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 $2.7 billion in candy.
Assuming 3,500 calories consumed results in a person gaining 1 lb (0.45 kg) in weight, estimate how many pounds (or kilograms) of weight the American population will gain. Add a comment below to post your entry.
The winner will receive public acknowledgement of their estimation skills, and I will send them a portion of the candy “tax” I collected from my kids.
Yes, we tax our kids for a portion of their candy collection, as mom and dad provide “infrastructure” and “chaperone” services.
It’s a useful lesson in taxation.
(We tax at a 33% tax rate.)
Mostly it is an excuse to reduce the amount of sugar they will otherwise end up consuming.
For my kids, it’s an excuse to get rid of the candy they don’t like anyways.
Good luck and Happy Halloween!
Entries will be accepted for next 72 hours, and only entries posted as comments below will be considered. A winner will be announced next week.
UPDATE as of Friday, November 4TH AT 12PM ET: New entries are welcome, but not eligible to win, as contest has closed.
329 thoughts on “A Sweet Estimation Question”
Americans will gain around 79 mln lb
To support my (gu)estimation I did the following:
1) Determined the product
I thought of what product would have higher demand and portion in 2.7 bln$ spent.
Considering this amount was bought for Halloween “trick or treat” purposes I would assume that the most popular were chocolate bars/bite size sweets (the pic you attached kind of confirms it)
2) Segmented the market by brand
Considering different brands have different market share in America/different prices/different products, I estimated what market share will each candy brand have, given the market share in general and the variety of chocolate bars (which we determined as a target product) supply from each brand. Approximates as follows:
Mars => 30%
Hershey’s => 30%
Lindt/Ghirardeli => 6%
Mondelez => 5%
Nestle => 5%
Other => 24%
3) Calculated the market share (total 2.7 bln$* #2)
Mars and Hershey’s: 2.7 bln$ * 30% = 810 mln$
Lindt/Ghirardeli: 2.7 bln$ * 6% = 162 mln$
Mondelez and Nestle: 2.7 bln$ * 5% = 135 mln$
Other: 2.7 bln$ * 24% = 648 mln$
4) Estimated the average price per candy
Mars: 2$
Hershey’s: 3$
Lindt/Ghirardeli: 2.5$
Mondelez: 1.5$
Nestle: 1.5$
Other: 2$
5) Calculated the amount of candies per Company (#3/#4)
Mars: 810 mln$/2$ = 405 mln candies
Hershey’s: 810 mln$/3$ = 270 mln candies
Lindt/Ghirardeli: 162 mln$/2.5$ = 64.8 mln candies
Mondelez and Nestle: 135 mln$/1.5$ = 90 mln candies
Other: 648 mln$/2$ = 324 mln candies
6) Estimated the average kkal per candy
Mars: 250 kkal
Hershey’s: 200 kkal
Lindt/Ghirardeli: 240 kkal
Mondelez: 250 kkal
Nestle: 200 kkal
Other: 200 kkal
7) Calculated total kkal for 2.7 bln$ (#5*#6)
Mars: 405 mln candies * 250 kkal = 101,250 mln kkal
Hershey’s: 270 mln candies * 200 kkal = 54 mln kkal
Lindt/Ghirardelli: 64.8 mln candies * 240 kkal = 15,552 mln kkal
Mondelez: 90 mln candies * 250 kkal = 22,500 mln kkal
Nestle: 90 mln candies * 200 kkal = 18,000 mln kkal
Other: 324 mln candies * 200 kkal = 64,800 mln kkal
Total kkal: 101,250 54 15,552 22,500 18,000 64,800 = 276,102 mln kkal
8) Calculated the amount of potentially gained weight for total American population
276,102 mln kkal/3500 kkal = 78.9 mln lb
So if your kids managed to capture 420 candies and taking into consideration 33% tax will be collected, this gives us 420 – 33% = 218 * avg. 200 kkal per candy = 56,200 kkal
Even assuming they will share equally between themselves it still give us 56,200 kkal/3 children = 18,733 kkal.
Seems like they better share some with their Mom and Dad…
Happy Halloween!
