How many piano tuners are there in Chicago?
How many quarters would you need to stack to be as tall as the Empire State Building?
If all digital data were stored on punch cards, how big would Google’s data warehouse be?
These questions are nearly impossible to answer accurately without extensive research. Enrico Fermi, 1938 Nobel Laureate and nuclear power forefather, was known for accurately estimating similarly hard-to-know answers with next to no information and posing similar questions. Most famously, he estimated the power of a nuclear blast by dropping bits of paper as the shockwave passed and then measuring how far they blew away. His estimate of 10 kilotons was amazingly close to the official U.S. Department of Energy 21-kiloton yield determined 50 years later using gamma-ray spectroscopy, whatever that is. His crude measurement led to a reasonable estimate within minutes. The actual answer took decades to determine.
Incredible.
Using Fermi’s technique of applying known concepts and quantities, we too can develop strategies to estimate hard-to-know answers with little effort and decent accuracy. In short, turn a random, nonsensical wild-ass guess into a scientific wild-ass guess or SWAG.
Munching on a chocolate creme Oreo the other day, I noticed a reversed wafer and wondered about Mondelēz’s quality control process. I also pondered how many Oreos are manufactured in the U.S. every year. For kicks, instead of Googling the answer right away, I opted to estimate it first, a la Fermi, and then see how I did.
First: Population of the U.S.
- I hear 300 and 330 million people get thrown around in the news.
- 300 million is rounder, we’ll start there.
Second: Number of households
- Two people per household seems low. Four seems high. Three sounds good.
- 300 million people / 3 people per household = 100 million households
Third: Households that consume Oreos
- Oreos are popular but stores are stocked with all kinds of cookies. Maybe ten percent? Why not.
- 100 million households * 10% = 10 million households consuming Oreos
Fourth: Oreos consumed per household per year
- My own empirical evidence suggests one bag of Oreos consumed per week
- Each bag has ~40 cookies (varies based on standard size, Family Size, etc.)
- 40 cookies/week x 52 weeks/year = 2,080
- Call it 2,000 Oreos per household per year.
Fifth: Final estimate
- 10 million households * 2,000 cookies per household per year
- 20 billion Oreos consumed per year.
That’s a lot of cookies.
How did I do? Well, somewhere between horrific and abysmal.
But that’s ok!
It turns out, the U.S. Oreo production is not readily available, at least where I was looking.
Mondelēz touts a worldwide Oreo production of over 40 billion per year and net revenue of $3.1 billion in 2019. That’s about 7.8 cents per Oreo.
With the net revenue per cookie, we can estimate U.S. consumption with sales numbers:
- 2016: $742 million / $0.078 per cookie = 9.6 billion
- 2017: $674.2 million / $0.078 per cookie = 8.7 billion
Some sites took a direct route and just estimated consumption:
- 1984: 6 billion per year
- 2007: 205,000 bags per day or ~3 billion cookies per year
- 2015: 778.8 million packages per year or ~31 billion cookies per year(!)
- 2017: 7.5 billion per year
Combining these results, estimates range from 3 to 32 billion Oreos per year. However, the 2007 and 2015 results seem to be oddballs compared to the other four. Our range narrows considerably to 6 to 9.6 billion per year once we throw those out. But now we’re stuck. Without official U.S. production data, there is no great way to narrow the range further.
All said, I’ll go with 8 billion Oreos per year and call it a day.
Summary of Oreo production: Labels are year of estimate.
Included data 
Two things I found useful from this exploration:
- Billions vs. millions
I had no idea how Oreos Americans eat annually. Before this, if someone asked me how many million are consumed annually, I would assume the number must be between 1 and 1000. In the best case, I’m off by a factor of 10! It turns out, my SWAG was bad, but not that bad.
For more extreme examples, try these questions out:
- How many thousands of dollars is Amazon worth?
- How many billions of people will read this blog post?
Messes with your head, doesn’t it?
Using “thousands” or “billions” frames the answer between 1 and 1000 when the right answer is either much smaller or much larger. It is surprisingly persuasive, especially without prior knowledge.
- Time vs. accuracy
My SWAG took about two minutes to build. The “close enough” result took about three hours of trawling through 10-K forms, press releases, and obscure blog posts to determine.
It took me 100 times longer to find a slightly more accurate answer.
For the sole purpose of satisfying a curiosity, that can be hard to justify. Spending more time makes sense when accuracy is valuable, be it marketing or physics.
Well, that was fun! Now you’ll have to excuse me. I have a tall glass of milk and a stack of Double Stufs to attend to.
For more Fermi questions, check out these links:
- http://www.lions.odu.edu/~lweinste/courses/309s08/estimation_list.pdf
- https://www.physics.umd.edu/perg/fermi/fermi.htm
- http://www.math.lsa.umich.edu/WCMTC/Fermi-Questions-Lesson-Plan.pdf
Many thanks to Stew, Joel, Chris, Jesse, and Dan for your feedback. It really leveled-up this post!
Compound Writing is making me better.
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