Last night, I took my kids out for an American children’s holiday known as Halloween.
Kids (and some ahem… adults) dress up in costume (I was a penguin this year), go door-to-door, saying “Trick or Treat” and get free candy from the neighbors.
My three kids brought back a record 420 pieces of candy. 
In today’s New York Times, I learned that in the weeks leading up to this holiday, Americans purchased $2.7 BILLION dollars in candy.
So here’s my challenge for you.
Assuming all of that candy is consumed by someone in America, estimate the total number of calories represented by $2.7 billion in candy.
Assuming 3,500 calories consumed results in a person gaining 1 lb (0.45 kg) in weight, estimate how many pounds (or kilograms) of weight the American population will gain. Add a comment below to post your entry.
The winner will receive public acknowledgement of their estimation skills, and I will send them a portion of the candy “tax” I collected from my kids.
Yes, we tax our kids for a portion of their candy collection, as mom and dad provide “infrastructure” and “chaperone” services.
It’s a useful lesson in taxation.
(We tax at a 33% tax rate.)
Mostly it is an excuse to reduce the amount of sugar they will otherwise end up consuming.
For my kids, it’s an excuse to get rid of the candy they don’t like anyways.
Good luck and Happy Halloween!
Entries will be accepted for next 72 hours, and only entries posted as comments below will be considered. A winner will be announced next week.
UPDATE as of Friday, November 4TH AT 12PM ET: New entries are welcome, but not eligible to win, as contest has closed.
329 thoughts on “A Sweet Estimation Question”
Hi Victor – thanks for this estimation challenge.. had a lot of fun doing this and went pretty in depth. Here’s my entry:
Total Candy Purchased in $ = $2.7B
We are looking to identify how many pounds gained assuming all candies were eaten by Americans. This can be derived by Total Calories Consumed / 3500.
At a high level, in order to arrive to the Total Calories Consumed, we need to identify the types of most popular Halloween candies (categories) bought and their average calories per ounce. We also need to identify the % share bought from the $2.7B of these categories in order to derive an amount purchased of that category in $. By finding the average bag price (Halloween candies typically bought in bags and not individually) for each category we can then divide by total purchased for that category to determine the # of bags bought. Next, we can find the average weight in ounces of bags for each category and multiply that by the average calories per ounce for the candy category to arrive to Total Calories per Bag. Next, we multiply the Total Calories per Bag by the # of Bags Purchased for each category to land with a total amount of calories from all bags bought for each candy category. Next, we sum up all these total amounts to arrive to our Total Calories Consumed. Finally, we can divide this number by 3500 back to our original formula to determine how many pounds were gained.
Our formula(s) for each category then looks like this:
Amount Purchased = $2.7B * % Share Bought
Bags Purchased = Amount Purchased / Avg. Bag Price
Calories from Bags Purchased = Bags Purchased * Avg. Bag Calories
Avg. Bag Calories = Avg. Calories per ounce * Avg. Bag Weight in ounces
Total Calories Consumed = Sum of candy category’s Calories from Bags
Total Pounds Gained = Total Calories Consumed / 3500
From an article by USAToday, the most popular Halloween candy categories and their % Share Bought for this 2016 Halloween were as follows: 1) Chocolate with 72%; Candy Corn with 12%; Chewy Candies with 6%; Hard Candies with 5%; and Gummies with 5%.
From these percentages we can derive each categories Amount Purchased in $ to be the following: 1) Chocolate $1.94B; 2) Candy Corn $324M; 3) Chewy $162M; 4) Hard $135M; and 5) Gummies $135M.
We then need to do some research online to find the Avg. Bag Price and Avg. Bag Calories for each candy category. Before this we need the Avg. Bag Calories which we can determine by also finding the Avg. Calories per ounce and the Avg. Bag weight in ounces for each category. By using Walmart (regular shopping store), Sams Club (wholesale store) for prices and bag weights as well as Google for nutritional value per ounce we can gather all this information.
