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Methodology

Stop Defending a Number. Present a Range.

Serre TeamFeb 14, 20268 min read

Key takeaways

  1. 1A single ROI number is either too high (unbelievable) or too low (unjustifiable). A defensible range escapes this trap.
  2. 2A credible range needs just three values anyone can estimate: low, expected, high — no statistics degree required.
  3. 3The expected case from a stress-tested model is more honest than a point estimate because it accounts for how uncertainty compounds across every variable.
  4. 4Three-scenario analysis can't capture variable combinations. Stress-testing the model across many runs explores them all.
  5. 5Leading with the conservative case anchors on a number the buyer can't easily dismiss.

"Sure, your product saves time. But how much time? For us? Really?"

If you've sold into enterprise accounts, you've heard some version of this. It's the attribution question — the moment where the buyer stops evaluating your product's capabilities and starts evaluating your numbers. And it's where most value conversations fall apart.

The problem isn't that your estimate is wrong. It's that any single number you give is either too high (they don't believe it) or too low (it doesn't justify the spend). You're stuck. Defend the number and you sound like a salesperson. Hedge it and you sound uncertain.

There's a better approach: stop presenting a number and start presenting a range — and the model behind it. The technique that produces it is called Monte Carlo simulation, and despite the name, it doesn't require a statistics degree to use or to explain.

How a Range Is Actually Built

The idea is simple: instead of calculating one answer from one set of assumptions, you run the same formula thousands of times — each with slightly different inputs — and look at the spread of results.

In practice, it works like this:

  1. You define a formula: the relationship between your inputs and the output. For example, annual savings = hours saved per week × hourly cost × number of affected employees × 52 weeks. The formula itself is fixed and fully auditable.
  2. For each input, instead of a single value, you give a range: a low estimate, an expected estimate, and a high estimate. Those three points define a simple shape that peaks at your expected value and tapers toward the extremes. — low / expected / high is all you need.
  3. You run the model thousands of times. In each run, every variable is drawn from its own low–expected–high range, and the formula produces one possible outcome.
  4. You sort the results and read off the range. The conservative case is the figure 90% of outcomes beat. The expected case is the middle. The upside is the figure only 10% of outcomes reach.

That's the whole method. The formula is fixed and auditable — same inputs, same result. The uncertainty comes from the explicit low and high bounds you set on each variable — not from any black box.

Why Low / Expected / High Beats a Bell Curve

If you remember anything from statistics class, you probably remember the bell curve. So why a low/expected/high shape instead?

Two reasons. First, it's defined by three values a human can actually estimate: the worst realistic case, the most likely case, and the best realistic case. Ask a customer "what's the low, expected, and high end for this number?" and you get a usable answer. Ask them for a mean and standard deviation and you get a blank stare.

Second, it has hard limits. A bell curve technically extends to infinity in both directions, which means a model can spit out absurd outliers. A low/expected/high shape stays inside the bounds your stakeholders agreed to. Every outcome is defensible because it falls within a range someone explicitly signed off on.

For discovery conversations

The easiest way to get these inputs from a prospect: ask three questions. "What's the absolute floor for this metric — the worst realistic case?" Then "What do you expect it actually is?" Then "What would a really good outcome look like?" That's your low, expected, and high. Done.

A Worked Example

Let's make this concrete. Suppose you're building a value case around a "manual process automation" driver. The formula is straightforward:

Annual Savings = Hours per Week × Hourly Rate × Affected Employees × 52

Your prospect is a mid-market operations team. After discovery, you and the prospect agree on ranges for each variable:

| Variable | Low | Expected | High | |---|---|---|---| | Hours saved per week per employee | 3 | 5 | 7 | | Fully loaded hourly rate | $55 | $65 | $75 | | Number of affected employees | 30 | 45 | 60 |

If you use just the expected values, you get a single point estimate:

5 hours × $65 × 45 employees × 52 weeks = $760,500/year

That's a fine number. But it's also a single number — one the CFO can poke at. "Do we really have 45 people affected? Is it really 5 hours?" Each challenge to any single variable undermines the entire output.

Now stress-test it. After thousands of runs, the sorted results might look like this:

  • Conservative case: $468,000/year
  • Expected case: $731,000/year
  • Upside: $1,080,000/year

Notice that the expected case isn't exactly the same as the point estimate from the expected values. That's correct — the middle of a distribution of products isn't the product of the middles. This is one of the subtle ways a stress-tested range is more honest than a simple three-scenario model.

