870: Advertising

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Advertising

Title text: I remember the exact moment in my childhood when I realized, while reading a flyer, that nobody would ever spend money solely to tell me they wanted to give me something for nothing. It's a much more vivid memory than the (related) parental Santa talk.

Explanation

This comic describes several annoyances Randall (and many other individuals of the math persuasion) have with advertising. Note that most of these specific examples come from the US.

• "Up to 15% or more" comes from Geico car insurance commercials ("15 minutes could save you up to 15% or more on car insurance."). In terms of the real number line, "up to 15%" describes all of the numbers less than and including 15%, and "or more" describes all of the numbers thereafter (indicated by the union shown above the number line). The more observant will note that this describes literally every number, which means the statement is vacuous: "15 minutes could save you any real number on car insurance" is only slightly more informative than "15 minutes could get you something."
• The second panel references the much-hated practice of putting "FREE" in large letters, followed by an asterisk pointing to a substantial amount of fine print that puts limitations on how the offer works, usually resulting in the offer being essentially worthless (for example, a free drink that would normally cost $1... but only with the purchase of a $6 meal). The math is simply calculating exactly how careful these offers are thought out - the simple truth is that companies advertise because they want money, and giving away something for nothing is not a way of making money, unless there's something else behind it.
• Some sales are based on a scaling percentage rate - for example, all items are 20% off, but if you spend more than $200, you get 50% off instead. (And you can keep going from there.) These are almost universally proclaimed with a phrase similar to "The more you spend, the more you save!" This is objectively false, of course, as "spending" is the opposite of "saving." Although passing a certain threshold will, in fact, reduce your total sale price, it will immediately go up again as you continue to buy more stuff, which is ultimately the goal of the advertisement. Remember, companies don't try to save you money for charity, they do it because it makes you spend more there and less elsewhere.

As a bit of trivia, the filename of the image (mathematically_annoying.png) differs from the name of the comic (Advertising). As it turned out, many (perhaps overly-zealous) adblockers took offense to an image named "advertising.png," so Randall renamed the image to accommodate those people.

Transcript

Mathematically Annoying Advertising:

[A union B = {x:x <= 15 or x > 15} = {R}]

[line graph representing the above equation]

When discussing real numbers, it is impossible to get more vague than "up to 15% or more".

["FREE*" in large text, with substantial illegible fine print]

If someone has paid $x to have the word "free" typeset for you and N other people to read, their expected value for the money that will move from you to them is at least $(x / (N+1))

[graph representing inverse relationship between "amount you spend" on the y axis and "amount you save" on the x axis]

It would be difficult for the phrase "the more you spend the more you save" to be more wrong.

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