Industry: Retail Product: ModelRisk Application: Marketing campaigns
A retail marketing team was about to greenlight a $1.2M, six-week media burst. The planning deck showed a clean, confident number: 3.3x return on ad spend (ROAS), a +38% campaign ROI — comfortably above the finance team's 3.0x hurdle. Sign here.
The deck was built the way most campaign forecasts are: point estimates multiplied down a funnel — budget into reach, reach into response, response into conversions, conversions into revenue — with one quietly fatal omission. It counted every measured conversion as caused by the campaign. In reality a large share of those buyers would have purchased anyway; that organic baseline is the difference between a campaign that moves revenue and one that merely takes credit for it. When the ModelRisk rebuild put the incrementality haircut back in, alongside honest uncertainty on every funnel stage, the picture inverted. Mean ROAS fell to 1.99x — below the 2.38x needed to cover the spend at a 42% margin — and the probability the campaign earns a positive ROI dropped to 26.3%.
A funnel forecast is a product of five uncertain fractions: cost-per-thousand, unique reach, response rate, conversion rate, and incrementality. Multiplying their averages gives the average of the product only if nothing is skewed and nothing co-moves — and in a campaign everything is skewed and everything co-moves. A soft demand week depresses reach and response together. Auction prices spike right when budgets compete. And incrementality — the single most-omitted input — is not a rounding error; it is a 40-to-60-cents-on-the-dollar haircut applied to the whole revenue line. A deterministic deck cannot show any of this. It returns one number with no probability attached, and that number is almost always the optimistic one, because the omitted incrementality haircut only ever cuts.
The whole case is in the ROAS distribution — incremental revenue divided by spend, across 80,000 simulated campaigns:
The distribution is heavily right-skewed: a long thin tail of blockbuster outcomes drags the mean ROAS to 1.99x, but the median is just 1.23x and the bulk of the mass sits below 2x. The margin-breakeven line is 2.38x (at 42% contribution margin, you need $2.38 of incremental revenue per $1 of spend just to recover the spend), and the finance hurdle is 3.0x. The deterministic deck's 3.30x sits out past the hurdle — but it is a single point with no company behind it. The shaded region shows the headline: P(ROAS below breakeven) = 73.7%. Nearly three campaigns in four, on these assumptions, fail to cover their own cost.
Translate the same simulation into ROI on a contribution-margin basis — incremental margin net of spend, as a percent of spend:
Mean ROI is -16.3% and P(ROI > 0) is only 26.3%. The deterministic deck's +38% sits well to the right of where the real mass lives, marked for contrast. The gap between the two is almost entirely the incrementality haircut: strip it out, as the deck did, and a losing campaign looks like a winner. The right tail is real — some campaigns genuinely return 200%+ — but a 26% chance of clearing zero is not a bet a finance committee approves once it can see the odds.
Because incrementality is both the largest haircut and the least observed input, the team swept it from 30% to 90% and watched the probability of a positive ROI track it:
At the modeled mean incrementality of 55%, P(ROI > 0) is 26%. The campaign's mean margin only breaks even once incrementality reaches 66% — but because the funnel is right-skewed, the mean breaking even is not the same as the median breaking even: to push P(ROI > 0) up to a coin-flip 50% would require incrementality above 90%, which is implausible for a broad-reach burst against an existing customer base. The slope of this line is the argument for spending on a holdout/geo-test before the burst: a measurement that pins incrementality is worth more than the media it informs, because the entire go/no-go decision pivots on it.
A tornado on mean incremental revenue ranks where the uncertainty comes from:
Response rate is the largest mover at +/-$1,092k, followed by conversion rate at +/-$926k and incrementality at +/-$856k — the three mid-funnel fractions dominate, while the market factor (+/-$238k) and the CPM auction price (+/-$125k) are secondary. The reading for the team is twofold: the media-buying levers (CPM) barely matter to the outcome, and the three things worth measuring before committing $1.2M are exactly the three that are hardest to see in a planning deck — response, conversion, and how much of either the campaign actually caused.
A campaign forecast that returns a single ROAS number is not a forecast — it is the optimistic corner of a wide, skewed distribution with the incrementality haircut quietly removed. Here the deck's confident 3.3x was really a 1.99x mean sitting on a 26% chance of profit. Monte Carlo simulation in ModelRisk does not make the campaign better or worse; it makes the actual odds visible before the $1.2M is committed, which is the only point at which the odds can still change the decision.