Key Takeaways
- A single-point cost or schedule estimate gives stakeholders the illusion of certainty in a situation that is inherently uncertain — probabilistic analysis replaces that number with a distribution that shows 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, maximum) for both probability and impact on each risk.
- P50 is the median outcome across thousands of simulated scenarios; P85 means there is an 85 percent chance the actual outcome will land at or below that figure — and which percentile you budget to depends on your organisation's risk appetite, not a convention.
- Expected monetary value and expected time value in Risk Companion translate the simulation distribution into a concrete contingency number you can defend in a budget conversation without waving your hands.
- The S-curve visualisation shows at a glance how uncertainty is distributed across a project, making it far easier to communicate the range of outcomes to a board or sponsor who is not a risk specialist.
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. In practice, it is 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. None of that ambiguity makes it into the estimate. The single number lands on a slide, a steering committee approves it, and the contingency is whatever felt right at the time.
Probabilistic analysis is the discipline that restores the uncertainty the single number removes. Instead of one outcome, it produces a full distribution of possible outcomes and tells you how likely each one is. That changes 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. 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. The most-likely value is your central estimate. Together, the three points describe the shape of uncertainty around a risk rather than 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. That matches 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 rather than a generic default.
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. Risk Companion presents that distribution 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 not the most optimistic case; it is the central case, which is already a more honest 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 most infrastructure and construction projects, P85 is a reasonable working threshold — it absorbs 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 the tail risk lives. For high-stakes projects where cost overruns carry serious consequences — regulatory penalties, contract forfeitures, reputational damage — budgeting to P95 is worth the extra reserve.
Which percentile you choose is not a technical question. It is a risk appetite question. A project team that can absorb a modest overrun without catastrophic consequences might be comfortable at P50 or P85. A team delivering a fixed-price contract with thin margins needs to be much further into the tail. Risk Companion generates all of them; the project team and its sponsors decide where to set the line.
Risk Companion also generates P90 outputs, so if your organisation's standard is P90, you have it. The P50, P85, and P95 figures are the ones most teams find useful for framing the contingency conversation.
Expected monetary value and expected time value: turning the distribution into a number
Percentile outputs tell you the confidence level for a given budget. 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 rather than euros.
Neither EMV nor ETV is a prediction. They are the average of the distribution, which means half the simulated outcomes are above them and half are below. What they give you is a defensible floor for contingency discussions. A budget that does not cover the EMV is almost certainly under-reserved. A contingency equal to the P85 output provides a meaningful buffer above it.
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 tells you what the numbers are. The S-curve shows you what the uncertainty looks like.
An S-curve plots cumulative probability on the vertical axis against outcome value (cost or schedule) on the horizontal axis. A flat, steep S-curve means your risks are relatively concentrated: the range between P10 and P90 is narrow, and you have good predictability. A wide, shallow S-curve means your risk portfolio carries significant spread: the range of plausible outcomes is large, and your contingency needs to reflect that.
The shape of the curve tells a story that a table of numbers does not. 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. 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. 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
Picture 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 10.000 scenarios. The outputs come back:
- 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. That is the conversation the simulation makes possible: not "should we have contingency?" but "are we reserving enough, given what we know?"
The team also runs the ETV calculation. The schedule equivalent of the risk exposure suggests a P85 buffer of six weeks beyond the planned completion date. The project director presents both figures to the client with the S-curve alongside, and the client approves an adjusted contingency rather than discovering the gap mid-project.
That is the practical value of probabilistic risk assessment: not more accurate predictions, but more honest ones, made at the point where something can still be done about them.
A note on what the simulation cannot do
Monte Carlo simulation is a powerful tool. It is also a model, and every model has limits worth naming.
The outputs are only as good as the estimates that go in. If your probability and impact ranges are optimistic, the distribution will be optimistic. If your register is missing significant risks, the simulation will not invent them. 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 at the same time as a schedule delay and a cost overrun, not as three separate events. Risk Companion's simulation captures the compounding effect across the full register, but it does not model explicit correlation between individual risks. For most SME and mid-market projects, that is a reasonable simplification. For very large programmes with complex interdependencies, it is a limitation worth knowing.
None of that undermines the core value. A distribution built on honest estimates, reviewed by a team that knows the project, is a far better basis for contingency decisions than a single number picked in a room. The simulation does not replace judgement. It gives judgement better raw material to work with.
Putting it to work
Probabilistic analysis in Risk Companion is not a feature for specialists. Any project team that has a risk register with probability and impact assessments already has most of what the simulation needs. 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 P95 look like in practice with your own project's risks, Risk Companion's free 14-day trial builds a demo project from your organisation's profile, so you can run the simulation and read the S-curve for yourself before you commit to anything. No credit card needed. Start at risk-companion.com.
Ready to improve your risk management?
See how Risk Companion can help you implement these best practices with powerful, easy-to-use tools. Sign up and we'll prepare a demo project tailored to your company.