Build best-case, base-case, and worst-case financial scenarios with probability weighting and expected value calculation.
Three scenarios beat one forecast. Enter a worst, base, and best outcome with a probability for each, and the calculator weights every outcome by its odds and returns the expected value - the long-run average if you faced the same decision many times - plus a standard deviation that measures how wide the range really is. The surprise most people hit: the expected value rarely equals any scenario you typed. It is a weighted blend, and it ignores risk unless you also read the dispersion.
A concrete input and expected output from the current implementation.
Input
Worst case: $60,000 profit at 30% | Base case: $120,000 profit at 50% | Best case: $180,000 profit at 20%
Expected output
Expected value: $114,000. Standard deviation: $42,000. Range: $60,000 to $180,000.
Each outcome contributes its value times its probability: 0.30 x 60,000 + 0.50 x 120,000 + 0.20 x 180,000 = 114,000. The variance is the probability-weighted average of the squared deviations from that mean, and its square root is exactly 42,000.
Each scenario contributes its value multiplied by its probability, and those contributions are summed: expected value = probability x value, summed across all scenarios. The probabilities are entered as percentages, so the rows should total 100%. The result always lands inside the typed range, pulled toward whichever scenarios carry the most probability and the largest values.
The tool also reports how spread out the outcomes are. Variance is the probability-weighted average of the squared deviations from the expected value, and standard deviation is the square root of that, expressed in the same dollars as the scenarios. Two plans can share an identical expected value while one has a standard deviation twice the other's - that gap is the measurable difference in risk.
Because the base case is a single most-likely outcome, while the expected value is the probability-weighted average of all three. Whenever the worst and best cases are asymmetric around the base - a small chance of a large loss, say - the average shifts away from the base. That shift is exactly the information the calculation exists to surface.
Only loosely. The rule of thumb that about 68% of outcomes fall within one standard deviation assumes a normal distribution, and three hand-picked scenarios are not one. Read the standard deviation as a relative risk measure - larger means a wider spread and lets you compare risk across plans. For a real probability statement about the worst case, rely on the probabilities you assigned to the scenarios.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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