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

Specifically, communication about percentage changes greater than 100% are pervasive in the marketplace. They are prolifically used in consumer goods, real estate, and personal finance, as well as in market trends analysis in energy data and expressions of customer growth. “You give people these numbers like 110% increase and they immediately, intuitively think it’s a 10% increase,” Fisher says, “they are off by an entire 100%.” This finding is rare in that many studies will show these effects on the margin, he adds. “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%.” This is striking.

According to Mormann, this effect is especially interesting in the context of today’s “attention economy” – a world in which we have very limited amounts of attention to allocate across tons of information. “When a consumer sees “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.

Though percentages are commonly used in marketing communications, little is known about how consumers process percentage changes greater than 100%. Given that this information influences consumer judgments and choice, how managers effectively communicate about these magnitudes is important. “Even numerate people get sidetracked by this phenomenon,” notes Fisher. “We find that roughly 50% of consumers, according to our studies, flat out get it wrong. That’s a large proportion of consumers missing by a lot.”

Previous research has shown that consumers sometimes employ low-effort heuristics, or rules-of-thumb, when offers include percentages instead of dollar amounts. Originally developed in ancient commercial contexts, then used to represent parts of a whole, an absolute plethora of percentage uses now describe many forms of relationships in our stats-laden world.

**Doing the math**

In the research, Fisher and Mormann tied the percent challenge to financial incentives to see if that focused people’s attention with skin in the game. Even then, it’s not just laziness as to why people get it wrong, says Fisher. As a default, we think of percent 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 going 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, that this was trickier than it should be. It happens persistently.

“Relative change is where people have problems, defaulting to basic thinking,” he explains. 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 (ie., 25% more). Thus, the authors show in their research, 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.

Consumers face difficulties processing percentages because they describe many forms of proportional relationships, each reflecting a different mathematical reality, the authors write. The authors focus on two distinct usages of percentages. Consider a consumer shopping for a pair of new headlight bulbs for her car. She examines a product on Amazon that claims a particular bulb gives “130% more light on the road” compared to a standard bulb. In this case, a product attribute (the length of the light beam cast on the road in front of a car, in feet) is communicated in the form of *relative change*. That is the magnitude of change relative to an initial quantity. Here, the amount of change, i.e., “130% more”, needs to be added to the initial 100%, or 60 feet of light cast by standard bulbs. So, the bulb gives 230% of the initial amount (100% + 100% + 30%) or 2.3 times as much light, which is 138 feet of light on the road.

Alternatively, percentages can also communicate *relative size*, that is, a size relative to an initial quantity. For example, a headlight bulb may offer “130% of the light” on the road compared to a standard bulb that projects 60 feet of light. This statement tells consumers that the first quantity is 30% larger than the second. For example, the bulb gives “30% more” or “1.3x” as much light, which equals 78 feet of light on the road. Consumers simply apply the relative size usage instead of the appropriate relative change usage, being “off by 100%” in their magnitude judgments.

So an understanding of percentages, while a show of numeracy, the off-by-100% biasexists, whether one is numerate or not, conclude the authors. Marketers and policymakers communicating numerical information should be aware in presenting information or statistics. People tend to overestimate or underestimate percent-related numbers. Bottomline: 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” by Marketing Professors Matthew Fisher and Milica Mormann of Cox School of Business, Southern Methodist University, is forthcoming in *Journal of Consumer Research*.

*Summary by Jennifer Warren.*