EVPI is the most you should ever pay to remove all uncertainty before deciding. It is the expected payoff when you always choose correctly for the state that actually occurs, minus the expected payoff of the single best decision you would make today. No study, pilot, survey or expert opinion can be worth more than EVPI.
That makes it an unusually practical number. Most organisations argue about whether to commission a study using adjectives — the risk feels high, the data feels thin, another month of testing would make everyone more comfortable. EVPI replaces the adjectives with a currency figure, and it does so before any money is spent. If the proposed study costs more than EVPI, the answer is no, and you can stop the discussion there: even a study that returned the truth with certainty could not repay it.
Its companion, the expected value of imperfect information (EVII), takes the next step. Real tests are wrong sometimes. EVII values a specific study at its actual error rate, and it is the number you compare with the study's price. EVPI tells you whether the conversation is worth having; EVII tells you whether to sign the purchase order.
The rest of this page works one decision all the way through, with every figure derived from the two before it. The arithmetic is deliberately simple enough to check by hand — the point is the logic, which does not change when the tree gets large.
A speciality chemicals plant is considering a $4.0 million retrofit to switch a production line onto a new catalyst. In laboratory conditions the catalyst raises yield substantially. Whether it holds that yield at full scale, in a real reactor with real feedstock variability, is the open question — and it is the only material uncertainty in the business case.
Engineering puts the probability that the catalyst holds its yield at full scale at 55%. The finance team has already modelled both outcomes over the asset's remaining life:
That is the whole decision, and it is small enough to draw. Here it is built in ModelChoice on an Excel worksheet, already rolled back — the bold green path is the one the arithmetic below will arrive at, and every figure on it is a figure from the table above:
There is a third option nobody has priced yet. A pilot campaign on the demonstration reactor would cost $250,000 and take three months. It is a good test but not a perfect one: from historical performance it correctly passes a catalyst that will hold its yield 90% of the time, and correctly fails one that will not 85% of the time.
The question in front of the investment committee is not really "should we retrofit?" It is "should we spend $250,000 to find out first?" Those are different questions with different answers, and only the second one needs value-of-information analysis.
Start with the decision as it stands. Roll the tree back: each chance node is replaced by the probability-weighted average of its branches, and each decision node by its best branch.
EV(retrofit) = 0.55 × $6.0 m + 0.45 × (−$3.0 m) = $3.30 m − $1.35 m = $1.95 m
Doing nothing is worth $0. So on today's information the recommendation is to retrofit, with an expected NPV of $1.95 million. That number is the baseline for everything that follows: it is what the committee walks away with if it refuses to spend anything on further study.
It is worth pausing on what that expected value conceals. It is an average of two outcomes, neither of which is $1.95 million: 55% of the time the company gains $6.0 million and 45% of the time it loses $3.0 million. A decision that is positive on average can still be a coin-flip you would rather not take, which is why a risk profile belongs alongside the rollback. But for valuing information, the expected value is the right starting point.
Now imagine an oracle. Before deciding, you are told with certainty whether the catalyst will hold its yield. You do not get to change the probabilities — the oracle still says "holds" 55% of the time, because that is genuinely how often it holds. What changes is that you can now act on the answer.
Told it holds, you retrofit and gain $6.0 million. Told it does not, you walk away and take $0 rather than losing $3.0 million. Weighting those by how often each message arrives:
EV(with perfect information) = 0.55 × $6.0 m + 0.45 × $0 = $3.30 m
EVPI = $3.30 m − $1.95 m = $1.35 million
There is a second route to the same figure that explains what EVPI actually measures. Without information the company retrofits every time. In the 45% of worlds where the catalyst fails, that decision destroys $3.0 million. Perfect information buys exactly the avoidance of that mistake:
0.45 × $3.0 m = $1.35 million
EVPI is the expected cost of the mistake you would otherwise make. That is the whole idea. It is not a measure of how uncertain you are; it is a measure of how much that uncertainty is going to cost you in wrong decisions. The two come apart constantly, and the difference between them is where most research budgets go wrong.
