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Consumers face difficulties when processing percentages, especially given their variety of uses in today’s information-heavy, marketing- and data-rich environment. In new research, assistant professors of marketing Matthew Fisher and Milica Mormann shed light on a surprising, persistent mistake that consumers make with important consequences. The “off-by-100%” bias the authors observe impacts purchase decisions, with implications for everyday shopping decisions and even on trading with platforms like Robinhood and E-Trade.

According to Mormann, this effect is especially interesting in the context of today’s “attention economy” — a world in which people have limited amounts of attention to allocate across tons of information. “When consumers see ‘130% more,’ they likely do not put much thought or effort into actually computing what it means,” she adds. Instead, the consumer’s mind “jumps” to the first thing that makes sense, the straight “30% more” calculation.

Communication about percentage changes greater than 100% are pervasive in the marketplace. “Here’s a little shift in how people will invest, based on some minor feature. It’s not like they’re off by 1%; it’s this whopping 100%,” says Fisher.

Fisher and Mormann tied the percentage challenge to financial incentives to see if that focused the attention of people with skin in the game. As a default, they say, people tend to think of percentage information like slices of a pie, using the “of” mentality. How much of the pie is that? My investment portfolio is worth $100,000. If you say it’s grown 90%, people can do that math. $100,000 x .9 = $90,000. We use relative size, the pie concept, versus relative change. But if you say the portfolio has grown 110%, they are likely to think it’s just 10% more, or $10,000. However, 110% is $100,000 X 100% = $100,000 plus the $10,000 added to the principal of $100,000 (100 + 100 + 10 = 210). That is 2.1 times the original $100,000, or $210,000.

Fisher caught himself making this very mistake. He thought: Is 100% more than 10% more? Was it 1.10 x 100 or 2.1 times more? “As a trained researcher, if I’m having to pause to work through such a basic question, I was wondering if it tripped people up,” Fisher recalls. The authors observed from their bottom-up process, and six studies later, they found this was trickier than it should be. It happens frequently.

“Relative change is where people have problems, defaulting to basic thinking,” he says. Part of the problem is that there are numerous usages of percentages. The relative change usage represents one of the most complex usages of percentages and, even after being taught how to compute it, people struggle with providing accurate estimates. While these two usages may appear similar (e.g., “125% more” vs. “125% of”), they lead to vastly different magnitudes.

Relative change, such as 125% more, leads to magnitudes 100% larger than those of relative size (i.e., 25% more). Their research indicates that when consumers encounter percentage changes greater than 100%, they tend to incorrectly apply the relative size usage, which utilizes part-whole logic, instead of the appropriate relative change usage. This leads many consumers to systematically underestimate percentage changes greater than 100% by exactly 100% (e.g., computing “25% more” runtime instead of “125% more” runtime) — the phenomenon they call the “off by 100%” bias.

Marketers and policymakers communicating numerical information should be aware in presenting information or statistics, say Fisher and Mormann. People tend to overestimate or underestimate percent-related numbers. Bottom line: The off-by-100% phenomenon is tricky and persistent. The paper, “The Off by 100% Bias: The Effects of Percentage Changes Greater Than 100% on Magnitude Judgments and Consumer Choice,” is forthcoming in the Journal of Consumer Research.