People are often asked about estimates in investments, the opening of new business areas, projects and budgeting. The estimates given are subject to uncertainty. No one can tell the exact amount, time etc., that will occur in the future.

Despite this uncertainty, there is a great demand for estimates given in a single number. So, give me a number!

What is going to be our revenue next year? Give me a number, not some soft statement. Give me a number I can use for my calculations.

In situations like this, when asked to give a number on tomorrow’s uncertainties, most provide an average. The average turnover from the past five years is X, so here is my estimate.

The average duration of such a project is Y months, so there you have my estimate.

Is that the right way to go about it when giving estimates about tomorrow’s uncertainties?

Imagine the following:

- Three separate teams are working in each their phase of a project.
- All three phases must be completed before the project is finished.
- The three phases can run parallel to each other.

To determine how long the project is estimated to take to finish, you gather estimates of the duration for each subphase. All three teams return with the same estimate of 4 weeks on average.

How long is the project going to take on average? 4 weeks, you might say. Try again. Are you still going with 4 weeks on average?

Then you might have fallen victim to “The Flaw of Averages”. The average output is not equal to the average of the inputs.

- It doesn’t take 4 weeks to finish a project, with each underlying phase taking 4 weeks since the phases, on average, take 4 weeks to complete.
- There is a risk that each one of the phases will take longer than 4 weeks to complete, with some probability.
- If the duration of the phases is normally distributed, then the probability of that happening is 50%.
- To finish within 4 weeks requires that each of the four phases finish on the right side of 4 weeks since if just one of them takes longer, the whole project will be delayed.
- What is the probability that this will happen? Again, if the variables are distributed normally, the answer is 12,5% (0,5
^{3}), which equals landing heads three times in a row.

The average duration of such a project is 4.8 weeks (assuming the standard error is 1).

No wonder people have a hard time finishing projects on time.

So, the next time you are asked to come up with a number, remember that the average output is not always equal to the average of the input.