# 870: Advertising

## [edit] Explanation

This comic pokes fun at some advertising tricks, analyzing them mathematically.

- "Up to 15% or more" is a reference to the Geico car insurance commercials: "15 minutes could save you up to 15% or more on car insurance." "Up to" means "less than or equal to," so the phrase means "less than, equal to, or more than 15%," which is a tautology.

- The first line uses notation from set theory and reads out as: The union of sets A and B equals the set of all x, such that x is less than or equal to 15, or greater than 15, which equals the set of all real numbers.

- Below is a number line (with the numbers being interpreted as percentages) the black dot indicates that the number 15 is included, and the white dot indicates that 15 is not included, but only strictly bigger numbers.

- Geico's ad is also referenced in 42: Geico

- Some things in life are free. However, typically not those aggressively advertised, with a capital "free!" splashed right over the ads, followed by a small asterisk, indicating the presence of a fine print, ensuring that they are only technically not guilty of false advertising. (Get a
**FREE*** drink!)

- The little formula Randall gives, is to calculate the least amount of money that they expect to make from you. The suggestion is that they expect their income from the ad to be more than what they paid for it. (*with the purchase of a $6 meal)

- 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 30% off instead, and so on. These are almost universally proclaimed with a phrase like "The more you spend, the more you save!" This is of course nonsense, as "spending" is the opposite of "saving", and the deal is there to make you spend more.

- Note that an alternative phrasing "The more you buy, the more you save" is not strictly a contradiction. In some situations, the total number of items you intend to buy may place you just below the spending threshold that would qualify you for an additional discount; you can strategically buy additional items to place you just past the threshold. Despite buying a greater quantity of items, after the discount is applied, you will have spent less money, and thus saved more. (Though savvy retailers will attempt to avert this by placing this exploitable range higher than the cost of what any consumer reasonably needs, forcing them to spend more to qualify for the discount.)

- Or, "The more you buy, the more you save" just means that that the more discounted products you buy, the more money you save as opposed to buying them at list price. For things we will buy anyway (e.g. food), it may be true.

For those who don't celebrate Christmas, Santa Claus is a mythical person responsible for delivering presents to good children on Christmas Eve. Randall explains in the title text that his realization of the middle panel is more vivid than when his parents first told him Santa Claus was not real. Although most small children are traumatized after learning Santa Claus is not real, it is a testament to Randall's level of geekiness that he is more concerned with the first revelation.

## [edit] Transcript

- Mathematically Annoying Advertising:

- A ∪ 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.

## [edit] Trivia

Randall changed the image name from advertising.png to mathematically_annoying.png, since adblocking extensions interpreted it as an ad and made the comic blank. He had the same problem again just three months later with 906: Advertising Discovery.

**add a comment!**

# Discussion

But the Geico commercial doesn't say up to, it says 15% or more... ~Jfreund

- That may depend on your region. 108.162.216.30 03:24, 30 November 2013 (UTC)
- Saying that something "could save you 15% or more" and saying it "could save you
*up to*15% or more" are the same thing. Both statements take into account the very real possibility that some percentage less than 15 could be saved.Orazor (talk) 13:37, 21 July 2014 (UTC)

Not to mention that Geico says "**Could** save you..." (In combination with "up to", the "could" should be "will".) Z (talk) 03:09, 18 June 2014 (UTC)

A justification for "The more you buy, the more you save" is that the more discounted products you buy, the more money you save as opposed to buying them at list price. For things we will buy anyway (e.g. food), it may be true. --Troy0 (talk) 20:01, 6 July 2014 (UTC)