2892: Banana Prices

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Banana Prices

Title text: It's a linear extrapolation, Michael. How big could the error be? 10%?

Explanation

This explanation may be incomplete or incorrect: Created by an IMPERIAL BANANA THERMAL DETONATOR - Please change this comment when editing this page. Do NOT delete this tag too soon. If you can address this issue, please edit the page! Thanks.

‘It’s one banana, Michael. What could it cost, $10?' is a line from an Arrested Development episode (Season 1, Episode 6, "Charity Drive", 2003) that became well known as a meme used to mock out-of-touch elites. The character who spoke this line – Lucille Bluth, a rich socialite – didn't know whether a banana cost $10 in 2003 because she never did any grocery shopping "because we have people for that." According to the graph, the banana price at the time of that episode was actually just under 25 cents, and the price "now" (2024) is around 30 cents.

This comic illustrates a whole suite of ways to violate statistical best practices and to 'lie with data.' And the additional use of an "unreliable narrator" device gives this comic several layers of meaning. The caption writer, in this case, is an unreliable narrator who is also humorously out-of-touch like Lucille Bluth, but in a different way. They speculate that the error in their result is less than 10%, even when their own three predictions (from 120 years to 220 years) differ by over 80%.

To initially mislead the reader and to ultimately demonstrate how easy it is to be fooled by various methods of 'lying with data,' Randall impressively combines several statistical 'sins' in one graph, such as:

• false precision
• extrapolating an order of magnitude deeper into the future than is advisable
• referring to a logarithmic extrapolation as linear
• ignoring historical norms and high variability in making future predictions
• articulating multiple potential scenarios that are actually highly correlated with each other.

At first, the comic looks like a wry observation that the irony of this sitcom line will be obsolete in a century or two. This comic shows a graph of three, different, projected, future prices for bananas over the next 250 years. One extrapolates from the current price and inflation rate in general. Another uses the more specific inflation rate for fresh fruit, which is made from less data but is more relevant than a general rate dominated by the cost of housing. The final line is an extrapolation from 50 years of historic banana prices. The comic seems to say that it will take a century or two before the irony of the sitcom quote becomes anachronistically meaningless.

(While these extrapolations look linear, they are in fact logarithmic, since a linear extrapolation on a graph with a logarithmic scale is actually a logarithmic extrapolation. The graph is log-linear, with price as a logarithmic scale on the vertical (left) axis, which makes it possible to visualize exponential growth as a straight line.)

The accuracy of this prediction depends on these particular extrapolations being valid. The "general inflation rate" line assumes an average rate of around 3%, matching the historic average in the USA. However, assuming a constant inflation rate for the next 200 years is extremely simplistic. Inflation fluctuates quite a lot in response to economic factors and government policies. It was as high as 6% during recent rounds of economic stimulus and caused fears of hyper-inflation.

Besides getting the inflation rate wrong, another way the extrapolation could be wrong was if – in the next 100 years – there were a massive banana crash or extinction, as has happened before, due to the banana's lack of genetic diversity. In which case, the sharply reduced supply of bananas could send the price past $10 very quickly.

An additional example of "lying with data" is the use of a logarithmic graph for economic data. It's highly unusual to graph economic data logarithmically, as economic variables rarely show exponential change over time – and even when they do, it's easier to show that change on a normal linear graph. If this same set of extrapolations were shown on a linear graph, the absurdly accelerating slope of the extrapolations would give away how imprecise these extrapolations are.

(The main exception is financial market analysis, in which some traders like to use logarithmic graphs as one of many tools to perceive and predict hidden price trends that don’t show up in normally scaled charts.)

Another, more subtle, illustration of false precision is the graph's use of three different models for the extrapolation of banana prices. At first glance, using three different trend lines seems to show a "range" of potential scenarios and acknowledge the prediction's uncertainty. However, all three underlying trends are correlated: general inflation is highly correlated to fruit price inflation and banana price inflation. Using three different trends that are all highly correlated is scant better than using just one.

Finally, the reference to "BLS/St. Louis Fred" – a widely respected source of economic data – appears to lend credibility to the graph, but the only data that is truly credible is the historic price data. It's one more example – citing respected sources – of a way to fool unsuspecting readers into giving a prediction more credibility than it deserves.

