Obvious not every decision we make is based on mathematics, but when we're spending money, especially other people's money, we'd better have so good reason to do so. Some reason other than gut feel for any sigifican value at risk. This is the principle of Microeconomics.
All Things Considered is running a series on how people interprete probability. From capturing a terrortist to the probability it will rain at your house today. The world lives on probabilitic outcomes. These probabilities are driven by underlying statistical process. These statistical processes create uncertainties in our decision making processes.
Both Aleatory and Epistemic uncertainty exist on projects. These two uncertainties create risk. This risk impacts how we make decisions. Minimizing risk, while maximizing reward is a project management process, as well as a microeconomics process. By applying statistical process control we can engage project participants in the decision making process. Making decision in the presence of uncertainty is sporty business and many example of poor forecasts abound. The flaws of statistical thinking are well documented.
When we encounter to notion that decisions can be made in the absence of statistical thinking, there are some questions that need to be answered. Here's one set of questions and answers from the point of view of the mathematics of decision making using probability and statistics.
The book opens with a simple example.
Here's a question. We're designing airplanes - during WWII - in ways that will prevent them getting shot down by enemy fighters, so we provide them with armour. But armor makes them heavier. Heavier planes are less maneuverable and use more fuel. Armoring planes too much is a proplem. Too little is a problem. Somewhere in between is optimum.
When the planes came back from a mission, the number of bullet holes was recorded. The damage was not uniformly distributed, but followed this pattern
The first thought was to provide armour where the need was the highest. But after some thought, the right answer was to provide amour where the bullet holes aren't - on the engines.
- Engine - 1.11 bullet holes per square foot (BH/SF)
- Fueselage - 1.73 BH/SF
- Fuel System - 1.55 BH/SF
- Rest of plane - 1.8 BH/SF
"where are the missing bullet holes?" The answer was onb the missing planes. The total number of planed leaving minus those returning were the number of planes that were hit in a location that caused them not to return - the engines.
The mathematics here is simple. Start with setting a variable to Zero. This variables is the probability that a plane that takes a hit in the enginer manages to staty in the air and return to base. The result of this analysis (pp. 5-7 of the book) can be applied to our project work.
This is an example of the thought processes needed for project management and the decision making processes needed for spending other peoples money. The mathematician approach is to ask what assumptions are we making? Are they justified? The first assumption - the errenous assumption - was tyhat the planes returning represented were a random sample of all the planes. If so, the conclusions could be drawn.
In The End
Show me the numbers. Numbers talk BS walks is the crude phrase, but true. When we hear some conjecture about the latest fad think about the numbers. But before that read Beyond the Hype: Rediscovedring the Essence of Management, Robert Eccles and Nitin Nohria. This is an important book that lays out the processes for sorting out the hype - and untested and liley untestable conjectures - from the testable processes.