Just as a handle helps you grasp something with your hand, I define a Mindle (first syllable rhymes with 'mind') as the analogous concept for the mind. In this section I will present five fundamental Mindles for grasping various aspects of uncertainty. Although you may have been exposed to these concepts in the past, they were likely cloaked in Steam Era anachronisms such as VARIANCE or STANDARD DEVIATION."
After the jump, my review.
The excerpt above reads a little like a late night television infomercial. That's the bad news about this book. Sam Savage is selling something: his book, his consulting services, his claim to be revolutionizing business planning with his purported brainchild, Probability Management. Hardly a chapter goes by without him sounding a little like a huckster for his system and its supporting Microsoft Excel plug-ins.
The problem is not that he's selling snake oil. He's not. It's that what he's selling isn't all that new. As Savage himself admits, "the Strong Form of the Flaw of Averages isn't news to mathematicians. They have known it for over a century as JENSEN's INEQUALITY. Of course, with a name like that, no wonder no one else has heard of it." Savage dismisses centuries of mathematical theory as "Steam Era Statistics." He demeans it by questioning its motives: "In Steam Era Statistics, distributions were often represented as smooth curves instead of bar graphs. This just gives statistics professors an excuse to slip CALCULUS into their courses, as if you weren't bored and confused enough already."
The shame is that Savage does have something to add without having to undermine the mathematics underlying it all. Savage explains why just taking an average of some variable input and plugging that into a simple Excel formula is likely to lead to a disastrously wrong business decision. Savage also offers a solution that wasn't possible until the advent of modern computers. It's now possible to "bury the math in a simulation" as Savage puts it. You don't need to remember the formula or do the calculus to compute, say, the expected return of a portfolio of investments. You can relatively easily set up a Monte Carlo spreadsheet simulation, run thousands of trials, and see the result, which will come as close to the exact answer as your purpose requires. The results might also go against your intuition.
That brings us back to the basics -- just what is the "flaw of averages?" This is where the book shines. Savage provides easily understood examples of the flaw. A drunk walking, staggering, down a busy highway is, on average, safely walking the center line, but in any real world scenario, almost certainly dead.
More relevant examples come from business. A typical, but naive, everyday business decision is to hold enough inventory to meet average demand. Say you manufacture medicines and need to decide on how much inventory to carry. Carry too much and you have the cost of disposing of old, unsold product. Carry too little and you have a different, maybe larger cost, the cost of having to meet rush orders when your inventory runs out. It's easy to compute that your cost in an average month is zero, that is when inventory equals demand, there is no waste, no rush orders. But your average cost, over many months and years, is unlikely to equal your cost in the average month. Thinking it does is the flaw of averages. Savage advises to plug in a distribution of demand instead of just a single number and run simulations over time computing the average cost over time for various levels of inventory, then choose the level that results in lowest average cost. With personal computers, that's now feasible to do even for business managers lacking the mathematical training to understand the statistical theory behind it.
Savage outlines all sorts of examples of the flaw of averages from all sorts of fields -- business, health care, terrorism, climate change, even sports. He explains the flaws behind people's intuition in each case. He emphasizes how computers, and computational statistics, give businesses a new tool to avoid the flaw of averages. Overall, there's much to recommend in this book, just don't let the hucksterism spoil it for you.
With much appreciation to glb.