Key Takeaways
- A single-point cost or schedule estimate hands stakeholders a number that feels like certainty in a situation that is inherently uncertain. Probabilistic analysis replaces that number with a distribution showing every plausible outcome and how likely each one is.
- Risk Companion generates P50, P85, and P95 outputs from Monte Carlo simulation using triangular estimates, minimum, most likely, and maximum, for both probability and impact on each risk. The simulation runs 1.000 scenarios and produces a full confidence curve alongside those headline figures.
- P50 is the median outcome across simulated scenarios. P85 means there is an 85 percent chance the actual outcome will land at or below that figure. Which percentile you budget to depends on your organisation's risk appetite: a team delivering a fixed-price contract with thin margins needs to be much further into the tail than one that can absorb a modest overrun.
- Expected monetary value translates the simulation distribution into a concrete floor for contingency discussions. A budget set below the EMV is almost certainly under-reserved, and the gap between EMV and P85 is where the contingency buffer lives.
- The S-curve shows at a glance how uncertainty is distributed across a project. A steep, narrow curve signals good predictability, a wide, shallow curve signals significant spread and a contingency that needs to reflect it. Both can be presented directly to a board or sponsor without translation into a different format.
The problem with a single number
A project team hands stakeholders one cost figure and one completion date, and that number feels like a commitment when it is, in practice, a guess with all the uncertainty stripped out.
The project manager knows the true picture: the ground conditions might be worse than the survey suggests, the lead-time on critical equipment could blow out, and the regulatory approval might take six weeks longer than planned. All of that ambiguity gets stripped from the estimate before it reaches the steering committee, and the contingency is whatever felt right at the time.
Probabilistic analysis restores the uncertainty the single number removes, producing a full distribution of possible outcomes and showing how likely each one is. That shifts the conversation from "what is the budget?" to "how confident do we need to be, and what does that confidence cost?"
Risk Companion supports probabilistic analysis through Monte Carlo simulation, using triangular estimates for probability and impact to generate a distribution of outcomes across your entire risk register. The outputs, P50, P85, and P95, give project teams a direct answer to the contingency question.
This article explains how those outputs are generated, what they mean in plain language, and how to use them to make concrete budget and schedule decisions.
If you want the conceptual foundation first, our earlier pieces on probabilistic risk assessment and Monte Carlo simulation in plain language cover the theory. This article is about what you do with it once Risk Companion has run the numbers.
What goes in: triangular estimates and why they matter
Monte Carlo simulation is only as good as the inputs you feed it, and the standard approach in project risk management is the triangular distribution: for each risk, you specify a minimum value, a most-likely value, and a maximum value for both probability and impact.
The minimum is the best realistic case, the maximum is the worst realistic case, and the most-likely value is your central estimate. Together, the three points describe the shape of uncertainty around a risk instead of collapsing it to a single figure.
Risk Companion uses a PERT-derived distribution under the hood, which weights the most-likely value more heavily than the extremes, matching how project risk actually behaves: extreme outcomes are possible but not equally probable.
A supply-chain delay that costs EUR 50.000 is far more likely than one that costs EUR 500.000, even if both are realistic.
When you assess a risk in Risk Companion, you set these triangular ranges per impact perspective: financial, schedule, HSE, reputational, and others. The probability and impact assessments draw from the framework your project is running on, so the level definitions, numeric ranges, and colour bands all reflect your organisation's own scoring methodology, with no generic defaults imposed.
The simulation then draws from those distributions thousands of times, combining the results across every risk in the register to produce an aggregate outcome distribution for the project.
What comes out: reading P50, P85, and P95
The output of a Monte Carlo simulation is a probability distribution, which Risk Companion presents as percentile figures and as an S-curve. The percentile figures are the ones you take to budget conversations.
P50 means there is a 50 percent chance the actual outcome will be at or below this value. It is the median scenario: as many simulated runs came in above it as below it. P50 is the central case, which is already a more defensible starting point than a single-point estimate built on best-case assumptions.
P85 means there is an 85 percent chance the actual outcome will be at or below this value. If you set your contingency at the P85 level, you are covered for 85 percent of the scenarios the simulation generated. For many infrastructure and construction projects, P85 is a reasonable working threshold, absorbing typical variability without over-reserving for the extreme tail.
P95 means there is a 95 percent chance the actual outcome will be at or below this figure. The gap between P85 and P95 is where tail risk lives, and for high-stakes projects where cost overruns carry serious consequences, including regulatory penalties, contract forfeitures, and reputational damage, budgeting to P95 is worth the extra reserve.
Which percentile you choose is a risk appetite question. The simulation generates all of them; the project team and its sponsors decide where to set the line based on how much uncertainty they can absorb.
A project team that can absorb a modest overrun might be comfortable at P50 or P85, while a team delivering a fixed-price contract with thin margins needs to be much further into the tail.
Risk Companion generates the full confidence curve in incremental steps, so whether your organisation frames contingency at P50, P85, P90, or P95, you can read your figure from the curve or ask the AI assistant directly.
