Sunday, January 3, 2021

Eggs-to-basket ratio


The oldest advice in risk management is this little ditty:  
"Don't put all your eggs in one basket"
 
It's obvious on its face: if you drop the one basket, you may lose all the eggs in just one accident. Why not carry two baskets, or three, or  four, or how many ..... ?

Well, what we're talking about here is diversifying the risk, and making the situation less fragile: that is more able to absorb shock without catastrophe. 
 
Of course we are also talking about cost: more baskets cost more money. And, there is the additional effort -- not free -- to distribute the eggs into multiple baskets, and then gather all the eggs from all the baskets so the eggs can be used where they are needed. 
 
And so arises the "eggs to basket ratio": how much diversification? How much less fragile? And at what cost?

First, the ideas from statistics:
It can be shown that if the eggs are separated into multiple baskets where the risks to an individual basket are completely independent from one basket to the next, then the overall range of risks outcomes is reduced exponentially. 
 
Actually, in the ideal case, the exponent is 1/2 applied to the number of baskets. So, by example, if the range of outcomes was "4" when there was one basket, the range of outcomes for two baskets taken together is only "2". This is the so-called rule of "square root of N", where N is the number of baskets. (*)

As a practical matter in projects, as elsewhere -- like the stock market -- it's pretty hard to meet the criteria of complete independence of risks among the baskets. If it rains, it may rain on all baskets. So, the exponent is less than 1/2 in the real world. Nonetheless, the principle holds: isolating risks will improve the chances that risk outcomes are reduced.
 
Second, common sense:
  • You're unlikely to drop all the baskets at the same time. Thus, the risks to all the baskets is not the same as the risk to any one basket
  • You can add redundancy: there can be more eggs overall than you really need. If you drop a basket, there will still be enough eggs to do the job
  • You can add "rip-stop" or containment: If one basket is damaged (or dropped) by some phenomenon, barriers may be erected to contain or stop the spread of the phenomenon to the other baskets or eggs
But at what cost?
Back to the original question: how does one get the right eggs-to-basket-ratio (the right degree of diversification)?
 
It's really a question of insurance (or overhead, or non-value-add): how much are you willing to pay to avoid or reduce the cost of a risk occurrence? Whatever you pay for insurance, the cost doesn't add to throughput, so it goes toward overhead or the non-value-add cost embedded in the project.
  • If you can absorb the total cost of a risk occurrence, then no insurance is needed, and thus the cost of diversification is a cost not worth bearing
  • If otherwise, then the case is situational to your project: you'll have to decide if 10% or 25% or whatever is a fair price to pay for diversifying the risk.
I wish I could end this with the formula for figuring all this out, but alas: there is no formula.
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A bit of math: "square root" is the name given to the exponent 1/2
Statistically, diversification reduces the "variance" of risk outcomes. "Variance" is a figure-of-merit for the range of risk outcomes



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