Your capex scenario wrong - AI knows it...

The 10% contingency assumption is statistically indefensible

Thirty years of empirical data on capital project performance reveals a distribution of outcomes that renders standard project finance contingency practice not merely conservative - but mathematically inconsistent with the evidence.

Executive summary - if you really don’t have time to read…..

Project finance practitioners routinely apply capex contingencies of 5% to 15% to construction cost estimates at Financial Investment Decision (FID). The implicit assumption is that these contingencies provide meaningful downside protection.

The empirical record contradicts this assumption. Ooops.

A review of peer-reviewed research spanning more than 16,000 projects across 136 countries and seven decades demonstrates three findings that directly challenge standard practice:

1. Capex overrun distributions are right-skewed with heavy tails - not normally distributed. The best-fit statistical models are lognormal and gamma distributions. This means the expected outcome materially exceeds the median, and the probability of severe overruns (>50%) is orders of magnitude higher than normal distribution assumptions imply. In plain English it’s either on the money or f*cked.

2. A 10% contingency provides below-median protection in every major infrastructure asset class studied. Across transport, energy, and industrial megaprojects, a 10% contingency positions a project at approximately the 25th to 40th percentile of the reference class distribution - below P50 in all cases.

3. Cost and schedule overruns are positively correlated and produce compounding financial effects- through interest during construction (IDC) that linear modelling cannot capture. A 40% schedule extension does not produce a 40% increase in financing costs - it produces a disproportionately larger impact due to compounding - savage.

The implications for lenders, sponsors, and financial modellers are significant. Models built on a 10% contingency assumption are not conservative base cases. They are optimistic scenarios with conservative-looking presentation.

The evidence base (skip this bit if you just want the good oil)

The empirical foundation for this analysis draws on five primary bodies of research conducted over the past three decades.

Flyvbjerg et al. (2002-2023), Oxford University and IT University of Copenhagen. The most comprehensive longitudinal study of project cost performance in existence, now encompassing more than 16,000 projects across 136 countries and 20+ project types. Core infrastructure findings published in the Journal of the American Planning Association, Transport Reviews, and synthesised in How Big Things Get Done (2023). Key finding: 91.5% of projects are over budget, over schedule, or both. Less than 1% deliver on time, on budget, and at promised scope.

Merrow, E.W. (2011), Independent Project Analysis (IPA). Industrial Megaprojects: Concepts, Strategies, and Practices for Success. Dataset of 318 commercial industrial megaprojects across oil and gas, chemicals, LNG, minerals, pipelines, and power generation. The most rigorous proprietary dataset on private-sector capital project performance globally.

Sovacool, Gilbert & Nugent (2014), Vermont Law School / Aarhus University. Analysis of 401 electricity infrastructure projects built between 1936 and 2014 across 57 countries, representing approximately $820 billion in aggregate investment. Published in Energy and The Electricity Journal.

Ansar, Flyvbjerg, Budzier & Lunn (2014), Oxford University. 245 hydropower projects globally. Published in Energy Policy.

Callegari, Szklo & Schaeffer (2018), Federal University of Rio de Janeiro. Probabilistic distribution fitting for energy megaproject cost and schedule overruns. Published in Energy Policy.

The breadth and consistency of findings across these independent datasets - spanning different methodologies, geographies, time periods, and asset classes - is itself statistically significant. The convergence on similar structural conclusions is not coincidental.

Finding 1: The distribution is wrong

RIP the normal distribution assumption

Standard project finance models treat construction cost risk using symmetric distributions - triangular, PERT, or implicitly normal - centred on the base estimate with modest variance. Sensitivity analysis typically varies capex +/- 10% to 20% and presents the outcomes as bounding cases.

This modelling approach is inconsistent with the empirical distribution of outcomes.

What the data shows

Multiple independent studies identify the best-fit distributions for capex overruns as lognormal or gamma - both right-skewed distributions with heavier right tails than a normal distribution.

For a lognormal distribution X ~ LN(μ, σ²), the relationship between mean and median is:

E[X] = e^(μ + σ²/2)
Median[X] = e^μ

The ratio E[X] / Median[X] = e^(σ²/2) exceeds 1 for all σ > 0, and grows rapidly as variance increases. In practical terms: a project modelled at P50 has a negative expected value when the underlying distribution is lognormal with realistic variance parameters. The expected outcome is above the median by a margin that increases with uncertainty.

Callegari et al. (2018) tested multiple distribution fits for energy megaproject overruns and found gamma distribution provided the best fit for cost overruns, and lognormal for schedule delays. Neither approximates normal.

Budzier and Flyvbjerg (2011) demonstrated that the tail behaviour of cost overrun distributions follows a power law:

P(X > x) ~ x^(-α)

With estimated exponent α ≈ 2.3 for the datasets studied. A power-law tail with α < 3 implies infinite variance - meaning no amount of historical data can reliably bound the upside risk. This is not a modelling artefact. It reflects the structural reality of complex, interconnected project systems where failure propagates non-linearly.