The title text is a wink from Randall about this unreliable narrator by using the ignorant tone of Lucille Bluth to wryly acknowledge that, in fact, that error of the extrapolations greatly exceeds 10%. Just as Lucille was very wrong about a $10 banana (a price threshold), so too is the speaker of the title text very wrong about the 10% error (a proportional change). It does so in the form of a meta-joke about the false precision of extrapolations, while continuing the theme of the speaker's extreme ignorance. Assuming that the error couldn't be more than 10% shows that the Lucille speaker continues to be hilariously off-base, presuming far more accuracy from a multi-century prediction than is warranted.

Overall, the comic is a clever commentary about the false precision of extrapolation and how easy it is to be fooled by it, illustrating its point by initially misleading the reader with its own false precision, and wrapping it all in a pop-culture reference. Any economic extrapolation into the distant future based on past data points is just an educated guess likely to be quite wrong, with an expected error far in excess of 10%. (A rare example of a field in which 75-year predictions are highly accurate is demographic age charts, since the number of babies born this year is causal of the # of 75-year-olds alive in 75 years.)

Log scales and their peculiarities are a recurring xkcd theme, and this is the second comic in a row to play with logarithms (the prior one being 2891: Log Cabin). It's also the second comic in the last four to involve predictions across centuries (i.e. 2889: Greenhouse Effect). Another comic whose subject is extrapolation is 605: Extrapolating. This comic looks a lot like 1007: Sustainable.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[A graph with the x-axis showing time, from the years 1950 to around 2275. The y-axis is a log scale showing the price of a banana from $0.10 to over $10.00. A label called "Price of a banana (BLS/St. Louis Fred[1])" show a rising trend in the price of a banana. There are two dots on that trend. One is labeled "Episode airs" and the other one "Now". 3 extrapolations shown as dashed lines labeled "General inflation rate", "Fresh fruit price trend" and "Banana price trend" extend until reaching the $10 mark, indicated by 3 dots.]

[Caption above the graph:] "It's one banana, Michael. What could it cost? $10?"

[Caption below the panel:] That line probably has another century or so left.

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Discussion

Is it a linear extrapolation? Or does it only appear so because the Y axis is logarithmic? Inflation is logarithmic, since it's expressed in percentages. Barmar (talk) 17:04, 9 February 2024 (UTC)

Well, the lines of extrapolation are (invoked as) linear, by dint of the height above the baseline being preconverted to a logarithmic function of the represented axial value. Rather than taking exponential-style extrapolation of data and 'happening' to linearise it through the subsequent transformation, it is almost certainly going to have been merely establishing some trend point(s) through which such an exponential would pass and using that to directly guide the linear plot that (on the converted scale) is the functionally equivalent result to doing it with every point. 172.71.178.77 17:26, 9 February 2024 (UTC)

OK, so... my reading of the comic after studying it for a while is that Randall is making a sophisticated meta-joke about 'lying with data" and unreliable precision and how easy it is to be fooled. He knows, of course, that this graph's "prediction" is completely arbitrary and is likely to be VERY wrong. He is intentionally breaking a whole set of statistical best practices in this graph. If so, I think this comic is one of the most-layerd and subtle he's ever done. You have to know a lot about statistical best practices to see what he's really doing here. .. What's so interesting to me is him using the voice of the caption-writer -- usually good ol' reliable Randall -- to actually be the butt of the joke. ... If someone wants to claim that this is more sarcasm than "unreliable narrator," I guess that's a reasonable interpreation, but the use of the word "probably" in the caption makes me think we're supposed to take the caption-writer seriously. Laser813 (talk) 18:38, 9 February 2024 (UTC)

I don't know, I think meta-humor is typically reserved for the title text. I think the comic is a cheap gag about bananas and that the line will eventually become outdated, and and it's oversimplified so that the logic of his joke is clear. The caption is written in a similar speech style to the quote, and I think the title text is Randall's admission that the graph isn't the best. I don't think flaws in the graph are intentional as part of some humor on graph design, just a consequence of making the graph clear enough to not be distracting from the joke. Kittyabbygirl (talk) 21:04, 9 February 2024 (UTC)

I think the comic is about how obvious it is that wealthy people are influencing our societies, because they know nothing about our lives, and then kind of how you can comment on that without as much lashback if you criticize yourself as well. Or course, people are getting less and less skilled as we more and more do what we are told and influenced instead of what we would find on our own. 108.162.245.168 01:25, 10 February 2024 (UTC)

