LogicalMANIPULATIVE

Extrapolation Fallacy

What it is

Extending a trend beyond the range of the data as if the process behind it had no limits, and presenting the extended line as a forecast — “at this rate” — when nothing in the data says the rate will hold.

How it works

A fitted line describes the past; a forecast needs a mechanism, and most mechanisms saturate, reverse or run out of something. Mark Twain's 1883 parody is still the best statement: the lower Mississippi had shortened by 242 miles in 176 years, so a million years ago it must have stuck out over the Gulf of Mexico like a fishing rod, and in 742 years it would be a mile and three-quarters long. In 2004 a letter in Nature fitted straight lines to Olympic 100-meter times and found women overtaking men at the 2156 Games. The persuasion lever is that a straight line is the simplest possible story, that limits which have not yet bitten are invisible, and that both fear and hope prefer lines that keep going. Worked: a start-up growing 20 percent a month for a year has grown nearly nine-fold; the pitch deck extends the line five years to a company larger than the industry it sells into. The device serves demographic panic, environmental doom, technology utopias and market bubbles alike. The tell is the phrase “if current trends continue” attached to a projection far beyond the span of the data, with no account of what would have to stay true for them to.

Real-world examples

  • •Twain's Life on the Mississippi (1883) extrapolated the river's shortening in both directions to absurdity, remarking that one gets such wholesale returns of conjecture out of such a trifling investment of fact.
  • •Tatem and colleagues' 2004 Nature letter, “Momentous sprint at the 2156 Olympics?”, fitted linear trends to men's and women's winning 100-meter times and reported the crossing point; the authors' point, widely missed in coverage, was that the fit was linear and the conclusion should not be trusted.
  • •Paul Ehrlich's The Population Bomb (1968) opened by predicting that hundreds of millions would starve in the 1970s on the strength of then-current growth rates; fertility fell and yields rose, and the famines did not come as forecast.
  • •Mark Steyn's America Alone (2006) projected Muslim-majority European countries from fertility differentials then current; those differentials have narrowed, and the Pew Research Center's 2017 projections put the Muslim share of Europe in 2050 between roughly 7 and 14 percent across scenarios.
  • •Venture pitch decks extend a launch-year growth rate across a decade to arrive at revenue figures larger than the addressable market, and pandemic-era forecasts in early 2020 extended exponential case curves without the behavioral and immunity limits that bent them within weeks.

Ethical guidelines

  • ●State the span of the data and do not project beyond it by more than the mechanism justifies; if the mechanism is unknown, say the projection is an assumption.
  • ●Give the conditions under which the trend continues and the ones under which it stops, and present scenarios rather than a single line.
  • ●Do not use “at this rate” as a forecast without saying what would have to remain true.
  • ●When a rival's projection is a straight line, say so; when yours is, say so first.

How to defend against it

  • ►Ask what would have to stay the same for the trend to continue, and whether any of those things is already changing.
  • ►Ask how far beyond the data the projection goes; a projection twice the length of the observed span is a guess with a ruler.
  • ►Ask what the limit is — the market size, the population, the physical maximum — and whether the projection crosses it; if it does, the model is wrong, not the limit.
  • ►Look for the older projections from the same source or method and check how they did; extrapolators have track records and they are usually poor.
  • ►Distinguish the fit from the forecast: a line that describes the last ten years well says nothing about the next ten without a reason.

From the Defense Playbook

Calibration Practicetakes practice

Regularly attach a probability to your predictions, record them, and score them against what happened, so that "I am sure" comes to mean something and you can recognize false certainty in others.

"Which Step, Specifically?"minutes

When told that one action will lead through a chain of events to a dramatic outcome, lay the chain out link by link, ask what makes each link likely, and remember that the probability of the whole chain is lower than that of its weakest link.

Every playbook entry states how strong its evidence is and when not to use it. Browse the full playbook.

References

  1. Twain, M. (1883). Life on the Mississippi. James R. Osgood and Company
    The Mississippi extrapolation passage.
  2. Tatem, A. J., Guerra, C. A., Atkinson, P. M., & Hay, S. I. (2004). Momentous sprint at the 2156 Olympics?. Nature, 431(7008), 525
    Linear extrapolation of sprint times to a crossing point, offered as a caution about the method.
  3. Ehrlich, P. R. (1968). The Population Bomb. Ballantine Books
    The famine predictions built on extrapolated growth rates.
  4. Silver, N. (2012). The Signal and the Noise: Why So Many Predictions Fail — but Some Don't. Penguin Press
    The track record of trend-based forecasting and the case for mechanism and probability over extended lines.
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