Off by 100% Bias

Today I learnt about Off by 100% bias.

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.

const number = 50;
const delta = 25;

const final = number + delta; // 75;

const percentage_increase = delta / number; // 25 / 50 = 0.5; i.e 50%;
const x_times = final / number; // 75/50 = 1.5; i.e, 1.5x

This is even more evident in increases of more than 100%;

const number = 50;
const increase = 75;

const final_number = number + delta; // 125;

const percentage_increase = delta / number; // 75 / 50 = 1.5; i.e 150%
const x_times = final / number; // 125 / 50 = 2.5; i.e 2.5x

The true reason is that the factors in percentage are the previous number and the delta. Whereas, when you calculate x times value, you factor the final number and the previous number.

The final number and the previous number will have a higher difference. Therefore, showing x times value will appear to have a higher magnitude.

Sources

https://coxtoday.smu.edu/2022/02/28/consumer-marketing-math-even-the-numerate-are-off-by-100/