## Sunday, March 20, 2011

### Three quantitative risk concepts

Repetition and review are good--Malcom Gladwell says it takes 10,000 hours to be expert at anything--so here's a few words that will take a few minutes on three important quantitative concepts every risk manager should know:

Concept 1: Centrality
Most phenomenon of interest to projects, particularly naturally occuring phenomenon, tend to cluster around a central value, given enough samples or examples. Obviously, this let's out the so-called long-tail 'black swans', but project managers can go a long way if they understand that central clustering is the norm ... in effect, the default.

The measures are average and expected value. The former is applicable when the data is known; the latter when the data is probabilistic and the numerical value is not known until an event occurs. In calculating the average, each value is equally weighted; in calculating the expected value, each value is weighted by its probability.

Concept 2: Variation
Yes, things cluster, but that simply means that around the central value there is a range within which things are nearby the center, but not exactly on the center.

It's more likely things are close to the center than not: that's an effect of centrality on variation

The measures of variation are variance and standard deviation.  Variance is a figure-of-merit related to the distance, or error, between a point in the range and the central value. Standard deviation is a more direct measurement of distance, having the same dimensions as the points in the range.  Engineers refer to the standard deviation as the root-mean-square, or RMS value.

Concept 3: Position
Sometimes it's enough to know just the position of a data value in the range.  Names associated with position are quartile and percentile, and the so-called 'Z' position.

Z is just a value in the 'standard range' divided by the standard deviation.  [A 'standard range' has a '0' average] For project management purposes, the 'Z-position' extends +/- 3 units from the average or expected value for most situations.

Dividing a range into 4 quartiles requires defining 3 boundary points: Q1, Q2, and Q3.  Quartile is all about count, not value per se.  Just rank all the values in the range in ascending order.  Divide the count into quarters.  Q1, Q2, and Q3 are the count values that divide the range.

If a value is in the first quartile, that means that 75% of all the values in the range are greater than the Q1 value, and by extension 75% of all the values are greater than any value in the first quartile.

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