# The Difficulty of Estimating Probabilities

The May Issue of the German Harvard Business Manager shows the results of a survey among corporate leaders on the importance of various risk factors (Die Sorgen der Konzernlenker, page 22). The survey was done at the World Economic Forum in Davos and asked about the estimated probability and expected effects for 50 predefined global risks. In the article, the results are plotted as the number of answers color coded in 5×5 grids (probability horizontal, effects vertical).

The striking result are not so much the five main problems identified in the article, but the similarity of the distributions of answers, particularly on the probability axis. Whereas the effects of some risks are actually (although not dramatically) seen as larger or smaller than the others, the probability estimates show a strong tendency towards the center of the scale. In other words, the 469 participating global leaders consider all but a handful of 50 global risks about equally probable. In fact, there are very similar distributions of probability estimates for things that are already happening, like the proliferation of weapons of mass destruction, deeply rooted organized crime or a rise of cronic diseases (the inevitable consequence of rising life expectations), versus largely imaginary risks like the vulnerability to geomagnetic storms or unwanted results of nanotechnology.

On the one hand, this shows a general problem with the use of standardized scales in surveys. There is, of course, a tendency towards the middle of the scale, and asked for numbers, different participants might actually assign very different numbers to a “medium” probability. Even the same participant might think of very different numbers for a “medium” probability dependent on the category the risk is assigned to.

But the strange probability distributions also show something else: We are simply not very good at estimating the probability of future events, especially if they are rare or even unprecedented. In fact, the only future events that we can assign a probability to with a certain degree of confidence are events that recur quite regularly and where there is no reason to expect the systematics to change. And, of course, any complicated probability calculations, most notably the value-at-risk approach commonly used in risk management, are voodoo if they hide the fact that the input probabilities are wild guesses.

Dr. Holm Gero Hümmler
Uncertainty Managers Consulting GmbH