Difference between revisions of "870: Advertising"

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| date      = March 9, 2011
 
| date      = March 9, 2011
 
| title    = Advertising
 
| title    = Advertising
| image    = mathematically_annoying.png
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| image    = mathematically annoying.png
 
| titletext = 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.
 
| titletext = 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==
 
==Explanation==
This comic describes several annoyances [[Randall Munroe|Randall]] (and many other individuals of the math persuasion) have with advertising. Note that most of these specific examples come from the US.
+
This comic pokes fun at some advertising tricks, analyzing them mathematically.
  
* "Up to 15% or more" comes from {{w|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''."
+
*In the first panel, "up to 15% or more" is a reference to the {{w|Geico}} car insurance commercial catchphrase: "15 minutes could save you up to 15% or more on car insurance", though some do not include the words "up to". The phrase in the comic means "less than, equal to, or more than 15%," which is true no matter whether you save anything or not (it's a {{w|tautology}}).
* 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.
+
:The equation at the top of the panel expresses the same thing using {{w|set theory}} notation.  It reads out as: The {{w|Union (set theory)|union}} of {{w|Set (mathematics)|sets}} A and B equals the set of all x, such that x is {{w|Inequality (mathematics)|less than or equal to}} 15, or greater than 15, which equals the set of all {{w|real numbers}}.
 +
 
 +
:The same is expressed again with a {{w|number line}}; the numbers being interpreted as {{w|percentages}}.  The first range, ending with a black dot, indicates that everything below, as well as the number 15, is included ("up to 15%"). The second range beginning with a white dot indicates that it only includes numbers strictly bigger than 15 ("more than 15%").  The two ranges combined clearly cover the entire number line.
 +
 
 +
:Geico's advertising is also referenced in [[42: Geico]].
 +
 
 +
*Second panel: Whatever is advertised with a big capital "FREE!" splashed over the ad, most likely does not belong to the things truly free.  The small asterisk, indicates the presence of a {{w|fine print}}, ensuring that the advertisers are only technically not guilty of {{w|false advertising}}.  The conditions attached in the fine typically reveals how they will (try to) make money from you.
 +
 
 +
:We are even given a little formula to calculate the average amount of money they expect to make from the readers. The assumption is that they expect to generate at least as much income from the ad as what they paid to print and publish it in the first place.
 +
 
 +
*The third panel relates to sales tactics that 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!" In absolute dollar terms, this is of course nonsense, as "spending" is the opposite of "saving", and the deal is there to make you spend more.  The graph shows this interpretation - spending zero money implies you have saved all your money (the dot where it intersects the X axis), whereas spending all your money implies you have saved none (the dot where it intersects the Y axis).  There is a linear relationship between the two: the amount of money spent, plus the amount of money saved, has to add up to a constant number (your original savings).
 +
 
 +
The title text compares Randall's realization of the "FREE"-fraud to the revelation that {{w|Santa Claus}} is not real.
  
 
==Transcript==
 
==Transcript==
 
:Mathematically Annoying Advertising:
 
:Mathematically Annoying Advertising:
  
:[A union B = {x:x <= 15 or x > 15} = {R}]
+
:A B = {x:x 15 or x > 15} =
:[line graph representing the above equation]
+
:[line graph representing the above equation.]
 
:When discussing real numbers, it is impossible to get more vague than "up to 15% or more".
 
: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]
+
:["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))
 
: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]
+
:[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.
 
:It would be difficult for the phrase "the more you spend the more you save" to be more wrong.
  
{{comic discussion}}  
+
==Trivia==
<!-- Include any categories below this line-->
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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]].
 +
 
 +
{{comic discussion}}
  
 +
[[Category:Charts]]
 +
[[Category:Line graphs]]
 
[[Category:Math]]
 
[[Category:Math]]
[[Category:Comics with charts]]
 

Revision as of 12:15, 5 March 2018

Advertising
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.