Bananas are a special case: Basically we have a monoculture. With no genetic variations, bananas are highly vulnerable to the emergence of specialized pathogens and currently Panama 4 is threatening the Cavendish banana: https://www.theguardian.com/food/ng-interactive/2022/apr/14/climate-crisis-food-systems-not-ready-biodiversity So trying to fit this question of "will it go extinct soon?" into a smooth inflation price increase might be another butt of the joke

172.71.246.88 18:49, 9 February 2024 (UTC)

Randall is way off-base here, by about an order of magnitude. The episode is about Bluth frozen bananas, which require refrigeration, chocolate, and custom labor; they also do not have the economies of scale of fresh bananas. The AD wiki says the prices are >$1; in "Top Banana," Maeby says they cost at least $1. In real life, frozen bananas cost $5 in LA, $8 at ice cream shops on LA-area beaches. This is a joke similar to the Pulp Fiction $5 milkshake; milkshakes have been much more expensive than that for years. --172.70.207.149 19:12, 9 February 2024 (UTC)

Randall sometimes ignores basic elements about how the real world works in order to make a nerdy joke or point. The comic last week about Black Hat being tracked 8,000 miles away by NIST is a good example of that. The whole thing rests on us entering into his (slightly) alternate universe with him. Laser813 (talk) 20:37, 9 February 2024 (UTC)

The joke set up in the original TV show (here) I think was about the wholesale price of bananas; Lucille says, "What could a banana cost? Ten dollars?". Then Michael replies, "you've never actually set foot in a supermarket, have you?" so certainly he thought she was talking about the banana stand's wholesale input cost rather than what they retail a frozen banana for NZUlysses (talk) 17:53, 10 February 2024 (UTC)

Given that these are a Bluth product, I'd be dubious about how much actual banana is involved in the first place.172.70.90.70 09:25, 12 February 2024 (UTC)

I am tempted to say "Keep the change." "What from a fiver." "Yes the world is going to end." At the time of the radio series, it would have been an excessive amount of change to give away. They did not keep it for the film, when a fiver would barely pay for one of the six beers. 172.69.195.23 19:38, 9 February 2024 (UTC)

given the extinction of Cavendish being imminent is the worth of a banana actually the worth of a banana?

The price of bananas these days is just bananas! 172.71.178.32 15:03, 12 February 2024 (UTC)

Miami fruit sells an 8-10 pound box of rare bananas for $250. At an average size of 5 ounces, that would mean about 30 some bananas, for an average cost of about $8.30 per banana. Given that the size of some of the bananas pictured seems quite small, it may be that some of those bananas can cost upwards of $10... (Miami fruit as sold on superior dishes) 172.70.34.35 18:13, 1 March 2024 (UTC)

You seem to be assuming that larger bananas are worth more... Could be the reverse... ;) 172.71.178.55 20:42, 1 March 2024 (UTC)

Using log scale here is not a joke. It's perfectly legit. Constant inflation is actually an exponential relation. For example, if prices go 10% up every year, in two years they won't be 20% higher but 21% because 1.10*1.10=1.21. And such an exponential relation becomes linear when plotted using a logarithmic y axis.--Pere prlpz (talk) 21:57, 9 February 2024 (UTC)

With 34 Trillion debt I would not expect a US dollar to be worth a tenth of a banana in a time frame of hundreds of years - How far they can kick the can is unknown but I would guess years or at best decades over centuries. "what can not be paid back will not be paid back" A banana is worth a banana - it is the money that is losing value and to sustain this circus that must accelerate. 108.162.241.216 22:33, 9 February 2024 (UTC)

As Pere points out, the logarithmic scale is in fact the correct scale for estimating the uncorrected price of an item, such as a banana. 172.71.103.214 22:40, 9 February 2024 (UTC)

The explanation is needlessly long and on occasion wrong. Some one tried to fix it by adding paragraphs in parentheses. If something is confusingly written or wrong it's generally best to rewrite instead of adding a paragraph. In my eyes the comic is Randall's comment on the fact that agricultural products have become relatively cheaper by having price increases below the inflation rate. This is a long sgandingytrend since the beginning of industrialization and the only reason we can afford new other things than food. --172.71.160.24 07:56, 10 February 2024 (UTC)

"That line probably has another century or so left." There seems to me to be a pun here - 'that line' could refer to either the line(s) on the graph, which cross the $10 threshhold in a bit over century AND to the "how much could it cost" line of dialogue. In a century that line (of dialogue) won't be amusing any more since by that point - assuming the projection is correct - bananas WILL cost about $10, so the irony and humour will become lost.

