## Friday, October 10, 2014

### If I flip a coin, the expected outcome is ...

It's likely that every project manager somewhere along the way has been taught the facts about a flip of a fair coin as an introduction to "statistics for project management"

Thus, we all understand that a fair coin has a 50-50 chance of heads or tails; that the expected value of the outcome -- outcome weighted by frequency -- is 50% heads or 50% tails. Less well understood is that sequences like HHHHHHH or TTTTTT can occur, even in a fair coin toss. Lest we be alarmed, the coin sequence eventually returns 50% heads ... just stick with it

Even less understood is that what I just wrote is largely inapplicable to project management. Not because we don't flip a lot of coins most days, but because the coin toss explanation is all about "memoryless" systems with protocols (rules) that are invariant to management intervention.

Shocking as it may seem, the coin simply does not remember the last toss. So, the rules of chance, even after HHHHHHH or TTTTTT only tell us that the next flip is 50-50 chance of heads or tails. But, of course, if this sequence were some project outcome, we'd be all over it! No HHHHHHH or TTTTTT.

In our world, for starters: we remember! And, we get in and mix it up, to wit: we intervene! No coins for us, by God!

Consequently: the rules of chance for memoryless events are pretty much inapplicable in project management.

So, does this make all statistical concepts inapplicable, or is there something to be known and appreciated, better yet: applied to project activity?

Of course, you know the answer: Of course there are valuable and applicable statistical concepts. Let's take this list for a "101" course in "I hate statistics for Project Managers"
• Central tendency: random stuff tends to gather about a central value. This gives rise to the ideas of average, expected value, grading on the curve, the bell curve, and the all important "regression to the mean".  The latter is useful when assessing your team performance: an above average performance is just as likely to be followed by a below average performance.
• Samples can be just as valid as having all the information. So, if you can't afford to test everything, measure everything, gather everything in a pile, etc, just take a sample... the results are more affordable and can be just as valid
• All you need for a simulation is some three point estimates. Another benefit of central tendency is that the Monte Carlo simulation is quite valid even if you know nothing at all about how outcomes are distributed, just so long as you can get a handle on some three point estimates. And, even the two points on the tails need not be too worrisome... a lot washes out in the simulation results, all a gift of central tendency.
• Ask me now, ask me later: Whatever estimates you come with now, they will change as time passes... risk estimates are not generally "stationary" in time. And, usually, the estimates migrate from optimistic to pessimistic. So, it only gets worse! (Keep your options dry)
• Expected value is outcome weighted by frequency. It's just a form of average, with frequency taken into effect.
• Prospect theory tells us we overweight pessimism and underweight optimism. And, even more subjectively, we all have different ideas about the weighting depending on how much we already have in the game. Where you stand depends on where you sit! Take note: this is pretty damn reliable; you can take it to the bank.
If you're tagged with putting together a risk register, put the last three on a sticky note and stare at it constantly.

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