The Power of Percentages To Convey Magnitude

Among the many irrationalities that define humans, one is our inconsistent interpretation of numbers. Behavioral economists for years have tallied the many ways by which their fixed meaning can bend and warp depending on context.

Yale SOM’s Joowon Klusowski and New York University’s Joshua Lewis, in an article forthcoming in Management Science, add to this picture by demonstrating the distinct power of percentages.

“Percentages can help convey large increases both compellingly and discriminably compared to equivalent multipliers or absolute numbers,” they write. “For example, if a quantity starts at 100, a change to ‘500% of the original’ feels larger than a change either to ‘5 times the original’ or to ‘500.’” In addition, 500% and 600% feel “more different” from each other than 5 and 6 times, or 500 and 600. This latter finding is particularly surprising, since people are typically less sensitive to differences among larger numbers.

To test this, the researchers ran several experiments in which participants were given the same information packaged in different ways. In one experiment, one group of people was told that their return on a particular investment was 500% of the average, which was $100. Another group was told that their return was $500 compared to the average of $100.

Both groups were asked three questions: “How unusual or surprising do you think the magnitude of this difference is?” “To what extent would you be interested in continuing to invest in this option?” and “What percentage of your investment budget would you allocate to this option?” They ran an identical experiment using credit card points instead of investment returns.

In both cases, people were more surprised by the numbers when they were presented as percentages; they were also more likely to continue investing larger sums, or making more credit card purchases, when the returns were in percentages.

“In other words,” the authors write, “expressing magnitudes as percentages made participants perceive them as larger and report they would behave accordingly, compared to expressing identical magnitudes as absolute numbers.” Another experiment shows people believe increases from 500% to 600%, or 600% to 700%, and so on, are perceived as larger than the same changes with absolute numbers — 500 to 600, or 600 to 700.

The researchers, working to discern what’s driving this result, arrive at two main conclusions. First, people tend to evaluate the magnitude of numbers based on their typical range. Because percentages most often land between one and 100 — something the researchers demonstrate by scraping data from 80,000 articles in the New York Times Business section — numbers like “500%” appear to be beyond the conventional range, and so abnormally large.

Second, when people evaluate changes in magnitude, they first look at the difference in the change and then compare that to a typical range. Looking at a change from 500% to 600%, for instance, people first note that the difference is 100%, and then they compare this to the normal range of percentages, (0-100); and so a 100% difference appears large.

These results speak directly to any occasion when people need to communicate through numbers. A sales manager, for instance, may want to motivate employees with bonuses by using percentages instead of specific dollar amounts. Or an internet provider may want to advertise its new plan speed as 200% of the old 100 Mbps speed, rather than saying it is 2 times the old speed or 200 Mbps. At the same time, offering a premium plan with a speed up to 800% of the old plan would remain enticing given the way people interpret differences.

Whatever the context, Klusowski and Lewis hope that this insight can help people working with numbers “frame information in the most compelling way possible.”

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