Is it worth mentioning that Randall has referenced this line before? The seventh citation in the Hot Banana What If? post says "It's 300 quadrillion bananas, Michael—what can it cost, 3 quintillion dollars?" Seems like it could be either in the first line (as proof of the meme being well known) or in the Trivia section. What do y'all think? Magicalus (talk) 15:20, 12 February 2024 (UTC)

Bad stats?

Are these really 'statistical sins'?

Hot take but I agree with comments that it's reading too much into this comic to call it "a meta-joke about lying with data". Here are the supposed "sins" listed:

1. false precision
2. extrapolating an order of magnitude deeper into the future than is advisable
3. assuming that a non-exponential quantity - prices - will grow exponentially
4. referring to a logarithmic extrapolation as linear
5. ignoring historical norms and high variability in making future predictions
6. articulating multiple potential scenarios that are actually highly correlated with each other.

Taking them one by one:

> 1. false precision

Projecting prices hundreds of years into the future is farcical, for sure, but I'm not sure that's "false precision". "False precision" would be saying "on January 6 2254 this joke will finally be stale". But the comic gives a very imprecise (and wrong!) range "another century or so". If anything the precision of the projection is downplayed.

> 2. extrapolating an order of magnitude deeper into the future than is advisable

This one is true, and is the source of the humor.

> 3. assuming that a non-exponential quantity - prices - will grow exponentially

Inflation _is_ an exponential process, _by design_. Monetary policy holds the explicit aim--more or less upheld since the 1980s--to keep long-range inflation within a low and positive percentage around the 2% mark. That is the aim. There are periods of higher (and lower!) inflation but overall, the Fed has been successful at keeping long-run inflation within the target range for the last 40 years or so in which inflation targeting has been the dominant monetary policy paradigm. And growth on a constant percentage rate in a series just _is_ exponential growth; that's what exponential means.

> 4. referring to a logarithmic extrapolation as linear

idk maybe. The graph is on a log scale but a log scale has the quality of allowing us to visualize an exponential trend on a straight (linear) line. That's the beauty of it. I don't think there's a "sin" here.

> 5. ignoring historical norms and high variability in making future predictions

What historical norms are being ignored here exactly? Long-run inflation is fairly stable. To the degree there's a sin here, it's already covered by (2).

> 6. articulating multiple potential scenarios that are actually highly correlated with each other.

idk can anyone find a quote from their preferred statistical Bible to support the idea this is a sin? To my mind, showing that multiple distinct models converge on an approximate answer is a very good way to test convergent validity of a prediction. There are problems with presenting models as independent when they are not in order to give a false impression of a consensus. I don't think using three different inflation series as alternative models is doing that.

So maybe 1 or 2 of the sins alleged are real, imo. NZUlysses (talk) 17:22, 10 February 2024 (UTC)

It looks like parts of this explanation were written by ChatGPT. The unnecessary bulleted list, "looks like a wry observation", "using the ignorant tone [...] to wryly acknowledge", "overall", "in truth". This is an unusual tone for this wiki but not unusual for a chatbot.

Its kind of hilarious. Maybe we should keep it. Ystem (talk) 18:26, 10 February 2024 (UTC)

The explanation (as of this writing) is wildly overcomplicating things. The simple, straightforward idea that it will probably take a century for Lucille to be correct is the most likely intent of the comic. 172.71.174.225 15:04, 11 February 2024 (UTC)