Immediately the committee has one hard answer: the $250,000 pilot is not obviously extravagant, because $250,000 is well inside a $1.35 million ceiling. Had the pilot been quoted at $2 million, the analysis would be over — no test, however good, could return that.
EVPI depends on the probabilities, and not in the direction people expect. Holding the payoffs fixed and varying only the probability that the catalyst holds its yield:
The value of information peaks where the decision is closest to a tie — here at a probability of one in three, where retrofitting and doing nothing are worth exactly the same and EVPI reaches $2.0 million. It falls away in both directions, and it reaches zero at certainty in either direction, because a decision you would make anyway cannot be improved by being told you were right.
This is the single most counter-intuitive result in the field, and the most useful. Research money tends to flow towards the frightening decision — the one with the large downside — when it should flow towards the balanced one. A project with a terrifying loss branch that you are 92% confident about barely justifies a study. A dull, moderate project you genuinely cannot call is where a study earns its fee. Value of information is one of the few tools that will tell an organisation to stop investigating something it is worried about.
The pilot is not an oracle. It passes a good catalyst 90% of the time and fails a bad one 85% of the time, so it produces false passes and false fails. Valuing it takes three steps: work out how often each result appears, work out what you would believe after each result, and work out what you would then do.
Combining the prior probabilities with the test's accuracy gives the joint probability of every combination of truth and result:
So the pilot passes 56.25% of the time. Reading down that column, a pass means the catalyst really holds with probability 0.495 / 0.5625 = 0.88. A fail means it holds with probability 0.055 / 0.4375 = 0.126. Now re-run the retrofit decision inside each branch:
This is the moment that creates the value: after a fail, the retrofit is no longer worth doing, and the company keeps its $4.0 million rather than spending it on a line that will underperform. Weighting the two branches:
EV(with the pilot, before its cost) = 0.5625 × $4.92 m + 0.4375 × $0 = $2.7675 m
EVII = $2.7675 m − $1.95 m = $817,500
The pilot is worth $817,500 and costs $250,000. Commission it: the expected gain is $567,500. Note also that $817,500 is 61% of the $1.35 million ceiling — a good but imperfect test captures a good but imperfect share of what perfect knowledge would be worth. That ratio is a useful sanity check in itself; an EVII that comes out above EVPI is an arithmetic error, every time.
One more number falls out for free: $817,500 is the most the company should pay for this pilot. If the demonstration reactor came back with a revised quote of $900,000, the answer flips to no — not because the test stopped working, but because the price passed what the test is worth.
Procurement will ask whether a cheaper, less accurate test would do. The same tree answers that directly. Holding everything else fixed and varying only how good the pilot is:
The bottom row is the one to sit with. A test that is right 70% of the time is not useless as a description of the world — it is considerably better than a coin. As a decision aid it is worth exactly nothing, because at that accuracy a failed pilot still leaves the retrofit marginally worth doing. Every result leads to the same action, so nothing about the decision changes, so there is no value to buy. You would have paid $250,000 to feel better informed while doing precisely what you were going to do anyway.
For this decision there are two thresholds, and both come out of the arithmetic rather than out of judgement. Below roughly 71% accuracy no result can flip the decision and the value is zero. Value then climbs, and the test must reach about 76% before it is worth a $250,000 fee at all. The gap between "reduces my uncertainty" and "changes what I do" is the whole subject.
Everything above is arithmetic on a decision tree, and it scales badly by hand: this example had one uncertainty and two options, while a real capital decision has a dozen of each and the Bayesian update alone becomes an error-prone spreadsheet exercise. ModelChoice builds the tree directly on the worksheet and derives value of information from it as one of sixteen standard reports on the same model.
You draw the structure — decision nodes, chance nodes, payoffs — and it stays a readable Excel workbook, laid out and re-solved as you type. That is the tree shown near the top of this page. Backward-induction rollback runs continuously and highlights the optimal path, so the $1.95 million baseline of Step 1 was on screen before anyone asked for it, and it moves the moment a probability or payoff changes.
