Estimating Part III

Sometimes I hear discussions or questions about the reasons for using the Fibonacci scale when estimating in story points. I think the main reason is that the Fibonacci scale jumps in steps of around 50% between the consecutive values. For estimating purposes this is fine, it is much easier to make a distinction between something of size 8 and 13, than between 10 and 11. To make this point more clear, let’s do a thought exercise.

Suppose we are looking at 4 buildings,  a 1 story building, a 2 story building, a 3 story building and a 4 story building. The buildings have flat roofs. The height of the stories in each building is not necessarily the same. The goal is to estimate the sum of the height if the buildings in meters just by looking at it. We will start using a linear scale. 

The 1 story building is probably between 2 and 4 meters high, the 2 story building between 5 and 7 meters, the 3 story building between 8 and 10 and the 4 story building between 10 and 14 meters high. In a table this looks like this:

So we have a minimum total height of 25 meters and a maximum of 35 meters with an average of 30 meters. We could have long discussions on each individual building and come up with any number in this range. Deciding for example whether building 3 is 8 or 9 meters high could be difficult, and any way it wouldn’t make a big difference on the total.

Now let’s do the same exercise using Fibonacci numbers, i.e.  we take the Fibonacci sequence as our possible values for the heights of the buildings. A reasonable estimate for each is then shown in the table below:

2 meters is probably a little low for a 1 story building and 5 too high, so we take 3. The 2 story building is obviously higher than 3 meters, but 8 is likely too much so we take 5 meters. The 3 story building is higher than 5 meters, but 13 meters sounds like too much, so we settle on 8 meters. The 4 story building is likely 13 meters high, since 21 meters is again too high. This gives a total of 29 meters, only 1 meter less than the average we calculated above, and without going into too much detail like the height of the individual floors of the buildings.

So by using Fibonacci numbers we can get to a reasonable estimate pretty quickly, even if we don’t know too much detail yet about the individual buildings and floors in this case. In my previous post I showed a table with the results of a fictional planning poker session using Fibonacci numbers and came to some conclusions about accuracy, precision and confidence. I repeat that table below.

How would that work out if we would replace the Fibonacci scale with a linear scale, i.e. 1, 2, and 3 point user stories stay the same, but a 5 point story becomes a 4 point story, an 8 point story becomes a 5 point story, a 13 point story becomes a 6 point story and so on? Below is the table with the individual estimates converted to a linear scale value.

You see that with the linear scale we get a lower estimate and a higher precision, the 2σ value of 12.14 is 28% of the average of 42.6, whereas with the Fibonacci sequence we had a precision of 53%.

We now repeat this exercise again but with a quadratic scale, i.e. a 1 point story and a 2 point story stay the same, but a 3 point story becomes a 4 point story, a 5 point story becomes an 8 point story, an 8 point story becomes a 16 point story, a 13 point story becomes a 32 point story and so on. The result is in the table below.

We now have a much higher average of 218.8 story points and a 2σ value of 163.29, or 75% of the mean. So with a quadratic scale we get much higher and much less precise estimates when compared to using the Fibonacci scale.

My conclusion is that by using Fibonacci numbers you have a good compromise between accuracy and precision, and it is also easier to use. There is no need for intermediate numbers like maybe one would be tempted to use when using the quadratic scale (and if you do, it would start to converge to the Fibonacci scale anyway). Likewise, there’s no need to skip numbers as you might be tempted to do when using the linear scale (and again, if you do that you converge towards the Fibonacci scale).