Practical implication

A financial model using a symmetric ±15% capex sensitivity is not capturing the actual risk space. It is capturing a narrow band around the centre of a distribution whose right tail extends significantly further. The P90 outcome in most infrastructure asset classes is not “base case + 15%.” It is “base case + 50% to 100%.”

Finding 2: The reference class data by sector

The following summarises mean cost overruns by asset class from the primary empirical literature. All figures are in real (inflation-adjusted) terms unless otherwise noted.

1. Transport infrastructure

Source: Flyvbjerg et al. (2002-2008), N = 258 projects, 20 countries, 70-year span.

The coefficient of variation (CV = σ/μ) for rail projects exceeds 0.5, indicating extreme dispersion. At P80, Flyvbjerg’s reference class forecasting framework requires uplifts of approximately 44% for roads and 65-80% for rail. A 10% contingency provides below-P40 protection for roads and below-P30 protection for rail.

Critically, Flyvbjerg et al. (2005) found no improvement in forecast accuracy over time and no significant geographic variation. This is not a developing-market problem or a historical artefact. It is a structural feature of how large infrastructure projects are estimated and delivered.

2. Electricity infrastructure

Source: Sovacool et al. (2014), N = 401 projects, 57 countries, 1936-2014.

Solar PV overruns were offset by panel price declines during the study period; CSP showed higher overruns.

Aggregate finding: costs were underestimated in 75% of the 401 projects. Total overruns across the sample reached $388 billion against $820 billion invested - a mean cost escalation of 66.3% per project. Only 39 of 401 projects experienced neither overrun nor underrun.

The financial implication is direct: for every dollar of base case capex modelled in this reference class, the expected outturn was approximately $1.66. A 10% contingency produces a funded position of $1.10 - a structural shortfall of $0.56 per dollar of base case investment, on average.

3. Hydropower (dedicated analysis)

Source: Ansar et al. (2014), N = 245 projects.

• Mean cost overrun: 96%
• Mean schedule overrun: 44%

4. Industrial megaprojects (oil, gas, chemicals, LNG)

Source: Merrow / IPA (2011), N = 318 projects.

• 65% of all industrial megaprojects qualify as failures (threshold: >25% cost overrun, >25% schedule slip, or significant production shortfall in first two years)
• For upstream oil and gas specifically: 78% failure rate
• Mean cost overrun for failing projects: 33% in real terms
• Mean execution schedule slip: 30%
• Only 22% of oil and gas megaprojects delivered successfully on all performance dimensions.

The IPA data also identifies a critical non-linearity between Front-End Loading (FEL) quality and cost outcomes. As FEL degrades from Good to Poor, cost growth accelerates sharply and non-linearly. Poor front-end definition does not produce proportionally worse outcomes - it produces disproportionately catastrophic outcomes. This is a structural feature of complex project systems, not a management failure at the margin.

Finding 3: Schedule overruns compound the financial impact

The correlation

Cost and schedule overruns are not independent variables. They are positively correlated in every major dataset studied.

Flyvbjerg et al. (2004) quantified the relationship: on average, a one-year delay correlates with a 4.64% increase in percentage cost overrun, holding other factors constant. The mechanism is direct: labour cost escalation, equipment re-mobilisation, redesign costs, and material price changes during extended construction periods all translate delay directly into cost.

Schedule data by asset class:

Source: Sovacool et al. (2014); Callegari et al. (2018).

The IDC compounding effect

The financial modelling implication of schedule overruns is non-linear and routinely underestimated.

For a project with $1 billion in base case capex drawn evenly over a 5-year construction period at 7% financing cost, the approximate IDC at scheduled completion is $175 million.

Under a 40% schedule extension (to 7 years), IDC does not increase by 40% to $245 million. Because later draws compound for longer periods under an extended schedule, total financing costs scale non-linearly with draw period length. The actual additional financing cost under a 40% schedule extension approaches $100-150 million on a $1 billion project - equivalent to an additional 10-15% of base case capex from schedule alone.

A 10% capex contingency absorbs none of this.

Furthermore, because cost and schedule overruns are positively correlated, the scenarios in which capex exceeds budget are the same scenarios in which IDC also exceeds budget. The risks are not diversifiable within a single project. They co-move in the direction that is most damaging to debt service coverage.

The bimodal structure of project outcomes

One of the most practically important - and least discussed - features of the empirical data is that project outcomes do not distribute smoothly from “a little over budget” to “a lot over budget.”

The IPA dataset and Flyvbjerg’s infrastructure data both suggest a pattern closer to bimodal: projects either deliver within a reasonable range of the base estimate, or they fail in a manner that is severe and multi-dimensional (simultaneously over budget, over schedule, and below operational targets). The mid-range outcomes - 10-20% over budget, slightly delayed, otherwise functional - are statistically underrepresented relative to what a smooth distribution would predict.

The structural explanation is that capital projects are complex adaptive systems. When a disturbance occurs (geological surprise, permitting delay, contractor insolvency, equipment delivery failure, design error), it propagates through interdependencies in a non-linear fashion. A 3-month delay in foundation works does not produce a 3-month schedule extension. It triggers redesign, equipment resequencing, labour cost escalation, IDC accrual, subcontractor schedule disruption, and frequently further delays. The system fails systemically, not incrementally.