Specific question to answer: total weight gain for US population
Formula to calculate estimation:
[Total weight gain] = (([Total amount spent]/[Price per unit]) * [Calories per piece]) / [Calories per lb]
where we’ve given
[Total amount spent] = 2,700,000,000$
[Calories per kg] = 3500 cal/lb
I asume 100 calories per piece and a price of 1$ per piece of candy hence
[Price per unit] = 1$/piece
[Calories per piece] = 100 cal/piece
plugging into the formula we get
[Total weight gain] = ((2,700,000,000 / 1) * 100) / 3500 = (2,700,000,000 * 100) / 3500 = 2,700,000,000 / 35 = approx. 80,000,000 lb
Assuming each candy bar (like Snickers) is weights about 50g, costs $1 and has about 250 cal:
Given each bar costs, $1, it represents 2.7 billion candy bars total.
Since each candy bar contains about 250 calories, it will represent 675 billion calories total.
Given each 3,500 calories represents a weight gain of 1lb or 0.45 kg, these 675 billion calories will represent a total population weight gain of about 192,800,000 lb or 86,800,00 kg.
Total Candy Sold $2,700,000,000
Cost/Candy 0.4
Total Candies 6,750,000,000
Calories/Candy 125
Total Calories Consumed 843,750,000,000
Calories Consumed/Lb 3500
Total Weight Gain 241,071,429
Total US Population 350,000,000
% Population Consuming Candy 60%
# of People 210000000
Avg Weight Gain 1.15
Thanks for the fun question.
I estimated 500B calories is represented by the $2.7B of sales, and 140M pounds gained, about a half pound per person on average.
1) First let’s assume the average child collects 100 pieces of candy (not quite the haul your kids brought in).
= 100 candies per child
2) Next, estimate the number of trick-or-treaters collecting these candies. My guess would be the main age range is 5-15 years old. Assuming uniform age distribution up to age 70, this is about 1/7 of the US population (320M).
= 320/7 ~ 45M
3) So, these 45M kids collect an average of 100 pieces.
= 4.5B pieces of candy
Let’s assume 90% of candy was collected, and the remaining 10% consumed by the givers. The number of candies represented by the $2.7B is then 4.5B/0.9
= 5B total pieces of candy
4) Assume average calories per piece of candy is 100. The total calories represented by $2.7B is then:
= 5B*100 = 500B calories
5) Divide this by 3500 gives total pounds gained in US:
=500B / 3500 = ~140,000,000 , or 140M pounds
6) Divide by the US population of 320M:
=140/320 ~ 0.45 pounds per person.
The most popular candies are Reese’s PB cups, Hersey bars, Milky Way and Twix bars (source: USA today). Let’s pick one representative, the Reese’s PB cups. One 10.5 oz bag contains 7 servings of 220 cal servings, and costs $2.81 in Walmart. On average, you can purchase 11540 calories with $2.81, averaging a 548 calories per dollar.
U.S. spent 2.7 billion dollars, can purchase approximately 1480 billion calories. If 3500 calories results in one lb of weight gain, that’s 4.3*10^9, which is 430 million lbs.
Hey, U.S. population is about 300 million, in 2016. On average, you gain 1.3 lbs from Halloween candies: but you know you are taking the gain for babies, toddlers, people who are not into candies et al. So don’t be surprised if 2 lbs are coming your way this November ;D !
Part-1: # of calories represented by $2.7B
Structure: (i) convert $2.7B to # of candies (ii) convert # of candies to calories
(i) Assume $2.7 (on avg.) is the cost of 1 candy => $2.7B represent 1B candies
(ii) Assume 1 candy is approx. 100 calories (on avg.) => 1B candies are 100B calories
Part-2: Weight gain (in lbs) for American population
Structure: (i) convert # of calories to # of lbs
(i) 3500 calories = 1lbs => 100B calories represent 100B/3500 = ~30M lbs
What does this mean?
Candies during Halloween are not a cause of weight gain issue. This is because American population of approx 300M gained 30M lbs so 1 person gained 0.1 lbs (30M/300M) so overall $2.7B do not represent a significant weight gain (assuming this was spread across the entire population).
