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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
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

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.