Why This Beats Best/Worst/Middle

You might be thinking: "I already do a three-scenario analysis. Low case, base case, high case. Same thing." It's not.

A three-scenario model gives you exactly three outcomes. Each one uses a single set of inputs — pessimistic inputs for the low case, expected inputs for the base case, optimistic inputs for the high case. But real outcomes don't work this way. In reality, one variable might come in high while another comes in low. The hourly rate might be closer to $75 while the number of affected employees is closer to 30. Three scenarios can't capture that combination.

Stress-testing explores thousands of combinations. Some runs pair a high hourly rate with a low headcount. Others pair moderate values across the board. The result is a continuous range of outcomes, not three disconnected guesses. That range tells you something three scenarios never can: the probability that the actual outcome falls within any given band.

A three-scenario model says "the base case is $760K." The model says "there's about an 80% chance the actual outcome falls between $468K and $1.08M, with $731K as the middle expectation." One is a claim. The other is a model.

Why CFOs Trust Ranges More Than Point Estimates

Finance teams evaluate risk for a living. When you present a single ROI number, a CFO's trained instinct is to stress-test it. Which assumptions are too aggressive? Where's the hidden optimism? How far does the number drop if one input is wrong?

When you present a range, you've already done that stress testing. The conservative figure is the answer to "what if things don't go as planned?" — and it's right there on the page. You're not defending a number anymore. You're walking through a model together.

This changes the dynamic of the conversation. Instead of the buyer picking apart your assumptions, they're discussing which assumptions they'd adjust. "We think the affected headcount is more like 35-50, not 30-60." That's a collaborative conversation about inputs, not a confrontational one about outputs. And because the formulas are fixed — visible and auditable — the prospect can trace any output back to the assumptions that produced it.

The goal isn't to make a bigger claim. It's to make a defensible one. A range that acknowledges uncertainty is more credible than a point estimate that pretends uncertainty doesn't exist.

How This Works in Practice

Each value driver in a business case has a formula and a set of input variables. Each variable has an expected value and explicit low and high bounds. These bounds are set deliberately. There's no hidden algorithm deciding how uncertain a number should be.

When the model runs, it draws each variable independently from its own range. The formula is evaluated with those drawn values. After thousands of runs, the results are sorted and the conservative, expected, and upside figures are read off. The process is repeatable given the same seed — run it twice with the same inputs and you get the same output.

For a multi-driver business case, each driver is stress-tested and the results are summed per run. This means the total conservative case isn't simply the sum of each driver's conservative case — it accounts for the statistical reality that it's unlikely for every driver to simultaneously hit its worst case. The portfolio effect works in your favor: spreading across multiple value drivers produces a tighter overall range than any single driver alone.

What the Buyer Actually Sees

The buyer doesn't see thousands of rows of data. They see three numbers:

  • The conservative case. "Even in a downside scenario, we expect at least this much value." This is the number the CFO will anchor on. It's the one that needs to clear the hurdle rate on its own.
  • The expected case. "This is the middle outcome across thousands of runs." It carries more weight than a point estimate because it was derived from a range, not picked from a spreadsheet.
  • The upside. "If conditions are favorable, it looks like this." It grounds the buyer's aspirational thinking without asking them to take it on faith.

Crucially, each of these numbers traces back to specific variable ranges. If a buyer questions the expected case, you don't defend the output — you walk through the inputs. "This assumes 3-7 hours per week saved, with 5 as the most likely. Does that match your experience?" The conversation stays collaborative because the model is transparent.

Stop Defending a Number. Present a Range.

The attribution question — "how much value can you actually deliver for us?" — doesn't have a single right answer. Pretending it does is what makes ROI conversations adversarial. The buyer knows your number is a guess. You know your number is a guess. Everyone is performing certainty that doesn't exist.

A range replaces that performance with honesty. It says: "We don't know the exact outcome. Nobody does. But given the bounds we've agreed on together, here's the full spread of likely outcomes." That's not a weaker claim. It's a stronger one — because it's the only claim that survives contact with a finance team.

The method behind it is straightforward: low/expected/high bounds, thousands of runs, sorted results. No black boxes. No AI-generated numbers. Just a transparent model that turns uncertain inputs into a defensible range.

That's how you stop arguing about a number and start discussing a model. And models, unlike numbers, are hard to dismiss.

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