Assuming that no candy is lost or uneaten in the process, I estimate that the US population will gain a total of 88,654,850 pounds from eating halloween candy.
However, some candy will be thrown out, lost, or remain uneaten for other reasons. Therefore the estimate should be discounted by an estimate of this waste. In addition, some may substitute candy for some more healthy options, and therefore an estimate of calories of other foods foregone should also be incorporated into the calculation.
It is nearly impossible to get a reasonable estimate of the discount from different factors, but assuming these to be 10% of the total, that would put the total weight gain to 79,789,365 pounds in total.
According to Google there are 535.1 kCal in 100 gram candy
This translates into 5.351 kCal per gram
According to the Candywrapper Archive the Average price per ounce of candy in 2015 was $1.30. I interpolated that to 1.32 in 2016 from their 2020 forecast of $1.40 (one fifth of the estimated 5 year increase.)
(Source: http://www.candywrapperarchive.com/candy-collector/candy-prices-over-the-years/)
2.7 $Bn worth of candy sold translates into
Candy sales ($US) 2,700,000,000
Ounces of candy sold (revenue divided by avg. price per ounce) 2,045,454,545
Grams of candy sold 57,987,660,886
kCal in total candy sold 310,291,973,403
Pounds gained (total kCal divided by 3,500) 88,654,850
Discounted pounds gained (-10%) 79,789,365
Definitions/assumptions
kCal/100 g candy 535.1
kCal/g candy 5.351
Price of candy per ounce in USD 1.32
Gram per ounce 28.3495231
kCal to gain a pound 3,500
My Guess is that the entire Americano Population would gain approximately 525,000,000 pounds
1. Question formulation
Given that:
Total Weight (lb) = Total Calories / 3500
We can first break down Total Calories into:
Total Calories = Total Pieces of Candy * Average Calories Per Piece
Total Pieces can be further broken down to:
Total Pieces = Total Price (2.7B) / Average Price per Piece
2. Estimation
Based on the above equations, there are two numbers we need to estimate, which are:
1) Average Price per Piece
We can segment Halloween candy into three types, high end (luxurious brands such as Ferrero Rocher), mass brand (Skittles, M&M) and non-branded
Assumptions are made with daily observation and educated guess:
a. A piece of High End candy is $1 on average ($10 per pack with 10 pieces)
b. A piece of Mass Brand candy is $0.4 on average
c. A piece of Non-branded candy is $0.1 on average
d. 10% of all Halloween candies are High End, 50% are Mass Brand and 40% are Non-branded, since most people wouldn’t spend too much money purchasing Halloween candies.
With the assumptions above, the estimated Average Price per Piece is $0.34
2) Average Calories per Piece
We can segment Halloween candy into two types, high cal (chocolate bar, nougat, taffy…) and low cal (hard or soft candy)
Assumptions:
a. A piece of High Cal candy has 80 calories on average
b. A piece of Low Cal candy has 30 calories on average
c. 50% of all Halloween candies are classified as High Cal and 50% are classified as Low Cal, from what we saw from Victor’s picture in the email.
With the assumptions above, the estimated Average Calories per Piece is 55.
3. Calculation
Now we can put our estimations into the equations,
1) Total Pieces = Total Price (2.7B) / Average Price per Piece ($0.34)
Total Pieces = 7.9 B
2) Total Calories = Total Pieces of Candy (7.9 B) * Average Calories Per Piece (55)
Total Calories = 435 B
3) Total Weight = Total Calories (435B) / 3500
Total Weight = 124 M (pounds)
Here we get the final answer, 124 million pounds of weight in total for the US population to gain by consuming Halloween candy.
As a sanity check, we can divide 124M by 310 M of US total population and get that an average person increases 0.4 pounds during Halloween.
This seems reasonable as we often hear people complaining but seldom actually notice people getting fat merely because of Halloween candy consumption. We don’t actually recognize any difference if a person increases 0.4 pounds, but if we add the calories of Halloween feasts, that will be another story 🙂