From this research, here are the findings:
Average Bag Price: 1) Chocolate $5.44 (this average includes prices from the top 10 popular Halloween chocolates which are Reeses, KitKat, Snickers, Hersheys, M&Ms, Twix, 3 Musketeers, Almond Joy, and Milky Way); 2) Candy Corn $4.50 (this includes several candy corn brands); 3) Chewy $5.67 (this includes top 4 popular Halloween candies which are Skittles, Twizzlers, Starburst, and Laffy Taffy); 4) Hard $6.77 (this includes top 3 popular Halloween candies which are Jolly Ranchers, Nerds, and SweeTarts); 5) Gummies $4.15 (includes several gummy brands).
Bags Purchased for each category: 1) Chocolate 357.1M; 2) Candy Corn 72M; 3) Chewy 28.6M; 4) Hard 20M; Gummies 32.5M
Average Bag Weight in ounces (averages here derived from taking same candies mentioned above within each category): 1) Chocolate 22.67; 2) Candy Corn 16; 3) Chewy 26.75; 4) Hard 16; 5) Gummies 16
Average Calories per ounces (averages here derived from taking same candies mentioned above within each category): 1) Chocolate 136.77; 2) Candy Corn 100; 3) Chewy 107.13; 4) Hard 110.67; 5) Gummies 112
Average Calories in Bag (averages here derived from taking same candies mentioned above within each category): 1) Chocolate 3,110; 2) Candy Corn 1,600; 3) Chewy 2,932; 4) Hard 1,770; 5) Gummies 1,792
Now that we have our numbers, we can get the Calories from Bags Purchased for each category from our formula above. Here are the numbers:
1) Chocolate 1.1T; 2) Candy Corn 115.2B; 3) 83.7B; 4) Hard 35.3B; Gummies 58.3B
For a Total Calories Consumed of 1.4 Trillion
And FINALLY .. 1.4 Trillion Calories / 3500 = 401 MILLION pounds gained from all the candy consumed in America from the $2.7 Billion candy purchased
Assumptions:
1. Calorific content of 10g jellybean=40 cal
2. 1 pound of jellybean is priced at $6.71
3. 1 pound=450 g
Therefore : Total weight gain of US popn=TWG
TWG=(($2.7 billion/$6.71 per pound)*4cal per g*450 )/3,500cal per pound
TWG=90 million Kg
Non-diabetic population who can consume sweet candies=296 million
Individual weight gain=300 g
Total candy purchased: $ 2.7 billion
Estimation 1: Total number of calories represented by $2.7 billion dollars of candy ?
One candy ~ 30 grams
Approximate Constituents of Candies: Carbs (50%), Proteins (15%), Fats (30%) and others (5%)
Total Calories: Carbs & Protein – 4 calories per gram and Fat – 9 calorie per gram and assume others to be 4 calories per gram
Therefore approx. calories in a candy = 30*.5*4 30*.15*4 30*.3*9 30*.05*4 = 165 calories
Hence, calories per gram – 165/30 =5.5 calories per gram.
Assuming one pack of 25 candies will cost $5.
So total number of candies: ($2700 mill / $5)*25 = 13.5 bill candies
Total number of calories represented by $2.7 billion dollars of candy is (13.5*165) bill calories ~ 2227.5 billion calories
Estimation 2: Weight Gain of the American population
2227.5 billion calories/ 3500= 636 mill pounds
Hi Victor,
Following my assumptions:
1 candy = 0,5 $
1 candy = 150 calories
So:
Total Calories = 2,7 billion $ * 0,5$ * 150 cal = 810 billion cal
Total Weight = 810 billion cal / 3500 cal = 200 million lb (roughly)
Thanks,
Lorenzo
My Approach
1. Total spend / American population = Average spend per person
calculation: $2.7 billion / 320 million = $8 (approx.)
