# Symmathesies follow a power law, not a bell curve

At my first real job, around the turn of the millenium, software engineers were graded on a bell curve. On a scale of 1 to 5, most people should get 3s, with a lower number of 4s and 2s and a much lower number of 1s and 5s.

The bell curve, also called the normal or Gaussian distribution, is a useful probability distribution for random variation. If you’re good at darts, the distance from the target to your dart’s landing will follow a normal distribution. When a bunch of random influences — air currents? bugs? finger unsteadiness? — affect the result independently of each other, you get a normal distribution.

Each random influence adds some distance farther from the target. Or closer to the target, as they can compensate for each other in their randomness. Each independent influence has an additive effect.

A normal distribution follows from component-dominant dynamics. That happens when the parts of the system are more significant than their interactions. Each air current can be evaluated regardless of finger unsteadiness, and both are unrelated to insects. Look at each part individually, and you’ll understand what’s happening. Like the review process tries to isolate each software engineer.

Does this fit with performance reviews? Are people subject to random independent influences like a well-thrown dart? If so, then a normal distribution is to be expected.

College classes, that’s an influence, and people we know, and books we read and lessons we learn on the job and — oh wait, these aren’t independent of each other.

I meet a new person, they recommend a book, I gain an interest that leads me to meet new people — these build on each other. We work in teams, and across teams, with other people, on systems that we build. Everything we do and say affects our possibilities in the future. A symmathesy (a learning system) has interaction-dominant dynamics.

What kind of distribution does that have? Not a bell curve! Interaction-dominant dynamics exhibit power law distributions. Like the number of friends people have, that’s a power law distribution. Frequencies of words. Sizes of earthquakes.

Power law distributions are related to fractal structures, which are associated with healthy systems that exhibit a balance of stability and adaptability. They’re often found in healthy systems.

I like this distribution, found in a paper by Turvey and others that models human response times for reading words aloud.

This distribution has a power law on the right, for slower responses being less likely. On the left, it represents a certain minimum response time using a lognormal distribution. The lognormal represents multiplicative effects, which impact each other in a constrained way. The power law represents feedback loops, where interactions feed each other.

In a real team that works together, interaction-dominant dynamics make a more reasonable distribution of performance. Anyone who doesn’t meet expectations moves to another job, so those numbers are tiny. Meanwhile, people who are doing well — learning stuff, developing relationships with others, becoming intimate with the code — get better and better.

The power law distribution has a fatter tail than the normal, representing our higher potential. In a learning system, every interaction feeds every future interaction. We get farther on purpose! Teams can do better than darts!

Grading individual software engineers has its own issues; teams are the unit of delivery. Grading on a bell curve makes it even worse. It says, “We think that you are all cogs, and don’t learn from each other or the software, so you will be randomly distributed like darts.”

If your organization’s people do not fit a normal distribution, if you have no poor performers, if you have way more significant contributors than the bell curve can account for, great! This points to a healthy system. You are on target.