Many managers of law departments would rather hear metrics stated as so-called “natural frequencies.” They are most comfortable with “one out of five times we prevail on this motion”– a way to explain a metric that makes it almost visual, tangible. You can touch the odds on your fingers. Not as real to many managers is the less familiar abstraction of a same metric to a percentage – “20 percent of the time we prevail.” Even more discomfiting and alien is “0.2,” the decimal expression of the same amount. The percentage and decimal forms are sometimes called “single-event statements,” unlike “some number out of another number” and its two actual events. Most people, in other words, have a more visceral, hands-on understanding if a lawyer estimates two chances out of 10 of being sued, rather than either cognitive functions of 20 percent or 0.20.
Evolutionary cognitive psychologists offer an explanation. They believe our brains developed to cope with a savannah that had observable and countable events; if two out of three waterholes were full, it was advantageous and normal for our forebears to favor use of the natural-frequency way of stating that fact. Statistics make more immediate sense when that tactile phrasing is used. Mathematical fluency tends to be a latent gene, so to speak, and so it is harder for many people to grasp and manipulate analytic metrics.
The expression for Pareto’s famous namesake, the 80/20 rule, gives the point another spin. It is shorthand for something like “8 out of 10 of our dollars went to 2 out of 10 of our firms.” When unpacked that mouthful doubles up on naturalistic frequencies.
Something cognitively similar may be going on with the difference in immediate comprehension between “lawyers per billion dollars of revenue” and its fraternal twin “hundreds of millions of dollars of revenue per lawyer.” The facts described are the same, but the feel of the two ways to summarize them is different.
Experiments might show that one of those formulations just goes down easier. My hunch is that the first, five per billion, is simply much easier to grasp (two single digits, 5 and 1), than $200 million per lawyer. Vast numbers with eight zeroes and two commas confound us all.
Even further out in the cognitive mists are exponents and roots. To an evolutionary advocate, there were no correlates to those abstract functions back in the cave days. It is easy to visualize five shiny pebbles out of twenty-five, but a base 10 log representation of 25 befuddles everyone. All this is to say, depending on your audience and your numbers, choose the expression that conveys your numbers in the way most easily and naturally understood.