2. Average spend per person / Average price of candy = Number of candy per person
calculation: $8 / $2 (assumed) = 4 candy per person
3. Number of candy per person x Calories per candy = Calories consumed per person
calculation: 4 x 500 calories(assumed) = 2000 calories consumed per person
4. Calories consumed per person / 3500 calories per 0.45 kg = frequency of 0.45 kg increase (y)
calculation: 2000 calories/ 3500 calories = 0.6 (approx.)
4B. 0.45(y) = kg gained per person
calculation: 0.45(0.6) = 0.27 kg gained per person
5. kg gained per person x population = kg gained by population
calculation: 0.27 kg x 320 million = 86.4 million kg gained by American population
I think the key assumption to make is how those calories are going to be consumed and by how many people. Calories alone are not an indicator of weight gain/loss: what matters is whether or not they are consumed on top of TDEE, or Total Daily Energy Expenditure. This is the amount of calories a person needs to maintain his/her regular weight.
With that point clear, let’s estimate bottom up, step by step.
Based on relatively small spread of candies in terms of kcal/lbs and price points, we can safely assume (1):
Average kcal/lbs of candy = 2500
Average cost/lbs = 8.5$
In other words, sweets are generally cheap and very calorie-dense. Previous figures give:
~318 Million lbs sold
~795 billion kcal sold
Now, let’s split american population in 3 age groups:
Kids 0-2: won’t be in scope
Kids 3-13: ~13.5% of population / 44 Million people
13 : 81% of population / 263 Million people
Now we assume (2) 50% of in scope age groups partake in Halloween celebrations, with the following consumption profile:
60% of candies are consumed by 3-13 group
30% are consumed by 13
10% are not eaten/wasted
I.e., most candies are consumed by kids, which seems reasonable. This gives:
~476 Billion kcal for 22 Million people aged 3-13
~238 Billion Kcal for 131 Million people aged 13
And now the critical question: how many of those calories will be consumed ON TOP of the food which is already part of a person’s regular diet (TDEE)? This is fundamental to understand because only those will contribute to weight gain.
I believe it’s again useful to split this into age groups:
3-13 group: 20% of candies consumed on TOP of TDEE
13 group: 90% of candies consumed on TOP of TDEE
The rationale (3) here is that parents will tend to limit the excess calorie intake of their kids, whether by imposing taxes or limiting daily consumption ;). On the other hand, adults might be much less efficient in controlling their own intake.
Assumptions (2) and (3) bring us to the following results:
3-13 group: ~95 Billion kcal for ~22 Million people
13 group: ~214 Billion kcal for ~131 Million people
Finally, we assume (4) that 100% of kids eat candy, while only 80% of adults do, which brings us to:
3-13 group: average of 4338 extra kcal per person
13 group: average of 2038 extra kcal per person
This translates into an average weight gain (for those partaking and consuming candy) of:
1.2 lbs for 3-13 group
0.6 lbs for 13 group
Overall, the total nation’s weight gain due to Halloween is:
(1.2 lbs/person) x (~22 Million people)
(0.6lbs/person) x (~131 Million people) = ~104 Million lbs
Looks like it makes sense 🙂
1.505 trillion pounds.
$2.7B ~700M#~2150 cal/# (skewed more heavily towards chocolate)
Dear Victor,
This is Euphie from Tokyo.
Thanks for sharing this interesting question.
I’d like to start from estimating the total mass of the candy to calculate the total number of calories.
Total mass of the candy=Total number of the candy*Average mass per candy
Total number of the candy=USD2.7b/The average unit price of the candy
Here I assume the average unit price of the candy is USD0.2 and the average mass per candy is 4g,
so total number of the candy=USD2.7b/USD0.2=13.5b and
total mass of the candy=54b(g)
Then I’d like to calculate the total number of calories using the following knowlodge:
1g of carbonhydrate/protein generates 4 calories
1g of fat generates 9 calories
And add one more assumption that 80% of the candy is composed of carbonhydrate or protein and the other 20 % is fat.
