P-values sound technical, but the idea is simple: a P50 budget has a 50% chance of being enough, a P90 budget a 90% chance. This page explains how to read those numbers off the S-curve, why the gap between them is the contingency, why the “average” is not the 50/50 figure, and which P-value each Australian framework actually funds at.
A P-value (the “P” is for percentile) is a cost paired with a probability that it will not be exceeded. A P50 estimate is the cost that has a 50% chance of being enough; a P90 estimate is the cost that has a 90% chance of being enough. The number is meaningless on its own — “the project will cost $118M” says nothing — but attach a confidence level — “$118M at P90” — and it becomes a statement a funding body can act on.
P-values exist because a cost estimate is a forecast under uncertainty, not a measurement. A Monte Carlo simulation rolls the uncertainty thousands of times and produces a whole distribution of possible outcomes. P-values are simply the way we name specific points on that distribution so two people can talk about the same level of confidence.
50% probability of not being exceeded. The actual cost is equally likely to land above or below it. This is the median outcome.
90% probability of not being exceeded. Only a 1-in-10 chance the project costs more than this. The number a funder relies on.
Intermediate confidence levels used at contract award — P75 in TMR, P60 in Victoria — once the estimate is sharper than at business case.
The single most important sentence on this page: a P-value is a probability of not exceeding a cost, not the cost of a specific scenario. P90 does not mean “the worst case” — it means a budget you would beat 9 times out of 10. The true worst case sits further out in the tail beyond P90.
Every P-value is just a point read off one chart: the cumulative probability curve, or S-curve, that a Monte Carlo run produces. Learn to read it once and every confidence level makes sense.
The S-curve plots, on the vertical axis, the probability that the project cost will not exceed a given value shown on the horizontal axis. It runs from 0% at the bottom-left (no budget is enough) to 100% at the top-right (any budget this large is certainly enough), and its characteristic stretched-S shape comes from the costs clustering around the middle and thinning out into the tails.
There are two ways to read it. Read across from a confidence level — pick 90% on the vertical axis, trace right to the curve, drop down to the cost — and you have your P90 budget. Or read up from a cost — trace a candidate budget up to the curve, across to the axis — and you have the confidence that budget buys.
Probability of not exceeding on the vertical axis; project cost on the horizontal. P50 reads off at the 50% line, P90 at the 90% line. The shaded band between them is the risk-based contingency.
Choose a confidence on the vertical axis, trace right to the curve, then drop to the cost axis. 90% confidence here lands on a $118M P90 budget.
Trace a candidate budget up to the curve and across to the axis to find the confidence it buys — useful for testing whether a fixed allocation is adequate.
The curve is steepest near the median (small budget changes buy a lot of confidence) and flattens past P90 (each extra dollar buys very little — chasing P99 is rarely worth it).
P50 and P90 are not two rival budgets. They are the base-plus-expected-cost figure and the high-confidence figure — and the money between them is, precisely, the risk-based contingency.
At the median, the project is as likely to come in under as over. It carries enough contingency for the “swings and roundabouts” to net out — the realistic central case, not a stretch target.
Used for: budget-setting, internal planning, and the baseline a project manager controls to.
At 90% confidence, the budget covers all but the most adverse 10% of outcomes. It is the figure a funding body holds to represent the project’s realistic total exposure.
Used for: funding approval, business cases, and the upper provision a portfolio holds against the project.
P90 − P50 = risk-based contingency
This is why probabilistic estimating beats a flat percentage. You do not assume a contingency — it falls out of the analysis as the distance on the cost axis between the P50 and the P90, traceable to specific modelled risks. In the S-curve above, a $100M P50 and a $118M P90 imply an $18M (18%) contingency — derived, not guessed, and re-runnable for a reviewer.
“Should we fund at P50 or P90?” is the wrong question if it implies choosing one number to the exclusion of the other. The frameworks report both: the P50 sets the controllable baseline, the P90 sizes the held reserve, and governance decides who holds the gap between them. The decision is about where the contingency sits, not which single figure to publish.
Almost everyone assumes the “average” cost is the 50/50 figure. On a real project cost distribution it is not — and the difference matters at a funding gate.
Cost distributions are right-skewed: there is a hard floor (a project can only be built so cheaply) but a long tail of expensive outcomes (a latent-condition claim, a market spike, a major rework). That long upper tail drags the mean (the arithmetic average) to the right of the median (the P50). RES notes that in energy and transport projects the mean — what RES calls the Central Estimate — typically sits around P30–P40, below the median.
The practical consequence: if someone funds a project at “the average” believing it is the 50/50 point, they have actually funded somewhere around a P30–P40 — a budget that will be exceeded 60–70% of the time. The 50/50 figure is the P50 median, and it is higher than the mean.
On a right-skewed cost density, the most-likely value (MODE) is the peak, the average (MEAN) sits to its right at roughly P30–P40, the 50/50 figure (P50, the MEDIAN) is higher still, and P90 sits well into the tail. The “average” is not the coin-flip.
