Estimating Probability

I have found that asking people to estimate the probability of a risk occurring as a percentage leads to them performing a pseudo-mathematical calculation in their head (System 2 thinking I suspect) which often ends up with a fairly high probability being estimated, especially when compared to base rates.

However, when I ask people to estimate using English language descriptions such as ‘once a week’ or ‘once a year’ then there is no noticeable pause (System 1 thinking I suspect) and the probability estimates tend to be lower and closer to the base rates.

I think by presenting the same question in a more accessible manner it reduces the opportunity for further errors from mental arithmetic to be added above and beyond the inherent uncertainty of the estimator.

There is some interesting work published on the impact of the differing perceptions of language used to agree risks. For example this paper [PDF] presents research in the area and acts as a decent gateway into previous research.

One slight annoyance is the constant need to switch back and forth between the English language and the numerical representations when capturing/presenting and calculating risk analysis. I created the following table to not have to calculate the same numbers over and over again and I’m leaving it here so that it may be useful to anyone else completing similar work.

Expected Rate of OccurrenceMonthly ProbabilityAnnual Probability
Once a week434.00%5200.00%
Once a month100.00%1200.00%
Once a quarter33.33%400.00%
Once every six months16.67%200.00%
Once a year8.33%100.00%
Once every two years4.17%50.00%
Once overy three years2.78%33.33%
Once every five years1.67%20.00%
Once every ten years0.83%10.00%
Once every fifteen years0.55%6.66%%
Once every twenty years0.42%5.00%
Once every twenty five years0.33%4.00%
Once every fifty years0.16%2.00%
Once every hundred years0.08%1.00%