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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

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.