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

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Flaw of Averages

• Name derives from Sam Savage
• It is a pun, integrating two concepts
• It refers to
• A mistake gt 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

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A motivating example

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

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Gulf of Mexico Platform Probability Mass
Functions
Note Most likely scenarios are 150 and 100
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Combined PMF
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Comparison of Values
Based on most likely estimates
Based on actual distribution of possibilities
Actual ENPV ? Value based on Mostly Likely
Conditions
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Another motivating example

• Decision Analysis example

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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
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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

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Mathematics of Flaw

• Jensens 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

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Consequences

• 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 theyre more, sometimes less)
• In short system behavior is non-linear

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3 Reasons for Non-Linearity

• System response is non-linear
• System response involves some discontinuity (step
  change)
• Management rationally imposes a discontinuity

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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)

Unit Cost
This is Usual Situation!
Scale
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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

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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

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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.