What is variance?

Variance measures how spread out a set of outcomes is. Two choices can have the same average result and very different risk, and variance is the number that tells them apart. A larger variance means less predictable outcomes.

How it works

To compute it, take each outcome, subtract the mean, square the difference, and average the squares. The square root of the variance is the standard deviation, which is in the same units as the data and is easier to read. Variance adds up for independent sources of uncertainty, so combining many independent small risks produces a total spread that grows more slowly than the total itself. It also depends heavily on extreme values, because squaring gives them extra weight.

In practice, decision makers often care about the downside more than the overall spread. Variance treats a surprise upward and a surprise downward in the same way, so it is wise to look at the lower tail of the outcomes as well.

Example

Say option A pays 100 every time. Option B pays 0 or 200 with equal chance. Both have a mean of 100. For A, the variance is 0. For B, each outcome is 100 away from the mean, so the squared distance is 10,000, and the variance is 10,000, with a standard deviation of 100. B is as good on average but far less predictable. This is an illustration with round numbers.

How to model it in Machinations

Play the diagram many times at once with a random Source or Gate, and read the spread of the chart for a Pool or Register. A wider band means a higher variance. Change a Lever that adds or removes randomness and watch the band widen or narrow while the average barely moves.