A probability distribution is a statistical function that shows the expected outcomes of possible values for a given data-generating process. Probability distributions can have different shapes and characteristics, but are typically portrayed in a bell-shaped graph.
The variables used in estimating the outcomes are what determine the distribution and the variance of outcomes..
The standard deviation of a distribution is a measure of its variance. A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.
The interquartile range (IQR) is another representation of variance. It is calculated as a measure of the spread of the middle 50% of a data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data and compared to a median of the data-set. In addition to standard deviation, this will also hint at the more likely outcomes.
There are many potential outcomes. In forecasting, the base-case will be wrong. Worst-case and best-case will also be wrong. While they will not be accurate, scenarios will hint at the variables that can be toggled to reach an array of possible outcomes.
Outcomes within the standard deviation or inside of the interquartile range are reasonably likely to occur. Additionally, the outcomes could be skewed above or below the mean or median. In other words the base case may be better or worse when taken in the context of the overall distribution of outcomes. Finally, there is still potential for outcomes outside of the standard deviation or interquartile range. These outliers are what is known as black-swan events and are often a function of a confluence of events impacting the outcome.
Probability distribution is a concept that can help illustrate potential outcomes when forecasting. While predicting future values, like cash-flows, is inherently difficult, it is important to understand that many variables can lead to many outcomes, that those outcomes may be skewed in a certain direction, and may eventually lead to an actual outcome that is outside of reasonable expectations.
Bell Curve