To understand probability in forecasting, we can take a trip to the grocery store.
What We're Going To Do
- Demonstrate Estimation by shopping for produce
- Look at reducing uncertainty
- Explain reducible vs irreducible uncertainty
The Basic Scenario
Lets say we're going to shop for ingredients for a fruit salad consisting of 2 apples, 1 banana and some grapes.
Without going any further, you probably can make a reasonable guess about how much things will cost. I'd say we'd spend roughly the following:
- Apples: Between $2 and $4, but most likely $2.50
- Bananas: $1 - $2, most likely $1.50
- Grapes: $2.50 - $4.00, most likely $3.00
Plus, at my store apples are on sale ~20% of the time which could take between .25 an .75 off. We can plug these estimates into DartCannon giving us the following model:
We can plus these numbers into DartCannon to get the following distribution:
One thing DartCannon does for us immediately which might not have been obvious otherwise is while our full range of estimates are between $4.75 and $10, a range of $5.25, the 90% range is only $2.
For some projects this level of estimation is good enough to make decisions, but perhaps we need more accuracy. For our grocery example, instead of relying on our existing feelings about prices and the historic chance of a sale, we could look up current prices and sales. Also finding average weights of the fruits.
While finding current prices would reduce much of the uncertainty, while fruit (at least where we're based) is priced by weight, it is sold by unit. Since no piece of fruit is exactly the same weight, if we need 2 apples we can't say precisely how much that will weigh, so we still have some uncertainty.
Lets say we went through this process
- Apples: Between $2.20 and $3, but most likely $2.60
- Bananas: $1.25 - $1.50, most likely $1.30
- Grapes: $3.50 - $3.60, most likely $3.50
We can see that the range is greatly reduced and the central 90% range is now only $0.50.
While not a huge effort for making fruit salad, it may not always be worth it depending on the decisions we need to make and how much improving those estimates cost
Reducible vs. Irreducible Uncertainty
The exact price of the produce is called a reducible source of uncertainty. We were able to eliminate that source of uncertainty by putting in the effort to eliminate it completely.
Not knowing the exact weight of our produce is irreducible as we can't know what it will be until we actually go to the store to buy them.
In most endeavours there are always a mix of reducible and irreducible sources of uncertainty. For reducible uncertainty, the question is always how much reducing the risk costs or can you live with it for the decisions you need to make.
For irreducible risk, there are similar questions only instead of spending to reduce the uncertainty, the question becomes one of buying insurance or mitigating the risk if it is difficult to live with.
DartCannon can help guide discussions of risk by exposing the range of risks and helping focus on the most likely range of outcomes rather than the unlikely extremes.