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RICHARD DE NEUFVILLE: Hi,
this is Richard again.

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And change of pace
now from the sequence,

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I'm going to be
talking about something

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called the flaw of averages.

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What is this?

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It's a fundamental problem
in the design and evaluating

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of projects.

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And I'm going to take some time
to explain it to you, and then

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in a following session,
to talk about what

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its implications are.

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So the flaw consists
of-- or is the pattern

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of designing,
evaluating projects

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based on the average or
most likely future forecast.

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That is, thinking
that, OK, here's

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what the forecast
is going to be,

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or here is our best
guess at the forecast.

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We know it's wrong,
you've told us so,

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but we're still going to analyze
it based upon one forecast.

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Then what often
happens is that people

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will take some variation around
it, plus or minus 10%, say.

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But the fundamental
choice is that they're

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looking at it from an
average or a projection.

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Now what happens
is that there is

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a fundamental misunderstanding
of probability and systems

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behavior when you do that.

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So let me explain the name.

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It's a pun by Sam Savage
who wrote the book, in fact,

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called Flaw of Averages.

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It integrates two concepts.

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First concept is that there
is a mistake, a flaw--

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F-L-A-W-- flaw.

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And it combines that with the
concept of the law of averages.

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That means that basically
things work out on the averages

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so that the pluses
balance the minuses

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and everything works out.

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So that if you design around
the average, you'll be OK.

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That is not correct.

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The error consists, in
general, of assuming

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that the analysis based
upon average or most likely

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should give correct answers.

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This is wrong.

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It's fundamentally wrong.

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And it's not a new
discovery, it's

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a very old mathematical fact.

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It's called Jensen's law.

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I don't know why.

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I suppose that somehow
he articulated it.

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But all it says is that the
expected value of something

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that's variable, the expected
value of a function that

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is, say, the profit
from a project,

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or its net present value,
or some measure of goodness

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is not equal to that
function evaluated

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using an expected value.

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In detail that says, if
it's a convex function,

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but in general, it
applies in all cases, so--

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all practical cases.

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So what it says is if you really
want to know the average value,

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the expected value of something,
you cannot do it around

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the looking at it and evaluating
it at its most likely,

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or average, or most
probable condition.

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And for the notation,
the E of x simply

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means that the arithmetical
average or expectation of that.

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And in words, we're talking
about that the average

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of all possible outcomes--

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that is, what's on the
left-hand side here--

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is not equal to the
outcome calculated

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by using the average value.

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Very simple concept.

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That is, put it another
way, that if you really

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want to get the right
value, you can't evaluate it

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around some most likely, or
most probable, or average,

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or median forecast.

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You have to look at
the whole distribution

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or some approximation of
the whole distribution.

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So in words, the
flaw of averages

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is the average of all
possible outcome associated

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with uncertain parameters.

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It generally does
not equal the value

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obtained from using the average
value of the parameters.

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That's the flow of
averages in words.

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