Flaw of averages
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Flaw of Averages. This presentation explains a common problem in the design and evaluation of systems This problem is the pattern of designing and evaluating systems based on the “average” or “most likely” future projections

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Flaw of Averages

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Flaw of averages

Flaw of Averages

  • This presentation explains a common problem in the design and evaluation of systems

  • This problem is the pattern of designing and evaluating systems based on the “average” or “most likely” future projections

  • Problem derives from misunderstanding of probability and systems behavior, known as


Flaw of averages1

Flaw of Averages

  • Name derives from Sam Savage

  • It is a pun, integrating two concepts

    It refers to

  • A mistake => a “flaw”

  • The concept of the “law of averages”, that is, that things balance out “on average”

  • The flaw consists of assuming that design or evaluation based on “average” (or most likely) conditions give correct answers

A motivating example

A motivating example

The design of an oil platform and wells in Golf of Mexico (Babajide)

Gulf of mexico platform probability mass functions

Gulf of Mexico Platform Probability Mass Functions

Note: “Most likely” scenarios are 150 and 100

Combined pmf

Combined PMF

Comparison of values

Comparison of Values

Based on “most likely” estimates

Based on actual distribution of possibilities

Actual ENPV  Value based on Mostly Likely Conditions

Another motivating example

Another motivating example

Decision Analysis example

Comparison of results

Comparison of Results

Value based on most likely event (No Carbon Tax) = 6.00

Value based on recognizing possibility of Carbon Tax is different = 10.8

Why does flaw occur

Why does Flaw occur?

  • Flaw is a pattern in systems design, Why?

    Several reasons converge

  • Difficult to evaluate system over many different possibilities – hard enough to create one design

  • Management fixes parameters (such as oil price) to facilitate comparisons in company

  • Uncertainties exist outside of technical specialty (markets, geology…) so that designers use “best estimates”

Mathematics of flaw

Mathematics of Flaw

  • Jensen’s law:

  • The Average of all the possible outcomes associated with uncertain parameters

    generally does not equal

  • the value obtained from using the average value of the parameters

    E [ f(x) ]  f [ E(x)] except when f(x) linear



  • In simple terms, this means that the answer you get from a realistic description differs – often greatly – from the answer you from using most likely estimates

  • This is because the gains when things do well do not balance the losses when things do not

  • (sometimes they’re more, sometimes less)

  • In short: system behavior is non-linear

3 reasons for non linearity

3 Reasons for Non-Linearity

  • System response is non-linear

  • System response involves some discontinuity (step change)

  • Management rationally imposes a discontinuity

System response is non linear

System Response is Non-Linear

  • Economies of Scale: Unit costs decrease with scale of production

  • Large initial costs prorated over volume, so that unit costs decrease as scale increases toward capacity

  • Increasing marginal costs as scale increases (labor, material costs higher)



This is Usual Situation!


System response involves some discontinuity

System Response involves some Discontinuity

Discontinuities = special form of non-linearity

Discontinuities are Common:

  • Expansion of a Project might only occur in large increments (new runways, for example)

  • A System may be capacity constrained, so that profitability or values increases with demand up to a point, and then levels off

Management creates discontinuity

Management Creates Discontinuity

  • Whenever the Managers or System Operators decide to take some major decision about a project – to enlarge it or change its function – this creates a step change in the performance of the system.

  • This can happen often – and does!

  • See “Flaw of Averages” draft chapter

Take aways


  • Do not be a victim of Flaw of Averages

  • Do not value projects or make design decisions based on average or most likely forecasts.

  • Do consider, as best you can, the entire range of possible events and examine the entire distribution of consequences.

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