Concept

False precision

Overview

False precision is presenting a number with more apparent exactness — more significant figures, a tighter range, finer resolution — than the method and inputs that produced it can support. It misrepresents an order-of-magnitude estimate as an exact one, and is among the most common ways an early-stage analysis loses credibility.

Body

What it is. Every reported figure carries an implied precision: writing “$805.43/t” implies the analysis can tell $805 from $806, while ”~$800/t ±30%” implies it cannot. False precision is any presentation whose implied precision exceeds the estimate’s true accuracy class. It is a property of how a number is written and shown, not of whether the number is right.

Where it shows up. Common forms:

• Excess significant figures — quoting a cost per tonne to the cent off inputs known only to ±tens of percent; spurious decimals carried straight from a spreadsheet cell.
• Over-tight ranges — a stated band narrower than the inputs justify.
• A bare point estimate — a single figure with no band, which implies zero uncertainty and is itself a false-precision claim by omission.
• Over-resolution — a cost broken into many decomposed line items, or a chart drawn to a resolution the data does not have, implying each part is independently pinned down.

Why it happens. Arithmetic preserves digits: multiply a few rounded anchors and the spreadsheet returns ten or twelve figures, none of them earned. The inputs to an early estimate are FEL-grade engineering proxies and round reference values carrying ±tens of percent, so the output cannot be sharper than they are. Precision is bounded by the weakest input, not by the cleanliness of the calculation.

Precision is not accuracy. A number can be accurate (close to the truth) yet falsely precise (written as though exact), and a number can be imprecise yet honest. The two axes are independent: how many digits a figure is shown to says nothing about how close it is to right. The honest presentation matches the displayed resolution to the real resolution — usually one or two significant figures with an explicit band, the resolution an order-of-magnitude gut-check would confirm.

Limits & typical error

• It is independent of accuracy, so it is not evidence of quality. A falsely precise number can be exactly right, and a correctly rounded one can be wrong; “the model returns $805.27” is not a sign the model is good — agreement-to-the-cent between two estimates is coincidence at this accuracy class, not corroboration.
• Precision is capped by the weakest load-bearing input. Stacking precise-looking arithmetic on a single ±40% anchor cannot yield a result tighter than ~±40%; every displayed digit beyond that point is noise dressed as signal, and the cap is set by the worst input, not the average.
• Over-rounding is the opposite, equally real error. Collapsing a genuinely resolved difference — two consistently-built figures that really do differ — into “about the same” discards decision-relevant signal. Because shared inputs cancel, a difference between two numbers built on the same anchors can be far better resolved than either absolute level, so rounding both to one figure can hide a real gap.
• Implied precision compounds through comparisons. Subtracting two falsely-precise numbers (a margin = price − cost) produces a difference whose apparent precision is more overstated than either input’s, because the two error bands add in the gap between them.
• A point estimate reads as a commitment. A figure shown with no band is taken as exact, so it sets expectations the ±30% analysis cannot meet; the omission of the band is read as more confident than an explicit wide range would be.
• Apparent precision can mask an unresolved driver. A key parameter carried as a sharp-looking number appears settled when it is the opposite; the digits hide that the answer turns on an input still only known to a wide band.

See also

• Uncertainty & accuracy class — the ±band (FEL-1/2, ~±30%) that defines how much precision a figure can honestly carry.
• Order-of-magnitude / gut-check — the mirror discipline that sets the realistic resolution a result should be stated at.
• The headline number — the single reported figure most exposed to a false-precision presentation.
• Engineering proxies & shorthands — the round, ±-laden inputs whose error caps the output’s precision.
• Levelized cost — the headline output most often quoted to more figures than its inputs support.
• Driver / key parameter — the high-leverage input a sharp-looking number can falsely make appear resolved.

Mini-example

Green ammonia’s levelized cost comes out of the spreadsheet as “$805.27/t” — capital $355.4 + electricity $400.0 + fixed $50.0, each carried to the cent. But every input is a round anchor: the electricity price is a ~$40/MWh market round number, the capex an order-of-magnitude ~$1.0bn (±30%), the intensity a 10 MWh/t proxy. The honest figure is **$800/t with a band of order ±30%** — roughly $550–1,050/t. Reporting $805.27 claims a resolution about a hundred times finer than the inputs carry; the four trailing figures are noise. Rounding to ~$800/t and stating the band presents exactly what the method knows.

Separately, to show the opposite error: a one-way sweep that moves the cost from ~$800/t to $810/t when one input is flexed is a real result about that input’s leverage — the other inputs are held fixed, so the $10 difference is controlled, even though $10 sits far inside the ±30% absolute band. Reporting both endpoints as “$800/t, indistinguishable” over-rounds away the very leverage the sweep was run to find. Matching resolution to reality cuts both ways.

See also

• Uncertainty & accuracy class (FEL-1/2, ±30%)
• Order-of-magnitude / gut-check
• The headline number
• Engineering proxies & shorthands
• Levelized cost (e.g., $/t NH₃)
• Driver / key parameter