Expected monetary value and expected time value: turning the distribution into a number
Percentile outputs tell you the confidence level for a given budget, while expected monetary value (EMV) and expected time value (ETV) give you the single-number summary of what the risk exposure is worth on average.
EMV is calculated by multiplying the probability of a risk by its financial impact and summing across all risks in the register. If a supply-chain disruption has a 30 percent probability and a most-likely financial impact of EUR 200.000, its EMV contribution is EUR 60.000. Across a register of twenty risks, those contributions add up to a total EMV figure that represents the statistically expected cost of the risk portfolio.
ETV does the same calculation for schedule impact, producing a number in working days or weeks instead of euros.
EMV and ETV represent the average of the distribution, which means half the simulated outcomes fall above them and half below. They tell you the statistically expected cost of your risk portfolio, with the full spread of outcomes visible in the percentile outputs alongside them.
They also provide a defensible floor for contingency discussions: a budget set below the EMV is almost certainly under-reserved.
Risk Companion surfaces both EMV and ETV in the project dashboard alongside the Monte Carlo outputs, so the connection between the expected value calculation and the full distribution is visible in one view. That matters because EMV alone can obscure tail risk: two projects with the same EMV can have very different P95 values if one has a small number of high-variance risks and the other has many small, low-variance risks.
The S-curve: communicating uncertainty to people who are not risk specialists
The percentile table gives you the numbers, and the S-curve shows you what the uncertainty behind them looks like.
An S-curve plots cumulative probability on the vertical axis against outcome value on the horizontal axis. A flat, steep curve means your risks are relatively concentrated, with a narrow range between P10 and P90 and good predictability overall. A wide, shallow curve means your risk portfolio carries significant spread, with a large range of plausible outcomes and a contingency that needs to reflect it.
A board member who has never opened a risk register can look at an S-curve and understand immediately whether the project is tightly bounded or genuinely uncertain, in a way that a table of numbers alone cannot convey.
The P50 and P85 markers on the curve make the contingency logic visible: this is where we are aiming, and this is what it covers.
Risk Companion generates the S-curve as part of the Monte Carlo simulation output in the project dashboard, and you can present it directly to sponsors or steering committees without translating it into a different format. The curve updates as the risk register changes, so if a major risk is closed out or a new one is added, the distribution shifts accordingly, and you can see exactly how much of the contingency buffer your risk management work has earned back.
From simulation to decision: a practical example
Consider a mid-sized construction project with a total budget of EUR 4.2 million.
The project team has built a risk register of eighteen risks in Risk Companion, each with triangular estimates for probability, minimum financial impact, most-likely financial impact, and maximum financial impact.
The Monte Carlo simulation runs 1.000 scenarios and returns the following outputs:
- EMV: EUR 310.000
- P50: EUR 290.000
- P85: EUR 480.000
- P95: EUR 640.000
The original contingency in the project budget was EUR 200.000, set by the project director based on experience. The simulation shows that figure sits well below the P50, meaning more than half the simulated scenarios exceed it.
Budgeting to P85 would require an additional EUR 280.000 in contingency, and that is the conversation the simulation makes possible: are we reserving enough, given what we know?
The project director presents both the EMV and the P85 figure to the client alongside the S-curve, and the client approves an adjusted contingency at the outset, with the gap visible before it becomes a problem.
That is the practical value of probabilistic risk assessment: better-grounded predictions, made at the point where something can still be done about them.
The limits of the simulation
Monte Carlo simulation is a powerful tool, and like every model it has limits worth naming.
The outputs are only as good as the estimates that go in. Optimistic probability and impact ranges produce an optimistic distribution, and a register missing significant risks produces a simulation that reflects only what was included.
The AI risk identification features in Risk Companion can help surface risks your team might have overlooked, but the final call on whether a risk belongs in the register, and what its impact range should be, belongs to the people who know the project.
The simulation also treats risks as independent unless the model accounts for correlation. In practice, risks cluster: a contract dispute often arrives alongside a schedule delay and a cost overrun, and the compounding effect is real even when the simulation treats them separately.
Risk Companion's simulation captures the compounding effect across the full register, but stops short of modelling explicit correlation between individual risks. For many SME and mid-market projects that is a reasonable simplification, though for very large programmes with complex interdependencies it is a limitation worth knowing.
A distribution built on carefully considered estimates and reviewed by a team that knows the project gives leadership a defensible basis for contingency decisions. The simulation improves the quality of that judgement, and the team remains responsible for making it.
Putting it to work
Probabilistic analysis in Risk Companion is available to any project team running a risk register with probability and impact assessments, whether that register was built in Risk Companion from the start or migrated from an existing process.
Adding minimum and maximum ranges to those assessments, the extra step that unlocks the Monte Carlo output, takes an hour on a typical register. What you get back is a contingency recommendation with a confidence level behind it, an S-curve you can show to a board, and a figure that updates as the project evolves.
If you want to see what P50 and P85 look like in practice with your own project's risks, start a free 14-day trial of Risk Companion. A demo project built from your organisation's profile is ready from day one, so you can run the simulation and read the S-curve for yourself.
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