What is probability distribution?

A probability distribution tells you which values an uncertain quantity can take and how likely each one is. Instead of saying demand will be 100, you say demand is usually around 100 and rarely below 70. Choosing the right shape is essential for honest forecasts.

How it works

Common shapes include the uniform, where every value in a range is equally likely, the normal bell curve, where values cluster around an average, and skewed or heavy-tailed shapes, where a few very large values occur. Two numbers often summarize a distribution: its center, such as the mean, and its spread, such as the standard deviation. For a normal distribution about 68 percent of values fall within one standard deviation of the mean and about 95 percent within two. Using the wrong shape, for example a bell curve for something with rare huge losses, understates risk.

If you have no data, a common approach is to ask experts for a low, a likely, and a high value and fit a triangular shape. This is crude but far better than a single guess, and it can be refined as evidence arrives.

Example

Say daily orders follow a bell curve with a mean of 200 and a standard deviation of 20. About 95 percent of days will have between 160 and 240 orders. A manager who staffs for exactly 200 will be short on roughly half of all days. Staffing for 240 covers about 97.5 percent of days, at a higher cost. This is an illustration with round numbers.

How to model it in Machinations

Give a Source a random rate, or use a Register with a random formula, using the shape that matches your data. Play many times at once and chart the Pool to see how the input's spread carries through to the result. Change the spread with a Lever to see how much the uncertainty matters.