Many tell me: "I hate statistics", or they tell me: "I don't know anything about statistics, so I don't use statistics in projects"
Hello!... actually you do use statistics; you're just not that aware of it.
Let's all cluster around the center
One of the most prominent principles you apply probably unwittingly and unconsciously is the Central Limit Theorem, affectionately: CLT.
From a risk management perspective, the CLT has these two ideas embedded that are useful day to day (look: no math!):
1. Central tendency: central tendency says that regardless of the underlying details of random effects, whether asymmetrical or not, uniform or not, the aggregation of all the independent effects will have a bell shape, with a pronounced central value.
That's handy because no matter how pessimistic or optimistic are the various work package managers about budgets and schedule, at the project level it all washes out and there will be a general bell curve around the central figure that is the sum of the durations or the sum of the budgets.
2. Long term, it's the average: most natural phenomenon have random variations but over time they find their way back to their long term average. (you may have heard this idea as "regression to the mean")
If your project is to paint the fence, then there may be a few warm days, a few dry days, a few cool days, but over enough time, the time to paint the fence will wander back to its long term average. Such dependable behavior gives you the basis for parametric estimating with relatively low risk.
Generally, biological systems, like people, regress to the mean unless there are material changes in environment, training, tools, etc. So, just because a team member performed really good (or bad) this time, such non-average performance does not predict the next time.
Ah, but the average drifts, long term
Malcolm Gladwell tells us it takes 10K hours to become an expert -- about 5 years in normal times -- so the drift of the mean with expertise is usually quite long. (Training, experience, evolution of ideas, and such are part of a 10,000 hour experience)
Short term, if there is tool wear, like the paint brush wearing out, then such non-random effects will bias results off their natural center.
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