I recently ran across a 2012 article from The Atlantic called The 11 Ways That Consumers Are Hopeless at Math. The title of this article hooked me, and as I began reading I found that there are indeed a few ways in which consumers misunderstand math – and pay the price as a result.

But I also found that most of the so-called “math tricks" that people get caught up in are really better described as number-based psychological hacks, which marketers use to extract every last penny from us that they can.

So it's not so much that consumers are hopeless at math as they are susceptible to being tricked. Which is precisely what a savvy shopper knows how to avoid.

What are some of these mathematical misunderstandings that you should be aware of? And what are some of the most common number-based psychological hacks? Those are exactly the questions we’ll be looking at today, as we finish up the year with a resolution to become even smarter shoppers in the new year.

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How Much Bang For Your Buck?

The article I mentioned from The Atlantic begins with an anecdote that nicely points out one of the biggest flaws in the way the average consumer shops. Namely, that when it comes to pricing and deals, most people go with their gut instead of taking a few seconds to think things through.

Here's the story: Imagine you walk into a coffee shop, take a look at the day’s specials, and see a sign that says, “Today only, your choice—get 33% more coffee for the regular price, or pay 33% less for the regular amount of coffee!” If you were presented with these two options, which would you choose?

In truth, choosing the best deal isn't always just a question of numbers. For example, if you really wanted more than your regular amount of coffee that day, then the extra coffee option would be a fine choice. But that’s not really what I’m talking about here, so let’s rephrase the question a bit to focus on the math.

The real question is this: Which option is the better deal in terms of dollars spent per ounce of coffee? After all, that’s what we’re really talking about when we speak of being a savvy shopper—getting the most bang for your buck.

Most people's gut instinct is that the two deals are about equally as good.

Most people’s gut instinct is that the two deals—33% more coffee for the same price or the same amount of coffee for 33% less money—are equally as good. After all, they both have the same 33% in them. But let’s do the math to see if this assumption is really true.

Imagine your usual 8 oz. cup of coffee costs $2. In this case, the first option gives you about 1.33 x 8 oz. = 10.6 oz. of coffee for $2, while the second option gives you your usual 8 oz. of coffee for a price of 0.67 x $2 = $1.34. That means you pay $2 / 10.6 oz. = 18.9 cents/oz. with the first option, but only $1.34 / 8 oz. = 16.8 cents/oz. with the second.

So, clearly, the second option is a better deal. While it's tempting to get something "free" for the same amount you usually pay (the first option), in this case, getting the amount you actually want for less money is a better deal—especially if you don't really need that extra coffee anyway. And, as always, the math is there to back you up.

What’s the Best Deal?

People prefer to make choices between similar and easily-comparable options.

As I mentioned at the outset, most savvy shopping skills are really less about math and more about avoiding the number-based psychological hacks that marketers (would love to) play on you. While perusing the news this week, I found an article discussing a perfect example of this kind of sneaky hackery.

This example was originally described in Dan Ariely's book Predictably Irrational, in which he talks about running across an advertisement to subscribe to the magazine The Economist. The advertisement lists 3 possible deals:

1. Web-only subscription for $59/year
2. Print-only subscription for $125/year
3. Print + web subscription for $125/year

If confronted with these options, which would you choose? If you’re anything like the 100 MIT students that Dan Ariely posed this question to, you’d pick the print + web subscription for $125/year; 84% of the MIT students chose that offer, while 16% chose the cheaper web-only subscription.

Not surprisingly, nobody chose the middle print-only option. After all, it’s a pretty bad deal compared to the third option, which gives you the same thing plus something extra, all for the same price. But if that middle option is such a bad deal, why did the marketers even bother to include it?

To answer this question, Dan Ariely removed the second option from the list and presented the two remaining options to another group of 100 MIT students. This time, with just the $59 web-only and $125 print + web subscriptions to choose from, 68% chose the cheaper web-only subscription and 32% chose the print + web subscription. Remember, when all three options were available, 84% of students chose the more expensive option and only 16% chose the cheaper subscription.

So why did the marketers include that strange print-only subscription option? Because they also figured out that more people would choose the more expensive subscription if the print-only option was there.

What’s the math behind this? There isn’t any—this one is purely psychological. Sure, there are numbers involved, but all they’re really doing here is pointing out that people prefer to make choices between similar and easily-comparable options – so when they’re given the opportunity to do so, they will.

It may not be rational, but it is very real. And knowing how to spot this kind of trick is a big part of learning how to use math—or at least numbers—to be a more savvy shopper.

Wrap Up

Okay, that’s all the math we have time for today.

For more fun with math, please check out my book, The Math Dude’s Quick and Dirty Guide to Algebra. And remember to become a fan of The Math Dude on Facebook, where you’ll find lots of great math posted throughout the week. If you’re on Twitter, please follow me there, too.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!

Calculator-in-a-shopping cart image courtesy of Shutterstock.

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