This has a direct modelling implication: Monte Carlo simulations that use smooth, independent input distributions for cost and schedule will understate the probability of severe, correlated outcomes. The tail behaviour of project outcomes is driven by systemic failure modes that are not captured by marginal variance in individual cost line items.

Implications for financial model construction

A financial model that accurately represents construction cost risk should incorporate the following:

1. Right-skewed input distributions. Capex uncertainty should be modelled using lognormal or gamma distributions, calibrated against the relevant reference class, not internal engineering estimates alone. The parameters should produce a distribution where E[Cost] > Median[Cost] by a margin consistent with the reference class data.
2. Correlated cost and schedule simulation. Cost and schedule overruns should be simulated jointly with a positive correlation coefficient (r = 0.4 to 0.7 is consistent with empirical data). Independent simulation understates tail risk.
3. Non-linear IDC modelling under delay scenarios. IDC should be recalculated as a function of the actual draw profile under each simulated schedule, not as a fixed percentage uplift. The compounding effect of extended draw periods is material.
4. P50/P80/P90 reporting as standard. The base case should be presented alongside P50, P80, and P90 outcomes from the simulation. For most infrastructure asset classes, the base case approximates P35-P40, not P50. Presenting it as the expected outcome is misleading.
5. Debt sizing against P80, not base case. If P80 capex is 50% above base case, debt sized to 70% of base case capex is effectively sized to 47% of P80 capex. This is not the leverage level lenders believe they are underwriting.
6. Reference class uplift as a validation check. Internal engineering estimates should be benchmarked against the reference class. If the internal estimate for a hydropower project implies a 15% contingency is sufficient, and the reference class median overrun is 71%, the internal estimate requires explanation - not acceptance.

Conclusion

The empirical literature on capital project performance presents a consistent and mathematically precise finding: standard project finance contingency practice is not calibrated to the actual distribution of outcomes.

The 10% contingency is not an industry standard in the sense of representing best practice. It is an industry norm in the sense that it is widely used. Those are different things.

A 10% contingency provides below-median protection in every major infrastructure asset class studied in the peer-reviewed literature. It provides below-P40 protection in transport infrastructure, below-P30 protection in energy infrastructure, and below-P25 protection in hydropower and nuclear. It provides no protection against the IDC compounding effect of schedule overruns, which can add a further 10-15% of base capex on large projects with 30-40% schedule extensions.

The financial models used at FID to justify investment decisions are, in the majority of cases, systematically optimistic. Not through error or bad faith, but through a structural failure to incorporate what the reference class data - now encompassing tens of thousands of projects and decades of evidence - actually shows.

Correcting this requires three changes: reference class calibration of input distributions, joint simulation of correlated cost and schedule risks, and reporting of P80/P90 outcomes as the primary decision metric for lenders and equity providers.

Until these changes are made, the 10% contingency line will continue to do what it has always done: provide the appearance of prudence while transferring unacknowledged risk to debt.

References

• Flyvbjerg, B., Skamris Holm, M.K., & Buhl, S.L. (2002). Underestimating costs in public works projects: Error or lie? Journal of the American Planning Association, 68(3), 279-295.
• Flyvbjerg, B., Skamris Holm, M.K., & Buhl, S.L. (2004). What causes cost overrun in transport infrastructure projects? Transport Reviews, 24(1), 3-18.
• Flyvbjerg, B., & COWI (2004). Procedures for dealing with optimism bias in transport planning. UK Department for Transport.
• Flyvbjerg, B. (2008). Curbing optimism bias and strategic misrepresentation in planning: Reference class forecasting in practice. European Planning Studies, 16(1), 3-21.
• Merrow, E.W. (2011). Industrial Megaprojects: Concepts, Strategies, and Practices for Success. John Wiley & Sons.
• Ansar, A., Flyvbjerg, B., Budzier, A., & Lunn, D. (2014). Should we build more large dams? Energy Policy, 69, 43-56.
• Sovacool, B.K., Nugent, D., & Gilbert, A. (2014). Construction cost overruns and electricity infrastructure: An unavoidable risk? The Electricity Journal, 27(4), 112-120.
• Sovacool, B.K., Gilbert, A., & Nugent, D. (2014). Risk, innovation, electricity infrastructure and construction cost overruns: Testing six hypotheses. Energy, 74, 906-917.
• Callegari, C., Szklo, A., & Schaeffer, R. (2018). Cost overruns and delays in energy megaprojects: How big is big enough? Energy Policy, 114, 211-220.
• Budzier, A., & Flyvbjerg, B. (2011). Double whammy: How ICT projects are fooled by randomness and screwed by political intent. Saïd Business School Working Papers.
• Kahneman, D. (2011). Thinking, Fast and Slow. Macmillan.
• Flyvbjerg, B., & Gardner, D. (2023). How Big Things Get Done. Macmillan.

First published on Nick Crawley’s Substack.