870: Advertising

Explain xkcd: It's 'cause you're dumb.
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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.
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.


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

  • "Up to 15% or more" comes from Geico car insurance commercials: "15 minutes could save you up to 15% or more on car insurance.". Some afterthought shows that the statement is a vacuous truism. They could even safely go wild and exchange the 'could' for a 'will'. It seems like they are saying something about the difference in the prices they offer compared to the prices of their competitors. The problem is just that "up to 15%" covers saving nothing at all, or even the scenario in wich they rob you of all your money and you "save" something like minus a few thousand percent (in comparision to staying with your current car insurance).
The first line of the comic 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, wich 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.
  • Some things in life are free. However, typically not those agressively advertised, with a capital "free!" splashed right over the ads, followed by a small asterisk, inticating the presence of a fine print, ensuring that they are only tecnically not guilty of false advertising. (Get a FREE* drink!)
The little formula Randall gives us, to calculate the least amount of money that they expect to make from you, doesn't quite make sense. The suggestion is that they expect their income from the ad to be more than what they paid for it. However, N*x/(N+1) is slightly less than x. A more apt formula would be x/(N-1). (*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.


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


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.
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Am I confused, or is the the third graph wrong with the independent and dependent variables. 21:06, 5 November 2017 (UTC) But the Geico commercial doesn't say up to, it says 15% or more... ~Jfreund

That may depend on your region. 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)

Added to the article. --Troy0 (talk) 04:10, 25 July 2014 (UTC)
It doesn't work when the items can expire. Cflare (talk) 14:38, 14 August 2014 (UTC)
it does to a certain point- my family can eat a lot of food before it expires, especially if it's something we like. (talk) (please sign your comments with ~~~~)

Brilliant comic Randall. I wonder what your next one is about.

I used Google News BEFORE it was clickbait (talk) 00:20, 24 January 2015 (UTC)

Doesn't the title text imply that Randall realised nothing is truly free and concluded that Santa wanted something from him, prompting his parents to reveal the big secret? (I conclude this based on Randall claiming that these two events are related) 21:16, 25 April 2015 (UTC)

Given that "up to x or more" must necessarily be true, how can it be "construed as false advertising?" Meaningless advertising, yes; false, no. 04:22, 4 September 2015 (UTC)

I just spent 2% of my life looking for the fine print to that FREE* drink (* given during time of kidney-harvesting scam test. Limit one per customer. No purchase necessary to win. Please see rules to apply.)Beastachu (talk) 10:33, 13 September 2015 (UTC)

Shouldn't the expression in panel 2 be (x+1)/n, not x/(n+1)? If we define Y as how much each person pays, then the company would earn $YN. YN > X ---> YN = X + 1 ---> Y = (X + 1)/N. 03:26, 18 October 2015 (UTC)

Randall defines N as the number of people other than you who read the flier. Therefore the total number of people who got the flier is N+1. The advertiser spent $X to produce the flier and assuming that it wants to make a profit on the advertisement, it needs to make at least X/(N+1) on average for each person that gets the flier. Given this your equation should be $Y(N+1) > X not $YN > X because the total number of people is N+1. Obviously Y(N+1) > X ---> Y > X/(N+1), which is exactly what we already found out. I'm not really clear on how you get the transformation YN > X ---> YN = X + 15:19, 11 November 2015 (UTC)

I've always been "mathematically annoyed" by 'X% off' signs (like "40% off"). OFF from what? From the price they asked for beforehand? But they couldn't sell this particular unit for that price; maybe they didn't even sell any unit at that price (and, even if they did, they clearly got more units to sell than available buyers at that price). So, the X% off is from a meaningless seller-wishful-thinking number, not anything resembling a fair market value (where willing sellers and willing buyers meet). Mountain Hikes (talk) 03:32, 6 January 2016 (UTC)