Coin Toss 101
As an experiment, toss a coin 100 times. Let heads represent
one estimate of the duration of a project task, say writing a specification, of
10 days, and let tails represent an estimate of duration of 15 days for the same
task. Both estimates seem reasonable. Let us flip a coin to choose. If the coin
were "fair" (that is, not biased in favor of landing on one side or the other),
we could reasonably "expect" that there would be 50 heads and 50 tails.
But what of the 101st toss? What will it be? Can we
predict the outcome of toss 101 or know with any certainty whether the outcome
of toss 101 will be heads or tails, 10 days duration or 15? No, actually, the
accumulation of a history of 50 heads and 50 tails provides no information
specifically about outcome of the 101st toss except that the range of
possible performance is now predictable: toss 101 will be either discretely
heads or tails, and the outcome of toss 101 is no more likely to come up heads
than tails. So with no other information, and only two choices, it does not
matter whether the project manager picks 10 or 15 days. Both are equally likely
and within the predicted or forecast range of performance. However, what of the
next 100 tosses? We can reasonably expect a repeat of results if no
circumstances change.
The phenomenon of random events is an
important concept to grasp for applications to projects: the outcome of any single event, whether it be a coin toss or a
project, cannot be known with certainty, but the pattern of behavior of an event
repeated many times is predictable.
However, projects rarely if ever repeat. Nonrepetitiveness is
at the core of their uncertainty. So how is a body of mathematics based on
repetition helpful to project managers? The answer lies in how project managers
estimate outcomes and forecast project behavior. We will see the many
disadvantages of a "single-point" estimate, sometimes called the deterministic
estimate, and appreciate the helpfulness of forecasting a reasonable range of
possibilities instead. In the coin toss, there
is a range of possible outcomes, heads or tails. If we toss the coin many times,
or simulate the tossing of many times, we can measure or
observe the behavior of the outcomes. We can infer (that is, draw a conclusion
from the facts presented) that the next specific toss will have similar behavior
and the outcome will lie within the observed space. So it is with projects. From
the nondeterministic probabilistic estimates of such elements as cost, schedule,
or quality errors, we can simulate the project behavior, drawing an inference
that a real project experience would likely lie within the observed
behavior.