Sam Savage – Chance-Informed Decisions

by Sam L. Savage

A Good Bad Example

Victor Hugo said: “I am not completely useless. I can serve as a bad example.” The same can be said of Operation Eagle Claw, the failed attempt to rescue the American hostages in Iran in 1980. It is highlighted in military operations research training as an egregious example of the Flaw of Averages, and yet military readiness planning is still subject to similar faulty thinking. Eagle Claw is such a good bad example that it has played a central role in our efforts at to promote a chance-informed approach to military readiness planning, as described in our latest publication for the Center for International Maritime Security. Our basic approach is to model the readiness of military units with SIP Libraries that allow readiness to be defined in terms of the chance that a unit, or combination of units, can accomplish a specified mission at some non-specified time in the future with little time to prepare.

You’d think we would all be getting tired of Eagle Claw by now, but some errors in reasoning are truly immortal, and I have now written two short docudramas on the subject below. But first, a short recap of the story.

The Story yet Again

The planners of the mission knew they needed six helicopters to rescue all the hostages, and given the hostile relationship with Iran, they had to either rescue them all or abandon the mission. The Sea Stallion aircraft involved were known to be 75% dependable. That is, on average (as in the Flaw of Averages), 25% of the helicopters would suffer mechanical difficulties, leaving 75% airworthy. The planners could do arithmetic and sent eight aircraft because 75% of eight is six. Imagine if the planners had been able to do the arithmetic of uncertainty, or had been aware of the binomial distribution worked out by Jacob Bernoulli 300 years earlier. Then they would have known that sending eight helicopters implied essentially one chance in three of having insufficient aircraft for one of the most important military missions in recent history. They also would have been able to calculate that this probability of failure would be cut roughly in half by sending nine helicopters, and in roughly half again by sending ten. Eagle Claw is remembered for a tragic refueling accident in the desert with the loss of eight servicemen, but that occurred after the mission had been scrubbed because three of the helicopters had mechanical problems, leaving them with only five.

ChanceCalc and the Arithmetic of Uncertainty

Arithmetic tells us that X+Y=Z. The Arithmetic of Uncertainty says: “What do you want Z to be? Here are your chances.” ChanceCalc, the revolutionary Excel add-in from, estimates the chances of achieving your goals without ever having heard of Bernoulli or the binomial distribution. This tool was designed for non-statisticians using the open, cross-platform stochastic libraries that our team has been proposing as a framework for estimating military readiness. But the same approach applies to risk management, financial modeling, and decision analysis in general. Although ChanceCalc is doing full on stochastic modeling, we have found that most people are less intimidated by the term “Chance-Informed decision making.”

To drive home the importance of this concept, I have written two very short docudramas called “Eagle Claw” and “Chance-Informed Eagle Claw,” which demonstrate the difference.


COMMANDER: How many helicopters do I have to send if I need six to complete the mission?

ANALYST: Eight, on average.


COMMANDER: How many helicopters do I have to send if I need six to complete the mission?

ANALYST: Eight, on average.

COMMANDER: What’s the chance I won’t have all six when I need them?

ANALYST: 32%. Why do you ask?

If you want to avoid acting out the “Eagle Claw” docudrama and bring chance-informed decision making to your organization, here are some things you can do:

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