Reference class forecasting (RCF) counters systematic cost underestimation in megaprojects by replacing a single project's bottom-up estimate with the distribution of cost outcomes from a class of comparable completed projects. Its accuracy hinges on the reference class being both large enough for stable statistical estimation and comparable enough - in technical scope and geography - that the pooled overrun distribution applies to the project at hand. For project types of which few or no realized instances exist, such as deeply tunnelled railway megaprojects like Stuttgart 21 or first-of-a-kind energy plants, these two requirements conflict: broad classes pool non-comparable projects, while narrow classes lack the observations needed for statistical smoothing. The problem was posed by the Stuttgart 21 study (Steininger, Groth and Weber, 2020) and is identified as an unresolved centerpiece of the research agenda by the most recent reviews (Baerenbold, 2023; Cantarelli, Davis, Pinto and Turner, 2025). The open problem is a validated, empirically grounded procedure for constructing reference classes under scarcity of comparables, together with explicit guidance on the breadth-versus-sample-size trade-off.

Background

Large infrastructure projects - megaprojects, conventionally those above roughly US$1 billion in investment - finish late and over budget with striking regularity. A landmark study of 258 transportation infrastructure projects worth about US$90 billion found the cost estimates used to justify such projects to be highly and systematically misleading: actual costs exceeded estimates in most cases, and the underestimation was better explained by strategic misrepresentation - deliberately favorable numbers produced under incentives to win approval - than by honest error (Flyvbjerg, Skamris Holm and Buhl, 2002). A companion behavioral explanation is optimism bias, the planning fallacy's tendency to underestimate cost and duration.

Reference class forecasting (RCF) is the standard corrective. Rooted in the 'outside view' from behavioral decision research - predicting an outcome from the distribution of similar past cases rather than from the specifics of the case at hand - and brought into project management by Flyvbjerg (2006, 2008), RCF proceeds in three steps: (1) identify a reference class of comparable completed projects; (2) obtain the empirical distribution of a performance measure, typically cost overrun relative to the estimate at the decision point, over that class; and (3) use a chosen percentile of that distribution as the uplift, i.e. the contingency added to the new project's estimate so that, for example, the budget has an 80% probability of not being exceeded. RCF has entered appraisal practice - the United Kingdom mandated it for major projects from 2003, and a before-and-after comparison of 107 projects found average overruns falling from 38% to 5% after its introduction (Park, 2021) - and it has been extended across sectors, from hydroelectric dams (Ansar, Flyvbjerg, Budzier and Lunn, 2014) to offshore oil and gas (Natarajan, 2022).

The method's weak point is the reference class itself. Steininger, Groth and Weber (2020) applied RCF to Stuttgart 21 - one of the largest German railway projects of the past century, with extensive tunnelling - and found its currently estimated costs inside the 95% interval implied by a reference class of comparable rail projects; their central stated limitation is 'the low number of comparable projects which are available'. The difficulty is structural, not incidental. Estimating an uplift distribution needs enough observations; comparability requires restricting the class by project type, technical characteristics, geography, and era - and each restriction removes observations. A broad class ('all road projects') is large but heterogeneous; a narrow class ('underground rail projects in comparable geology, built in the same decade in Western Europe') may contain a handful of projects or none. For rare project types - nuclear plants, fusion facilities (Brown, Lux and Cowan, 2024) - a sufficient sample may be unattainable in principle. Empirical work confirms both horns of the dilemma: RCF outperforms conventional methods only when the project at hand is sufficiently similar to the class members (Batselier and Vanhoucke, 2016), and although considering more similarity properties when forming the class improves forecast accuracy, it shrinks the class until statistical reliability is lost (Servranckx, Vanhoucke and Aouam, 2021). Partial methodological responses to the scarcity problem have been proposed - weighting class members by similarity to overcome unavailable reference data (Zani and Adey, 2025), pooling cost deviations at work-package level (Zani, Adey and Carroll, 2024), hierarchical or Bayesian borrowing of strength across classes, or partial pooling, in which a small class's estimate is stabilized by information from related, larger classes (Bordley, 2014), and analogical classes matched on novelty and complexity for first-of-a-kind technologies (Brown, Lux and Cowan, 2024) - but none has been validated as a general construction procedure for scarce classes. Whether megaprojects can legitimately be treated as exchangeable draws - statistically interchangeable outcomes of a common generating process - is itself contested (Ika, Love and Pinto, 2022).

Problem Statement

How should reference classes for reference class forecasting be constructed when the population of genuinely comparable projects is small or empty - the question stated by Steininger, Groth and Weber (2020) and still identified as unresolved by the 2023 and 2025 reviews?

Given a target megaproject whose type has few realized instances (motivating case: large rail projects with extensive tunnelling, such as Stuttgart 21) or none at all (first-of-a-kind facilities such as fusion power plants), the required deliverable is one coherent scientific objective: a defensible, empirically validated way to assemble the reference sample, such that the uplift distribution derived from it applies to the target project. Three linked requirements jointly define completion.

  1. Comparability: criteria - technical characteristics, geography, era, institutional setting - determining which completed projects enter the class, or with what weights, so that their overrun distribution is informative for the target project rather than for a different population.

  2. Sufficiency: how large the effective sample must be for the chosen percentile of the overrun distribution (the uplift) to be statistically stable, and what to do when no attainable class meets that threshold.

  3. Validation: out-of-sample evidence that classes constructed by the procedure yield calibrated uplifts - prediction intervals with approximately their nominal coverage - in the scarce-comparable regime that defines the problem, together with practical guidance on the breadth-versus-sample-size trade-off.

The construction procedure and its validation are parts of one answer: a demonstration confined to data-rich mainstream classes (for example ordinary road projects) does not address the problem, and neither does an unvalidated weighting scheme regardless of its theoretical appeal.

References

  1. Steininger, Bertram I., Groth, Martin, Weber, Brigitte L. (2020). Cost overruns and delays in infrastructure projects: the case of Stuttgart 21. Journal of Property Investment & Finance 39(3), 256-282. DOI: 10.1108/jpif-11-2019-0144. https://doi.org/10.1108/jpif-11-2019-0144
  2. Flyvbjerg, Bent, Skamris Holm, Mette, Buhl, Soren (2002). Underestimating Costs in Public Works Projects: Error or Lie? Journal of the American Planning Association 68(3), 279-295. DOI: 10.1080/01944360208976273. https://doi.org/10.1080/01944360208976273
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  13. Brown, Chris, Lux, Hanni, Cowan, James R. (2024). Reference Class Forecasting and Its Application to Fusion Power Plant Cost Estimates. IEEE Transactions on Plasma Science 52(9), 3628-3633. DOI: 10.1109/TPS.2024.3405631. https://doi.org/10.1109/TPS.2024.3405631
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