So the total calories of the candy=(Total mass of carbonhydrate or protein)*4 (Total mass of fat)*9=(54b*80%)*4 (54b*20%)*9=54b*(3.2 1.8)=270b(calories)
Using 3500 calories consumed results in a person gaining 0.45 kg in weight, we get:
Total weight the American population will gain around
(270b/3500)*0.45=34.7 million kg
Thank you for taking your time viewing my answer.
If you don’t mind, could you give me some feedback, please?
Appreciate your help.
Euphie Liu
Data:
2,7 B$ spent on candy bu U.S. population
3.500 cal = 1 lb=
Assumptions:
Average cost of candy : 21,2 $/kg (estimate based on a standard size US candy bar)
Average calories per 100 gr of candy: 535 , which meand 5.350 cal/kg
Given these assumptions, U.S. population bought 2,7B/21,2=127.358.490 kg of candy, which result in 681.367.924.528 calories.
Since we know that 3.500 cal results in a person gains 1 lb, 681 B calories will result in a weight gain equal to 194.676.549 lbs (for the whole U.S. population).
Part A – Estimation of total calories generated from $2.7 Billion from Candies :
Candies can be divided into 2 segments of avg price and avg calories contained :
(1) Smaller Candies – avg price per candy 2$. avg calories per candy 100.
(2) Bigger Candies(Bars) – avg price per bar 5$. avg calories per bar 500.
Assuming 70% revenue is generated from segment 1 and 30% revenue is generated by segment 2 (This is usually how I buy candies / chocolates for distributions), below are steps for calculation of total calories generated from $2.7 Billion:
Step 1: segment 2 dollar to cal conversion :
$5 -> 500 Cal
$10 -> 1000 Cal
$1 Million -> 10^8 cal
segment 1 dollar to cal conversion :
$2 -> 100 cal
$10 -> 500 cal (half of respective number from segment 1)
hence $1 million -> 1/2 * 10^8 cal
Outcome of step 1 : each million dollar revenue from segment 1 generates 1/2 *10^8 cal. and each million dollar revenue from segment 2 generates 10^8 cal.
Step 2: calculate revenues for each segments. Segment 1 is 70% and segment 2 is 30% as per assumption.
total revenue : $2.7 Billion = $2.7 * 10^9
Segment 1 revenue : 2.7 * 10^9 * (70 / 100)
Segment 2 revenue : 2.7 * 10^9 * (30 / 100)
looks like not-an-easy calculation. So correction 1 here. I will divide revenues in 2:1 ratio than 70-30%
Segment 1 revenue : 2.7 * 10^9 * (2/3) — 27 is completely divisible by 3 hence the calculation becomes easy. looks like no more corrections required.I will also divide 10^9 into two parts 10^6 (1 million) and 1000 – to avoid decimal calculation.
= 2700 * (2/3) * 10^6 = 1800 * 10^6 = 1800 million
segment 2 revenue : since it is 2:1 ration – segment 2 revenue will be half of segment 1 revenue
= 1/2 * 1800 million
Step 3: total calories from entire revenues :
= segment 1 calories segment 2 calories
= (segment 1 revenue in million * segment 1 calories per million) (segment 2 revenue in million * segment 2 calories per million)
= (1800 * 10^8 cal) (1/2 * 1800 * 1/2 * 10^8 cal)
= 10^8 [(Part 1 = 1800) (part 2 = part 1 / 4)]
= 10^8 [1800 450] —18/4 = 4.5 is easy
= 10^8 * 2250 cal = 225 * 10^9 cal = 225 Billion calories
I combined step 2 and step 3 in one step while calculating.
Part B – Estimation of total weight gained by population based on calories consumed.
As stated – all of these calories will be consumed by someone and 3500 cal consumed results in 1 lb weight gain, total weight gain
= total weight gained per cal * total cal consumed
= (1 / 3500 ) * 225 * 10^9 lb
Basically 225/3500 and rest is adjustment of zeros = (200/3) * 10^6 = 66 Million lb.
So – the total Halloween candy sales of $2.7 Billion in USA resulted in estimated 225 Billion Cal consumption and 66 Million lb weight gain for US population.
*PS: writing down took way more time than actual calculation.