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Distribution In, Distribution Out

February 22, 2010

A common catch-phrase at school is: “Point Estimates are for Suckers”.  The reason they say this was highlighted by something my Decision Modeling professor said in our last class: “A point estimate is basically a 0% confidence interval.”  For those of you that don’t have a background in statistics, what this basically means is that we can gauge the likelihood that the true value of something we are trying to estimate lies between two values.  This is called a confidence interval.  So, a 90% confidence interval means that we are 90% sure that the true value lies between the two ends of that interval.  For instance, I could say that I am 90% confident that the gas mileage of my car lies between 20 mpg and 35 mpg.  Basically, this is a calculus equation finding the area under the curve for a given range of a given distribution.

If, however, we posit a guess of an exact amount (say, 28 mpg in my example) we have selected a range that has a length of zero.  The area under the curve for a single point is infinitesimally small: the value under that point approaches zero.  In that way, our confidence that our point-estimate is right is 0%; our confidence that the real value is something else entirely is near 100%.

Which is all an argument for using distributions and meaningful confidence intervals in our modeling instead of pure point estimates when dealing with inputs for which we cannot and do not know the exact value.

The folks who are forecasting revenue at work struggle every day to deal with this problem: they get input from the sales and channel representatives who supposedly know the likelihood that this deal or that deal will succeed.  If it succeeds, we’ll get a certain amount of revenue (an amount that, itself, ought to be a distribution).  If it fails… we’ll get none of that potential revenue.  How ought they forecast revenues, then?  If they could model the inputs – the likelihood of sealing a deal, the value of that deal – as uncertainties and distributions, then they could generate distributions at the end that give a range of likely revenue scenarios.  I wonder if providing confidence intervals like this would make decision-making at higher levels in my company better.

Anyway, that’s the update from Decision Modeling for this week. 

This week, I need to spend a little more time really focusing on my career planning.  I’ll report on how that goes, as time permits.  As for writing… well, my brain has been just dry this past week.  We’re almost halfway through the semester, and my brain just needs a recharge break before writing ideas start percolating again.

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