Chapter 02
Confidence bands and credibility
Why a defensible business case publishes ranges, sources, and assumptions, and why a single confident number tends to lose finance trust before the meeting starts.
01
What ranges signal
A range tells the reader the analyst understood the inputs were uncertain and refused to pretend otherwise. A single confident number tells the reader the opposite. Finance partners are trained to read both signals quickly. The first earns time. The second earns scepticism. Ranges are not hedging. A 12,000 to 19,000 euro saving on manual reporting is not a worse claim than a 17,000 euro point estimate; it is the more truthful version of the same claim. The width of the band is itself information. A narrow band means the inputs are well understood. A wide band means the analyst is honest about how much is still estimate. Both are acceptable; what is not acceptable is a narrow band on inputs that are obviously uncertain. Publish low, mid, and high for each line of value. Carry that discipline through to the total. The board pack tends to quote the mid, but the appendix shows the bracket. Credibility comes from the visibility of the bracket, not from the cleverness of the mid. Be sceptical of round numbers. A reported 100,000 euro annual saving almost never reflects measurement; it reflects rounding to the nearest psychologically comfortable threshold. The same reported as 92,000 to 118,000 euro signals that someone counted. A useful self-test before submission: scan every total in the document. If more than two sit on a round multiple of 5,000 or 10,000 euro, the document is probably hiding the real working. Either narrow the bands by interrogating the inputs, or accept the rougher numbers and present them as ranges. Either response builds credibility; the rounded point estimate erodes it.
02
The mechanics of building a band
A defensible band is not one number plus and minus ten per cent. It is built from the inputs. For each input — hours, frequency, probability, cost — write a low, mid, and high estimate with a one-line source. Multiply them through. The output band is the natural product of the input bands; it is not negotiated. A worked illustration on a manual reporting line. Hours per pack: 4 to 7. Packs per month: 3 to 5. Loaded rate: 90 to 130 euro. Contract life: 30 months. Multiplied through, the low end is 4 x 3 x 90 x 30 = 32,400 euro and the high end is 7 x 5 x 130 x 30 = 136,500 euro. That is too wide for a board pack. The discipline is to interrogate the widest input — usually frequency — and tighten it with project-specific data. The narrowed band might land at 45,000 to 80,000 euro. Show the working. The reader who can see the inputs cannot accuse the model of being a conjuring trick. Two refinements are worth the small additional effort. First, treat correlated inputs together rather than independently. Hours and frequency tend to move in the same direction on the same project, so multiplying their independent extremes overstates the true band. The honest way to handle this is to define a low scenario, a mid scenario, and a high scenario, each with its own consistent set of input values. Second, distinguish irreducible uncertainty from reducible uncertainty. The loaded rate is reducible — the budget partner can confirm it tomorrow. The probability of a major dispute is irreducible without project history. Mark the reducible inputs and commit to narrowing them before a defined date. The case becomes a living document with a closing band, which is both more useful and more credible.
03
Sensitivity tables and the inputs that move the result
A one-page sensitivity table is the single highest-yield artefact in a credible case. Five rows, three columns. Each row names an input. Each column shows the total at the low, mid, and high value of that input, holding others at mid. The reader instantly sees which inputs matter. Typically, two inputs move the result by more than 60 per cent of its range, and the rest barely matter. That is useful for two reasons. First, it tells the reader where the analyst should be most careful. Second, it tells reviewers which assumptions to argue about. A case without a sensitivity table forces every assumption to be relitigated; a case with one focuses the conversation. As a rule of thumb in RDI cases, the heaviest sensitivities tend to be the proportion of report preparation time replaced, the probability of the largest risk event, and the loaded cost rate. Senior reviewers will go for those three first. Be ready. A useful refinement is the two-way sensitivity grid for the largest pair of drivers. A small five-by-five matrix showing the total at combined values of the two inputs communicates the joint risk in a way that one-way tables cannot. Reviewers tend to look at the worst corner of the grid first; if that corner is still positive after workflow cost and discount, the case is robust to the two largest sources of uncertainty simultaneously. If it is negative, the document should say so, name the corner explicitly, and describe the conditions under which that corner becomes plausible. That sentence is the single highest-trust paragraph the case can contain.
04
When the honest model says no
Sometimes the honest model says the case does not pay back. The discipline is to report that finding rather than to massage the inputs. A case that does not pay back at the low end may pay back at the mid; a case that does not pay back at the mid is probably not the right investment, and the team that says so out loud earns trust for the next round. Models that always come out positive eventually stop being read. A specific failure mode to avoid: anchoring on an internal threshold — say, a 30 per cent IRR — and walking the inputs back until the answer clears it. Reviewers spot this. The fingerprint is suspiciously round numbers, suspiciously narrow bands, and a sensitivity table whose total moves by less than the inputs. The role of the model is to support the decision, not to predetermine it. The teams that publish a no-go finding once tend to have their yes-go findings believed for years afterwards. A no-go finding is rarely binary. Often the right output is a smaller go: a phased pilot on two projects rather than a portfolio rollout, or a narrower workflow scope that targets the strongest line and defers the weaker ones. The case that distinguishes a full no from a partial yes is the one finance partners reach for first. It saves the organisation the political cost of a hard rejection while preserving the discipline of letting the numbers speak. The author who proposes a smaller go in response to the honest model demonstrates the calibration the next case will need.
05
Failure modes that cost cases
Three patterns recur. First, false precision: a 23,847 euro line item read as if the analyst measured it to the euro when the inputs are estimates accurate to plus or minus 25 per cent. Second, asymmetric ranges: a low end ten per cent below the mid and a high end forty per cent above, designed to nudge the reader toward the upside. Third, missing sources: a benchmark with no citation, a probability with no derivation. Each pattern is small on its own. Together they signal that the analyst is selling rather than measuring. Fix all three before submission. Round to two significant figures where the inputs justify nothing more. Make the band roughly symmetric or explain why it is not. Cite every benchmark. The finance partner who reads a case with these three patterns absent will read the next one from the same team carefully. The one who reads them present will read the next one more sceptically than the work deserves. A fourth pattern is more subtle and more damaging: counting the same hour twice. The senior commercial manager who is freed from progress pack preparation appears on a saving line. The same hour reappears on a capacity line on the basis that the freed time enables a new activity. Pick one. Either the saving is operational and the time is recovered, or the saving is strategic and the time is reallocated. Counting both is the single most common reason credible operational savings get challenged unfairly, because it taints the whole document with the suspicion of double counting once a reviewer spots one instance.
Practice
01. Build a five-row sensitivity table for the case you are working on. For each row, hold all other inputs at mid and vary the named input across its low, mid, and high. Note which two inputs explain most of the range.
Look for: A table with five rows and three result columns. Two of the five rows produce noticeably wider columns than the others; those are the inputs to interrogate first. The other three are real but secondary.
02. Take one line of your case where you wrote a point estimate. Rewrite it as low — mid — high, with each input given its own band and a one-line source.
Look for: A line item showing input bands, sources, and the resulting output band. The output band is wider than the original point estimate. The width is acceptable because it is now defensible.
Checkpoint
For a current case, are the assumptions, sources, and ranges visible enough that finance could interrogate any single line in under five minutes?
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