Reported June 2007

BACKGROUND: Which of the following two sales pitches is more likely to convince you to spend money: “Buy one, get one free” or “Buy two and get 50% off”? The two are the same, but most consumers would find the first offer more appealing. Now a physicist at Loyola College in Baltimore has applied his math skills to all sorts of sales pitches – from houses, credit cards, insurance, and zero-percent financing – in a new book, The Two-Headed Quarter: How to See Through Deceptive Numbers and Save Money on Everything You Buy.

THE CONCEPT: Sales pitches are designed to manipulate or trick consumers with numbers, taking advantage of the fact that many of us are uncomfortable with numbers – and yet we trust them. Depending on how the figures are presented, you might believe you are saving money, when in fact you are paying the same, if not more. Three years ago, physicist Joseph Ganem looked at credit-card solicitations offering low introductory rates. He factored in the transaction fees detailed in the fine print and concluded that consumers would pay about the same under the new card as they would using their old card.

BIG NUMBERS ARE BETTER: People respond positively to very big numbers, so an internet provider might run a promotion offering 1025 hours of free Internet access. The small print reveals the offer is only good for 45 days. There are 1080 hours in 45 days, so customers would have to use their Internet access nearly 24/7 in order to take full advantage of the offer. Similarly, a food label that says a product is “90% fat free” will be more appealing than one that says it has “10% fat.” People also lend more credence to exact numbers, preferring “50%” to the less specific “half.” But it’s easy to confuse precision with accuracy, such as with food packaging. Compare a soft drink that has 39 grams of sugar and 140 calories per serving to a fruit drink with 31 grams of sugar and 120 calories. But the serving size of the soft drink is 12 ounces, while the fruit drink is only 8 ounces. So ounce for ounce, the soft drink has fewer calories and less sugar than the fruit drink.

LOSS AVERSION: Human beings are psychologically averse to losses, so sales pitches are often framed to turn a loss into a perceived gain: for example, zero percent financing. If a car costs $15,000, and you pay cash, you receive a $2000 rebate. The car actually costs $13,000. If you need to borrow to buy, you pay $15,000 but get zero percent financing for three years. The car still costs $13,000; the extra $2000 is essentially a finance charge paid up front. But people can be led to believe it is a gain, and will be more likely to buy the car.

The American Mathematical Society and the Mathematical Association of America contributed to the information contained in the TV portion of this report.

If you would like more information, please contact:

Joseph Ganem, Ph.D., Physicist
Loyola College
410-617-2048
jganem@loyola.edu

For more tricks with math (and how to avoid them):

American Mathematical Society
Providence, RI 02904-2294
1-800-321-4267
www.ams.org

Mathematical Association of America
Washington, DC 20036-1358
1-800-741-9415
http://www.maa.org

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