The long right tail pulls the mean above the mode, yet by probability rank the mean still sits below the median — RES places it at roughly P30–P40. Funding “the average” therefore under-funds the project.
The median splits the distribution into two equally-likely halves by outcome count. If you want a budget that is as likely to be over as under, that is the P50 — never the mean or the mode.
It is a recurring review failure to present a “Central Estimate” (the mean) as if it were the 50/50 budget. State it explicitly: the mean sits at ~P30–P40, the median is the P50, and the funded figure is whichever P-value the framework requires.
All the major Australian frameworks report P50 and P90 — but they fund, approve and reset at different points. Here is where each one sits on a common probability axis.
A shared 0–100% confidence axis. Each row marks the P-values a framework uses: TMR (P50 budget, P75 at award, P90 mandated), DITRDCA (P50 approval, P90 held), RES (P50 to PMB, P90 to Management Reserve), and Victoria (P60 at award, P90 approval).
No framework funds at a single secret percentile. Each reports a lower figure (P50, or P60 for VIC) and the P90, and governs who holds the gap between them.
TMR locks an Approved Project Delivery Value at P75 at tender award; Victoria resets to P60 at contract award. Once the estimate is sharper, the held confidence steps down and the saving returns to the program.
P50 for budget-setting, with the project manager holding contingency to P50. P90 is mandated for all estimates beyond the business-case milestone — the total out-turn cost. The P90−P50 gap is held at portfolio level. At tender award, an Approved Project Delivery Value is set at P75; the saving (business-case P90 − tender P75) returns to the program.
TMR risk & contingency →Funding approval decisions are made on validated P50 out-turn cost, re-escalated each phase. P90 is notionally held against the project to represent the funder’s total exposure and released to jurisdictions only on a demonstrated-needs basis. Both are reported — a $100M base tags to a P50 $115M / P90 $140M project estimate in the guidance’s own worked example.
DITRDCA cost estimation →RES pairs P50 with the Performance Measurement Baseline and P90 with a Management Reserve held at a higher delegation — the chosen level a function of organisational risk appetite. Across jurisdictions the pattern holds: Victoria approves at P90 and resets to P60 at award; NSW, SA and WA all report P50 & P90.
RES contingency guideline →The frameworks differ on where the contingency sits and when confidence steps down, not on the method that produces the numbers. See them lined up in full in Frameworks Compared, or read how the underlying simulation generates these P-values in The Monte Carlo Method.
Each of these surfaces routinely in independent review. Avoiding them is most of what makes a P50/P90 defensible.
P90 is a budget you beat 9 times in 10 — not the maximum possible cost. The true worst case lives in the tail beyond P90; do not present P90 as a ceiling that “cannot” be exceeded.
The mean (Central Estimate) sits at roughly P30–P40, not P50. Fund at the average believing it is the coin-flip and you have under-budgeted by a full confidence band.
P50 and P90 are points on one curve, not two separate provisions to stack. The P90 already contains the P50 contingency plus more — the additional amount is P90−P50.
A P90 in real dollars is not comparable to a P90 in out-turn dollars. Always state whether a P-value is on the base estimate, the project estimate, or the escalated out-turn cost.
“That’s our P90” means nothing without the simulation behind it. A defensible P-value is re-runnable, traceable to ranged line items and a dollarised risk register, with correlation modelled.
The S-curve flattens past P90 — each extra point of confidence costs disproportionately more for negligible risk reduction. Frameworks stop at P90 for good reason; P99 budgets are rarely defensible.
If the distance between the P10 and P90 outcomes is implausibly narrow, the model has almost certainly understated uncertainty — ranges too tight, correlation ignored, or contingent risks missing. DITRDCA explicitly flags narrow spreads with thin tails as a sign of an unrealistic model. A credible P90 needs a credible spread behind it.
A P50 or P90 is only as good as the model behind it. Cenex produces the figure and the evidence pack that lets it survive an independent Commonwealth or TMR review.
@RISK at 5,000–10,000 iterations producing the S-curve, histogram and tornado — with P5–P95 reported at 5% intervals where the framework (e.g. TMR) requires it.
We report the Central Estimate (mean, ~P30–P40), the P50 median and the P90 side by side — so no reviewer can mistake the average for the 50/50 figure.
P50 budget and P90 out-turn for TMR with P75 at award; P50 approval and held-P90 for DITRDCA; P50 PMB and P90 reserve for RES; P60 award where Victoria applies.
With no downstream delivery interest, the P90 is sized to genuine residual risk, cross-checked with reference-class forecasting, and signed off by a Chartered Engineer with re-runnable model files.
Start with the Introduction, learn how the numbers are generated in The Monte Carlo Method, see the independent cross-check in Reference Class Forecasting, then read the framework pages — TMR, RES, DITRDCA — or see them compared side by side. Return to the hub overview any time. For the engagement view, see Risk Modelling & Management.
Tell us the framework your project is funded under — TMR, Commonwealth / DITRDCA, or a state mandate — and Cenex will build the probabilistic model and report the P-values it requires, with the evidence to back them.