Decision Tree & Expected Value Calculator

What this tool does

CM8-359 lays out a decision as options and outcomes, weights each outcome by how likely it is, and works out what each option is worth on average. It then puts three things next to that answer that expected value on its own hides: the worst case, the chance of losing money, and how much of the calculation rests on guesses.

Everything runs inside this single file — no account, no upload, no network request of any kind.

How a decision is laid out here

A decision tree is a decision node with branches, and a chance node under each branch with its own branches. Here that becomes a flat table: one row per outcome, per option. Rows sharing an option name belong to the same branch of the tree, and the tool groups them automatically.

The trade is deliberate. A drawn tree is prettier and handles several decisions in sequence; a table handles one decision with any number of options and outcomes, can be edited by anybody, sorts, filters, prints and goes into a spreadsheet. For the decision most businesses actually face — four options, three or four things that could happen under each — the table loses nothing.

What one row is

One row is one thing that could happen under one option. Two rules make the arithmetic work:

• The outcomes under an option must be mutually exclusive and must cover everything. Exactly one of them will happen, which is why their probabilities have to add up to 100%. The tool checks and flags any option that does not, within a tolerance you set for rounding.
• The upfront cost is a property of the option, not the outcome. Put the same figure on every row of an option; the tool takes it off once. It refuses to save rows of one option carrying different costs, because that silently produces a wrong answer.

Three or four outcomes per option is usually right. Two is often a false binary — "it works" and "it does not" — and hides the middle case, which is frequently the most likely one. More than five and you are estimating differences you cannot really tell apart.

Expected value

That is the whole calculation, and its simplicity is the point: every figure in the branches table can be checked by hand in a few seconds, which matters when somebody disagrees with the conclusion.

The upfront cost

Keep the cost of the option out of the payoffs. Two reasons: the cost is usually known far better than any payoff, so mixing them buries a reliable number inside three unreliable ones; and putting it in each payoff means it gets multiplied by each probability and counted a fraction of a time.

The worst case shown in the tables is the worst payoff after the cost, which is the figure you would actually be looking at.

Discounting

Only worth using when options resolve over genuinely different timescales — a two-year lease against a five-year purchase. Where everything lands at roughly the same time, discounting moves every option by about the same proportion and changes nothing except the size of the numbers. It is off by default for that reason.

Why the worst case gets equal billing

Expected value answers "what is this worth on average". It does not answer "what happens if it goes badly", and those are different questions with different consequences.

Set the serious-loss level in Settings to the size of loss that would genuinely hurt — the point at which you would be raising money, cutting staff or losing the business. Any option whose worst case is worse than that is flagged in the decision table however high its expected value, and any single outcome that is both that bad and irreversible is flagged on its own row.

One-shot decisions

This is the honest limitation of expected value and it deserves to be stated plainly.

Expected value is an average over many repetitions. It is exactly the right tool for a decision you make weekly: accept the higher average and the swings cancel out over a year. It is a much weaker guide for a decision you make once, and a dangerous one where a bad outcome would stop you making any further decisions at all. A 90% chance of gaining a million and a 10% chance of losing everything has a wonderful expected value and is not a bet a sensible business takes.

The practical test is simple: could you survive the worst case and go again? If yes, follow the expected value. If no, the worst case is the number that decides, and the expected value is interesting rather than decisive.

Getting probabilities out of people

People are bad at stating probabilities directly and much better at comparisons. Three questions that work in a room:

• "Out of the next ten times we do something like this, how many times does this happen?"
• "Would you rather bet on this, or on a coin?" — that brackets it above or below 50%.
• "What would have to be true for this to happen?" — if nobody can answer, the probability is lower than they said.

Do the payoffs first and the probabilities afterwards, separately. Doing both at once lets people adjust the probability to reach the answer they already prefer, which is the most common way a decision analysis becomes theatre.

Recording where a number came from

Every branch records whether its probability came from evidence, from informed judgement, or is a guess. The donut chart shows the mix, and it exists to stop the most damaging thing that happens to this kind of analysis: a number built from four guesses being quoted three weeks later as a fact, with its decimal places intact.

Recording something as a guess is not a weakness in the analysis. The sample includes a guessed probability on a quality failure precisely because leaving the outcome out entirely would have been a much stronger claim — that it cannot happen.

Doing nothing is an option with outcomes

Always add it, and give it real outcomes rather than a single zero. "Do nothing" almost never means "nothing happens": the customer goes elsewhere, the backlog grows, the opportunity passes to a competitor. In the sample, doing nothing has the worst expected value of the four options, which is exactly the sort of thing that stays invisible until somebody writes it down.

What this does not do

• It handles one decision, not a sequence of them. Where a first choice changes what is available later, model the sequence as separate options — "buy now", "lease then buy", "wait and buy" — rather than trying to nest them.
• It has no view about whether your probabilities are right, and small changes to them can reverse the ranking. If two options are close, test whether a ten-point shift changes the answer; if it does, the analysis is telling you the options are equivalent and something else should decide.
• It does not model correlation. If two options both fail in the same downturn, that shared cause is not represented anywhere.
• It cannot value things that are not money: reputation, the effect on people, what an option does to what you can do next. Record those in the reasoning and weigh them separately.

Printing and sharing

The Report tab prints the tiles, charts and both tables with a title block you fill in. The branches table with its reasoning is the part worth keeping: in a year, the record of why you believed something will be more useful than the answer.

Saving your work

The decision is held in this browser, on this computer, and stays there between visits. Use the backup button to write a JSON file you control.

Accuracy & disclaimer

Every probability and payoff here is your own estimate. The tool multiplies and adds them exactly as entered and has no view about whether any of them is plausible. It is a way of making a judgement explicit and arguable, not a way of making it correct.