870: Advertising

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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 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.


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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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)

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