When the math is off

How Developers Rate Their Own Programming SkillsMax Woolf @minimaxir

Here is a common interview question that is typically gets asked in interviews:
"Please rate yourself in your best skill, on a scale of 1 to 10, where 5 is average."

The answers most often are between 7 and 9.5 inclusive, with an occasional 10.
Lets consider what that means.

Skills and ability to contribute have been shown to be distributed according to a Pareto Principle: 20% of the population possess 80% of the skills and deliver 80% of the results. Suppose, it is a Pareto distribution with the slope of 1, and a minimum skill value of 1. There is no max value for the true Pareto distribution, but the way developers are asked to use the scale, the max value is set at 10.

A few runs on University of Alabama in Huntsville Special Distribution Simulator show that for a 1000-point simulation the mean is in the 7-9 range. So far so good.

However, the randomly generated values have no set maximum, and can go well above 10. Even a few higher values in a large set skew the mean significantly.  To get back to the allowed range of values 1 through 10, replace all values in the 1000-point dataset, that are above maximum allowed value of 10, with 10.5. The average drops down to ~4.  The median is ~2, i.e. half the data points have values of less than 2.

That contradicts the initial question, which sets 5 as being the average.  A distribution of skills is likely to have an average level skewing lower than half the range. In this example of modeling skill distribution with a Pareto distribution 1,1 - way lower, at the mean value of 2.  More importantly, it raises the question on how well the interviewers understand the question they are asking the candidates.

"The best and the rest: Revising the norm of normality of individual performance."
by Ernesto'Boyle Jr., Herman Aguinis

All of the above is just a long way of saying that when a typical candidate for a position rates himself in response to the question, they are, so to speak, gaming the situation.

The more interesting observation is that not only the question is asked regularly, by many, if not most, developers acting in the interviewer capacity. The answer is taken seriously and can influence how the interview proceeds, as well as the outcome. People with higher self-rating (those claiming to be above 8) are more likely to be hired and promoted.