Perfect information needs nothing beyond the tree, because it makes no assumption about how the uncertainty would be resolved — only that it is. Run the value-of-information report on the tree above and the $1,350,000 ceiling comes straight back. That is the cheap screening test: any study quoted above it is refused on the spot, and no further analysis is needed.
A real test has to be described before it can be valued, and the description is short. ModelChoice asks for four things and returns four:
Here is that report, run on the tree above — the figures in it are the figures you have just read:
That is the whole of this article's Step 3 — the joint-probability table, the two posteriors, the conditional decisions and the weighting — done as one report on the model that produced the rollback. The accuracy table further up is the same report run five times with a different likelihood matrix, which is why it takes minutes rather than a rebuilt spreadsheet each time. Adding the pilot to the tree as an explicit decision node — test first, then decide — is the general form, and the tree then reports the whole strategy rather than a single figure.
Two extensions matter in practice. Our catalyst was a clean two-branch split, but many uncertainties are genuinely continuous — a feedstock price, a demand level, a project duration. There, ModelChoice replaces the chance branch with a distribution and runs full Monte Carlo simulation through the tree via ModelRisk, and value of information survives the move: the Perfect Information Bounds simulation mode computes EVPI under continuous uncertainty by picking the truly best decision given each iteration's resolved outcomes. And when the decision is not only about money, multi-criteria analysis with AHP weight elicitation sits on the same tree. For a survey of the wider tooling landscape, see our comparison of the seven best decision analysis tools.
For the committee itself, the Decision Brief compresses all of it onto a single page that can go straight into the pack. This is the brief for the decision worked through above — generated from the same tree, in seconds:
Three things on it are worth pointing out, because they are the argument of this whole page restated by the software. The value-of-information line says perfect information about all uncertainties is worth at most $1.4 million — no study or test costing more can be justified, which is the ceiling from Step 2. The robustness score of 37 out of 100 flags the recommendation as fragile, and names what would overturn it: the nearest competing strategy is doing nothing, and it becomes optimal if the probability of the catalyst holding drops by 39%. That fragility is precisely why the pilot is worth buying — a robust decision would not have been. The brief rounds to one decimal place in millions, so the $1.95 million expected value appears as $2.0M and the $1.35 million ceiling as $1.4M; the exact figures are in the value-of-information report above.
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The most you should ever pay to remove all uncertainty before choosing. It is the expected payoff when you always pick the best option for the state that actually occurs, minus the expected payoff of the best single option you would choose today. No study can be worth more.
Find the best decision under each possible state, weight those payoffs by the probability of each state, and sum them — that is the expected value with perfect information. Subtract the expected value of the best decision you would make without information.
EVPI assumes the uncertainty is resolved completely, so it is a theoretical ceiling. EVII values a specific real test at its known error rate. EVII is always less than or equal to EVPI, and it is the figure you compare with the price of the study.
Yes, and often is. If no possible result would change which option you choose, the study is worth nothing however much it reduces doubt. In the table above, a test that is right 70% of the time has an EVII of exactly zero.
When the decision is closest to a tie. EVPI peaks at the probability that makes two options equal in expected value and falls to zero as one becomes clearly dominant — the opposite of how research budgets are usually allocated.
There are two thresholds. It must first be accurate enough that some result would flip the decision, or its value is zero. Only above that does value accumulate, and it must then exceed the price. Both are computed from the tree, not judged.
Only in one direction. If the study costs more than EVPI, decline it at once — even a perfect study could not repay it. If it costs less, you still need EVII at the test's real accuracy before concluding that it pays.
ModelChoice builds the decision tree on the worksheet and computes value of information from it. Both EVPI and EVII are standard reports on the same tree that produces the rollback, so they update whenever a probability or payoff changes.
Build the tree on the worksheet, roll it back as you type, and get EVPI, EVII, sensitivity, risk profile and a board-ready Decision Brief from the same model. Free 15-day trial.