Estimation values: near-Fibonacci vs. true Fibonacci

This excerpt from the Kindle pocket guide, Practical Estimation, discusses the relative merits of using the familiar “near Fibonacci” sequence vs. the true Fibonacci sequence for estimating work effort.

Fibonacci Numbers

Estimates are educated guesses. They are predictions based on past information, therefore we cannot expect them to have a lot of precision. If I spend time agonizing over deciding whether a task is either, say, 50% or 51% larger than another task, I am probably wasting time. Any individual estimate, being an educated guess, is not going to be correct with that kind of precision. Sometimes an individual estimate will be too large and other times too small. We can, given a number of samples, expect these anomalies to cancel each other out over time, yielding fairly reliable predictability of schedule.

We can limit the amount of precision that our estimates imply by using numbers from sets that are not contiguous. The Fibonacci sequence is an example of one of those sets.

A number in the Fibonacci sequence is created by summing the prior two numbers. Starting with zero, the sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, …

The extra “1″ is unnecessary, so we can ignore it. Likewise, some may find that the “0″ is superfluous.

The Fibonacci sequence is handy for several reasons:

  • The formula to generate the sequence is easy to remember and perform.
  • The gaps between numbers grow as the numbers get larger, and can be thought of as representing the “uncertainty” of an estimate.
  • Throughout the sequence, the numbers grow at a rate that makes it possible to represent useful relationships such as (roughly) one-and-a-halftwicethree times larger, etc.

Near-Fibonacci vs. True Fibonacci

Some teams use what might be called a near-Fibonacci sequence, which looks like:

1, 2, 3, 5, 8, 13, 20, 40, 100

Notice that this sequence differs from the true Fibonacci sequence after 13. Early on, when I first started practicing relative estimation, I was encouraged to use this “near” sequence, and to think of the smaller numbers (1-13) as being the proper sizes for work items. Anything larger than a 13 was assumed to need decomposition into smaller items.

But tying a specific range of numbers to a specific block of calendar time can have the unfortunate side effect of causing team members to mentally (and unconsciously) map individual estimates to absolute time. When that happens, estimates become little more than alternate representations of calendar time, an unnecessary complication. We might just as well have estimated in hours (which we’re not especially good at).

I like to use the true Fibonacci sequence because it allows expression of relationships between work items of all durations. Using numbers from this larger sequence enables quick, up-front estimation of entire projects, even when its components have not necessarily been broken down into work-sized items.

I also favor the true Fibonacci sequence for its re-scalability. If, for example, I initially estimate a work item as a “1″, then eventually encounter other work items that are smaller, I can re-label any existing work items so that my “1″ becomes a “13″ and then I have all of the smaller numbers (1,  2, 3, 5, 8) to work within. In other words, I can make all of my estimates consistent relative to each other, regardless of size, because there is no upper bound to the sequence.

Another way to think about this is to consider the idea that the following two sequences are roughly equivalent to each other:

1, 2, 3, 5, 8

13, 21, 34, 55, 89

If you’re doing relative estimation, since all you’re really interested in are the ratios of the numbers (and not the absolute values of the numbers), then you should be able to use the above two sequences interchangeably. For example 2:1 is roughly equal to 21:13; likewise 3:2 is roughly equivalent to 34:21 (given a level of precision that is appropriate for estimates).

See other interesting things at the Agile Unlimited website. “To Agility and Beyond!”

Read more about estimation in the 99-cent Kindle pocket guide, Practical Estimation.

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