I disagree that correlations of projections are a problem. Often the future projections are "best case, worst case, most probable case", or at least 25th/50th/75th percentiles of a whole glob of simulated predictions, and will be highly correlated (but divergent, thus representing a potential uncertainty or highlighting when actuality confounds even the edge conditions).
In this graph, those are three trends that might (in different amounts of specificity) direct the onward trend of the actual figure, depending upon what factors dominate. Bananas might be 'less price-rising than fruit', which in turn might be 'less price-rising than the general economy' (taking the projections at face value), but if the relative inexpensiveness of bananas hits a 'floor' (by general fruit terms or the wider economic issues) and fails to be disproportionately discounted as it clearly(!) has been then it would be forced to 'jump tracks' to a similarly (but more so) rising cost now parallel to where the successor projection was leading. (That's before other price-shocks like Banana Extinction or Inflationary Recession make the naïve trends of any or all of the lines completely wrong.)
An example of an actually uncorrelated trend would be something Moore's Law-related, which would apparently be allowed here (by the "sin" objections), though it's difficult to say how that would be any more relevent than what actually is there. Of course, understanding (or explanation) of the potentially confounding (and hopefully relevent) co-dependent extrapolations plays a part in this. But this isn't even a significant "bad graph, just for the sake of laughs" element, IMO. If anything, it's the very squiggly nature of the historic data being projected off into 'likely directions' (dominated by the most recent true-instantaneous-gradient, which is clearly curved upards from any historic rolling average) without any consideration that the future-line might turn out to be just as 'squiggly' (except that it might be mostly rattling around between the upper and lower 'estimates', even as their true paths also rattle around... the most litteral 'banana price' trend obviously rewriting itself as the actual banana-price line). 172.69.194.20 16:23, 11 February 2024 (UTC)

I agree with the commenters above, and I removed all the “unreliable narrator” and bad stats stuff. I was assuming he was being “Bluthian” about the whole graph, but now I realize there’s not much evidence for that. Hopefully it’s better now. Laser813 (talk) 21:06, 11 February 2024 (UTC)

Separately: Can non-hyphen-dash editors consider this edit reason as a suggestion. If I see two words separated by just a line, it litterally screams of being a hyphen (even when it is typographically different). I will gladly dash (or even "—") an inadvertent hyphen-as-a-dash (or a two-hyphens-as-a-dash!), but to have no spacing makes it then tend towards dash-as-a-hyphen. And unnecessary when, as in these cases, sometimes a simple commaing will serve the same purpose. And parentheses can also be used when already there's too much commaing to be easily read in, out and across the various commas that might be there, with the advantage of clarifying the ins-and-outs of the rhetorical flourishes. 172.69.194.20 16:23, 11 February 2024 (UTC)

Another meta-joke might be that this whole extrapolation business displayed here is a bit "bananas"... ;-) [no signature]

Hold on, does the joke work as well now as it did in 2003? By my calculations, it only works 75-80% as well. (I got those values by dividing $10 by the actual (estimated) price of a banana now and in 2003. Which is a very scientific way to measure how well a joke works, because it involves numbers.) GreatWyrmGold (talk) 17:07, 13 February 2024 (UTC)

Counter-analysis: if you took the $10 in 2003 and respoke the value as its 2024 (the one and only place I queried on this matter just said $31.15) would the joke be at its original strength?

There are inherently funny numbers/strings of digits. c.f 42, 69, 99.999, maybe, which hold their strength of comedy even whilst they become devalued against buying-power. A simple, strong number-name like "ten" might be still considered the apex of funny compared with the arhythmical "thirty one dollars, fifteen cents", or even the slightly rounded "thirty dollars". "Ten dollars" might be as ok (or the best, given the circumstances) up until it gets too unexceptional to be considered 'wrong enough'. By the time 'true cost' gets to $5, though, we'd have to be looking for a higher wrong-value. (Compare original HHGTTG situation of saying "keep the change" from a fiver, having bought several pints of beer and peanut snacks. Quite the gesture in the '80s. The post-millenium film had to offer a fifty, as a fiver might not even have covered a single pint (and snack) in many bars, and barely would have in all the rest.)

See also Dr. Evil (and Goldmember) having funny and/or realistic numbers in mind for Evil Plan Non-Enacting ransoms at various points in time... There's not necessary a continuum of values, just a time when "one meeelion!" isn't going to cut it (or now will be funny for being so wrong). 141.101.99.117 20:24, 13 February 2024 (UTC)

The quote previously similarly occurred in https://what-if.xkcd.com/158/ (in note [7]: "It's 300 quadrillion bananas, Michael—what can it cost, 3 quintillion dollars?" --198.41.242.210 12:58, 19 February 2024 (UTC)