Industry: Real Estate Product: ModelRisk Application: Urban Sprawl Analysis
A metropolitan planning organization had to service 12,000 new dwellings and two ways to do it: a compact plan (infill near the existing service edge, high density) or a sprawl plan (low-density, leapfrog parcels further out). The servicing bill — roads, water and sewer trunk, transit, schools — depends on how far the dwellings sit from the existing network and how densely they are packed. A single deterministic comparison put the sprawl premium at 71%. The Monte Carlo, propagating the real uncertainty in distance, density, the leapfrog share and the cost gradient, put the mean premium at 48%, with an 80% band of 29% to 68% and a 95% probability the sprawl plan costs at least 25% more than compact. Both numbers say sprawl is dearer — but the distribution says how confidently, and it reveals that the headline deterministic figure overstates the typical outcome.
ModelRisk was used to turn "sprawl costs more" into "the distribution of the per-dwelling servicing premium, and the probability it exceeds a planning threshold."
The deterministic comparison multiplies one distance assumption by one density assumption by one leapfrog share by one cost gradient. Because the per-dwelling cost is a product of these factors, stacking each at its modal value compounds them into a premium that lands high — the 71% point estimate sits above the simulated 90th percentile. The realised premium is lower and more variable than the point figure suggests, because the factors do not all line up at their pessimistic values at once. A point estimate cannot show that the premium is high and uncertain, nor can it answer the planning question that actually matters: how likely is the premium to clear the threshold that triggers a compact-development mandate?
Each dwelling's servicing cost starts from a base of $38,000 at the network edge and is scaled by three physical effects: a distance term (trunk extension cost rising with kilometres from the edge), a density term (fewer dwellings per hectare means more linear feet of infrastructure per home), and a leapfrog penalty (scattered parcels each needing their own extension). The compact plan draws short distances (mean 1.8 km) and high density (mean 34 dwellings/ha); the sprawl plan draws long, variable distances (mean 8.5 km) and low density (mean 18 dwellings/ha) with a much larger leapfrog share.
Crucially, a single regional construction-cost environment multiplies both plans' unit costs together. Without it, two sums of 12,000 lot costs would each collapse to a narrow Normal (the central-limit effect), making the premium look spuriously precise. The shared factor keeps both totals genuinely uncertain while the systematic distance-and-density gap produces the premium. The model confirmed the structure: compact and sprawl total costs are positively correlated (correlation 0.83) through the shared environment; within the sprawl plan, per-dwelling cost rises with distance (rank correlation 0.26) and falls with density (rank correlation -0.30), both with the expected sign.
The mean sprawl premium is 48%, with a median of 46% and an 80% band running from 29% to 68%. The probability the sprawl plan costs more than 25% above compact is 95%; the probability it costs more than 50% above is 40%. The deterministic point estimate of 71% sits above the 90th percentile — a planner anchored on it would over-state the typical penalty while paradoxically under-appreciating how often the premium still lands in the merely-expensive 30–50% range.
Laid side by side, the compact plan averages $457M (P10 $365M, P90 $556M) and the sprawl plan averages $674M (P10 $519M, P90 $847M). The mean extra cost of choosing sprawl to house the same 12,000 dwellings is $217M. The two cumulative curves barely overlap — even a lucky sprawl outcome rarely beats an unlucky compact one, which is what makes the premium so robustly positive.
Against a mean premium of 48%, sprawl development density moves the premium by about ±8.5 percentage points and lot distance from the network by about ±7.6 points — the two physical geometry levers dominate. The leapfrog share (±5.3 pp), the distance cost gradient (±4.7 pp) and the leapfrog penalty (±4.2 pp) follow. The regional cost environment barely moves the premium (±0.03 pp) — because it hits both plans equally, it cancels in the ratio, which is exactly why the shared factor belongs in the model: it inflates each plan's total uncertainty without contaminating the comparison.
The costliest sprawl trials live in one corner: parcels both far from the network (over 11 km) and at low density (under 14 dwellings/ha). That corner occurs in 3.5% of trials. Because distance and density were drawn independently here, the joint probability equals the product of the marginals — the model does not manufacture a correlation that is not there. The median sprawl dwelling costs about $55,000 to service against $37,600 for the median compact dwelling, and the far-low-density tail is where the worst overruns concentrate.
The MPO adopted a compact-development mandate triggered on the probabilistic finding rather than the point estimate: with a 95% chance the sprawl premium exceeds 25% and a mean extra cost of $217M to service the same housing, the case for infill no longer rested on a single contestable number. Density and network-distance targets — the two dominant drivers — were written into the zoning standard, and the regional cost environment was excluded from the decision because it washes out of the comparison.
For a compact-versus-sprawl decision, a single premium figure is the wrong deliverable. Monte Carlo turns "sprawl costs more" into "the premium distribution and the probability it clears the threshold that triggers policy" — which is the question a planning mandate actually has to answer.