Flaw of Averages

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# Flaw of Averages - PowerPoint PPT Presentation

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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Presentation Transcript
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

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

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

Gulf of Mexico Platform Probability Mass Functions

Note: “Most likely” scenarios are 150 and 100

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

Decision Analysis example

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?
• 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
• 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

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 they’re more, sometimes less)
• In short: system behavior is non-linear
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
• 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

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
• 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.