law. The values in the Fibonacci sequence are about 60% higher than the previous value, and hence applying relative sizing is much easier.

It is very challenging to distinguish the size of two numbers which are adjacent to each other, by just looking at the objects. Let us take an example of a football and cricket ball. The approximate diameter of a cricket ball would be 2.8 to 2.86 inches whereas the diameter of a football would be 8.66 inches. It is easy to distinguish the relative size of these two (i.e., approximately the diameter of a football is 3 times that of a cricket ball).

However, it is very challenging to distinguish between two cricket balls that vary 1 inch in diameter, unless you measure both. If you look at the Fibonacci sequence, the relative size between two adjacent numbers is more than 60% and this helps us to be able to size them accordingly.

The smaller value assigned from the Fibonacci sequence to a user story usually means that the story is well understood, and the user story follows INVEST (Independent, Negotiable, Valuable, Estimable, Small and Testable) guidelines. Whereas the largest value denotes the story is not well understood or it needs to be broken down further. Smaller stories can be confidently estimated by the team in detail.

A general practice from matured Agile teams is that the Fibonacci sequence is restricted up to 21 (0,1,1,2,3,5,8,13,21) and any story which is of size beyond 21 will have to be broken down further. This ensures that the team is not giving any room for greater uncertainty and good practice for the team to write better stories under the INVEST guidelines.

Though it is not mandatory to use Fibonacci sequence for story point estimations, the sequence is easier to understand and adoptable by the team. Individuals are better at comparison than estimation.

The easy sequence and distinguishable values of Fibonacci sequence helps to estimate by not measuring the objects but by comparison.

When do you think is the right time for the Agile team to estimate user stories that are prioritized by the Product Owner in the product backlog?

In my experience, I would say that the estimates (story point sizing) should happen during the Iteration/Sprint backlog grooming sessions. This gives the team the time to go through the user stories in detail, collaborate and mutually agree using the Planning Poker exercise.

Then what do we do in Sprint Planning? – This ceremony should be used to pick the stories from the product backlog (fulfils Definition of Ready), that can be completed within the iteration/sprint and then breakdown the stories into tasks and do one more level of estimation which is effort estimation denoted in hours.

Let us say a team is assigned a task to estimate a reporting module to be developed:

There are various methods to estimate user stories, like T-Shirt sizing, Dot voting, Affinity Mapping etc. Story points is the widely used measurement for sizing the user stories. Fibonacci series helps the team to compare between two storiesand its very nature of distinguishable values helps them to fit the story into the right size that reflects uncertainties, which further helps the team to refine the story to remove those uncertainties.