ROLLING DICE WITH THE BERNOULLI BROTHERS …
Acknowledgements: George Scheer (thisaviationlife.com)
(Ed. Note: The following is an abridged version of George’s article from July 2018, which can be read in full at the website www.thisaviationlife.com)
“Decisions are the choices we make when the outcome is uncertain. Risk is a crazy business. But it is understandable. Even quantifiable. Mostly. Game theory, investment strategy, actuarial science, military strategy, weather forecasting, economic prediction, and the mundane choices we make every day – which route to take to work, which checkout line at the grocery, what to have for breakfast, with whom to flirt – are all exercises in risk. So, also, is the way we fly. Risk is where the laws of probability meet the consequences of our actions.
SOME DAYS I think I am teaching people to fly airplanes. EVERY DAY I know my job is to teach people to evaluate and mitigate risk.
Understanding risk is not something we do well .... A coin comes up heads 50 consecutive times; some of us believe that the odds have now become greater that the next flip will be tails .... One in four of us will be involved in an auto accident, yet we drive as if the accident will never happen to us .... Most of us who fly airplanes seldom practice emergency procedures because emergencies happen to other pilots not so virtuous as us.
We pilots are similarly lousy at estimating risk. We worry what will happen to us if the engine stops, when the data shows clearly that this is not how we will come to grief in an airplane. Sudden, unforeseeable engine failures in a well-maintained airplane figure in a vanishingly small percentage of serious flying accidents.
We have long known the choices that lead to grim outcomes in flying: running out of fuel; flying into weather for which either the pilot or the airplane is ill-equipped; and low-level manoeuvring. These are deliberate decisions. These are actions that we choose. Why pilots keep making these choices is the baffling part.
The calculations are simple; the choices are apparently harder than we suppose. We are talking here of risk; how we balance risk and reward; how we hope to make choices that avoid emergencies; how we make decisions when the outcome is uncertain.
The first element of risk analysis, probability, required the mathematics that began to take shape first in the heart of the gambler .... Which is more likely? Rolling a 6 on four throws of a dice or rolling a “double six” on 24 throws with two dice? Of such questions were early calculations of probabilityfounded .... Once probabilitywas calculable, the nature and magnitude of outcome, began to arise as the second, equally important, component of the risk equation .... “Fear of harm ought to be proportional not merely to the gravity of the harm, but also to the probability of the event” .... This is the risk matrix we know today.
In 1731 Daniel Bernoulli, he of the Bernoulli Principle which we are told makes airplanes fly, wrote “only the foolhardy considers only the probability while ignoring the consequences. Even an unlikely consequence is too risky if it is truly dire.”
So, today we are interested in Bernoulli’s study of risk; one of the most profound explorations of the complicated relationship between the objective measurement of probability and the instinctive, often subjective, sense of consequences; Daniel Bernoulli, who gave us the principle known to every student of the wing, also gave us the two challenges given to us aviators – how to fly the contraption, and, how to keep it from killing us.
We have for the first time the two elements of risk assessment: probability which can be an objective measure, and consequence which is a subjective judgment, more difficult to quantify and has challenged anyone who takes a risk. Bernoulli drew a distinction between expected value and expected utility; the probabilities are the same for everyone, the “utility/value” is dependent on the particular circumstances of the person making the estimate. A drink of water means nothing to the comfortable, and survival to the parched .... a pilot unafraid of the darkness, places greater utility on a successful outcome, while the more cautious finds less utility in success compared with the fear of failure.
Here we have one of the fallacies of the way we teach risk to pilots. Tools such as personal minimums deny the simple fact that, because of our personal circumstances, some of us at certain times are willing to assume greater risk. Why? Because the utility of the outcome will at times be greater or lesser, shifting the risk vs. reward equation. Think of the Medivac pilot who, by assuming a slightly greater probability of a crash, may substantially increase the likelihood of saving one or more lives. He may be justified in taking a flight in conditions that would be foolhardy on a simple pleasure flight. The problem is that risk is not necessarily linear, and we may fail to appreciate that both its probability and its consequences may be increasing more rapidly than we appreciate - the fact is that, as we assume more risk, the consequence can increase exponentially.
Daniel Bernoulli gave us the concept of utility to describe the variability of an outcome’s benefit to a given risk-taker. Utility correlates with our desire, want or need; desire is measured by what we will barter for it. Think of that night you really, really wanted to fly home despite dangerous weather that, assessed without the degree to which you wanted to fulfil your desire to get home, would have been an easy no-go decision. That is the “expected utility” that can be the multiplier to the objective measurement of probability and can leave us scattered across a mountain slope. This outcome too often proves to be the price we were willing to pay for the utility we sought.
When we pilots have access to better equipment, we tend to use it not to increase our safety margin, but to increase our utility; to fly in weather we would have otherwise eschewed, or to fly closer to weather we would have otherwise given a wide berth. Given better tools we stand closer to the fire because we feel that a clearer picture of its boundary gives us more warmth without an increase in a level of risk we have long since accepted. The problem arises when we kid ourselves that we are increasing our safety, when we are in fact accepting no improvement in safety in pursuit of greater utility. More of one, less of the other. More utility, less safety. More safety, less utility. This, particularly when the outcome is a loss rather than a reward, leads to self-deceptive behaviour. If you have ever been frightened away from a flight by the mere mention of icing, you may have over-weighteda low probability. If you have ever talked yourself into a flight by concocting a complicated route penetrating a line of frontal thunderstorms, or seizing upon and taking to heart a weather briefer’s few encouraging words in the midst of a cautionary report, you may have been under-weighting a high probability of a serious outcome. Who among us has not cherry-picked the words we want to hear from a forecast?
Risk is the product of two factors: probability and outcome. Taken together, these provide the risk matrix that is the basis for any understanding, in our case as pilots, of risk and calamity.
We need the statistical data and the mathematics of probability, from both of which we can determine the likelihood of an event, good or bad, and finally we need to understand the consequences of the various possible outcomes, not just in universal terms but how those consequences impact our own lives given our specific circumstances. Those elements of knowledge have evolved over thousands of years – and yet even today we misunderstand them all too often. We see it written in the NTSB reports.
In the words of my friend, fellow aviator and instructor and airline pilot, Ronney Moss, “We each should fly one airplane at a time, preferably the one we are in.” The same could be said of the one life we are given to live. To that end, I give you my Risk Matrix for Life. Apply it where you will”. (George Scheer)