Explanation

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

  • In the first panel, "up to 15% or more" is a reference to the Geico car insurance commercial catchphrase: "15 minutes could save you up to 15% or more on car insurance", though some do not include the words "up to". The phrase in the comic means "less than, equal to, or more than 15%," which is true no matter whether you save anything or not (it's a tautology).
The equation at the top of the panel expresses the same thing using set theory notation. It 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.
The same is expressed again with a number line; the numbers being interpreted as percentages. The first range, ending with a black dot, indicates that everything below, as well as the number 15, is included ("up to 15%"). The second range beginning with a white dot indicates that it only includes numbers strictly bigger than 15 ("more than 15%"). The two ranges combined clearly cover the entire number line.
Geico's advertising is also referenced in 42: Geico.
  • Second panel: Whatever is advertised with a big capital "FREE!" splashed over the ad, most likely does not belong to the things truly free. The small asterisk, indicates the presence of a fine print, ensuring that the advertisers are only technically not guilty of false advertising. The conditions attached in the fine typically reveals how they will (try to) make money from you.
We are even given a little formula to calculate the average amount of money they expect to make from the readers. The assumption is that they expect to generate at least as much income from the ad as what they paid to print and publish it in the first place.
  • The third panel relates to sales tactics that 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!" In absolute dollar terms, this is of course nonsense, as "spending" is the opposite of "saving", and the deal is there to make you spend more. The graph shows this interpretation - spending zero money implies you have saved all your money (the dot where it intersects the X axis), whereas spending all your money implies you have saved none (the dot where it intersects the Y axis). There is a linear relationship between the two: the amount of money spent, plus the amount of money saved, has to add up to a constant number (your original savings).

The title text compares Randall's realization of the "FREE"-fraud to the revelation that Santa Claus is not real.

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.

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.


comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!

Discussion

Am I confused, or is the the third graph wrong with the independent and dependent variables. 172.68.132.95 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. 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)

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. 108.162.237.163 (talk) (please sign your comments with ~~~~)
It's true if calculated in price-per-unit-bought. A 100-pack of something often costs less than 10 packs of 10 each. Still, without the "per item" qualifier, it's not really a true statement.172.70.55.16 16:18, 19 July 2022 (UTC)

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) 141.101.104.49 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.173.245.50.174 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. 162.158.255.144 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 + 1.162.158.60.11 15:19, 11 November 2015 (UTC)
I just came across this comic and noticed, that the 2nd one is not necessarily true, as the add can also have influence on other people who not read it (e.g. me telling my brother to come with me to the great place offering free oranges), and also they do not care if it is money moving in from me or other places. If they e.g. just harvest my data, the money flows from a company buying my data to them.--Lupo (talk) 15:26, 12 December 2019 (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)

You forget, that the fair market value is usually found in a process, in which the buyer goes in with a low price and the seller with a high price, until they find the "fair" price, somewhere in between. Part of this process can be to advertise, as a seller, that you are now willing to try finding the sweet spot x% below what was originally asked. So this is very much in line with the usual concept of supply and demand. --Lupo (talk) 08:23, 22 October 2019 (UTC)
At least one local art supplier offers 40% off list price for custom frames. All the time. (Except when they run a 60% off sale.) It's % off of list price, not necessarily what it would actually be sold for. Unfortunately the same is true of some medical billing in the US - most basic blood tests are "billed" for $200+, but the insurance discount brings it down to <$20, before the insurance company pays anything.172.70.55.16 16:18, 19 July 2022 (UTC)
You could also have a "loss leader" kind of situation, where the reduced price does represent a loss to the seller, as an attempt to attract customers who may also purchase other, more profitable items. L-Space Traveler (talk) 14:26, 6 November 2022 (UTC)

The one that annoys me is "save x% off Y!" You would SAVE x% ON something, or GET x% OFF something - not SAVE x% OFF! L-Space Traveler (talk) 14:26, 6 November 2022 (UTC)

I think I actually mentioned this in an Edit Summary for something, recently (not sure where or when, except probably this wiki, and no expectation of it actually even being noticed... But, as we're talking about it now...): "Up to 50% off!" Effectively "We may or may not discount anything, but certainly there's nothing at less than half the pre-deal price...", but it pulls the mental levers in a more attractive way than it should do. (And is a subset of the "Up to 15% or more" item in the first panel, as I have just realised by looking at the comic related to this Talk page.)
On the 'really the wrong way round' front, I have a mental flinch whenever I see a bus service plastered with something like "<this scheduled service> Every 15 Minutes Or More!" - ironically, often seen on a Sunday when its route is actually reduced to an arrival every hour (which is indeed more than 15 minutes!), for a far shorter total timespan of the day, or the fancy route-branded bus is actually conspicuously doing the Sunday service of a completely different route (also at lowered frequency) than its weekday/possibly-Saturday commuter/shopping/etc provision, just because unspecifically-liveried vehicles are being maintained and this is one of the free ones currently available and unnecessary for its branded-route. 172.70.90.172 16:26, 6 November 2022 (UTC)