Report Intelligibly on Ratios and Percentages

The people who read your survey report may not be comfortable with purely numeric ratios or percentages. If you write that the odds of an unsatisfactory rating are six times the odds of a satisfactory rating, some readers will draw a blank. Or if you write that the ratio of lawyers to staff in a law firm is 1.4 to 1, it might pause them, puzzle them, and pass them by.

More people are comfortable with whole-number comparisons: for every three partners who favor the compensation system, two partners do not. People can visualize three smiling people with two frowning people more readily than a ratio like 60% favor the system or, worse, 0.60 favor it. Many managers of lawyers would rather hear metrics stated as these so-called natural frequencies. They are most comfortable with “one out of five paralegals favor training budgets” – a way to explain a metric that makes it almost visual and tangible. You can touch the odds on your fingers.

Not as real to many managers is the less familiar abstraction of a benchmark to a percentage – “20 percent of the paralegals favor training budgets.” Even more discomfiting and alien is “0.2 of paralegals favor budgets,” the decimal version. The percentage and decimal forms are sometimes called “single-event statements,” unlike “some number out of another number” and its two actual events. 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 natural frequencies. Most people, in other words, have a more visceral, hands-on understanding if a survey report states one out of five, rather than either mathematical equivalent of 20% or 0.20.

With survey results, findings other than purely descriptive statistics are commonly expressed as a ratio, one number divided by another number. Total legal costs (internal budget plus external spending) divided by the revenue of the company produces a benchmark ratio of legal costs as a percentage of revenue. With such a ratio, a small company stands on the same footing as a large company because of this form of normalizing the result. If readers do not follow that modest mathematics, there’s more to do for them – say something like for every dollar of revenue the company spends approximately four cents on the legal department.

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.” Or, “revenue per lawyer” has a familiar ring, unlike “lawyers per million dollars of revenue.” The facts described are the same but the feel of the two ways to summarize them is different. Perhaps this sense follows simply from familiarity.

Experiments might show that one of those formulations just goes down easier. My hunch is that the first, five lawyers per billion, is simply much easier to grasp (two single digits, 5 and 1), than $200,000,000 per lawyer. Vast numbers with eight zeroes and two commas confound us all.

Further out in the cognitive mists are exponents and roots. It is easy to visualize five shiny pebbles out of twenty-five, but the log to base 10 log of 25 befuddles everyone. Plots that show values on a logarithmic scale confound most readers. Even more confusing are statements of odds: four-to-one paralegals favor technology training.

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.