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,
1 bar (56g) has aprox. 250-270 calories and costs $1
$2.7 billion = 2.7 candy bars (56g, and 270 calories)
2.7 billion candies x 270 calories =
27 x 10^8 x 27 x 10 -> 27 x 27 x 10^9
729 x 10^9 – total calories consumed
729 is about 1/5 of 3,500 calories which translate into 1lb of gained weight. Therefore,
0.2 x 10^9 = 2 x 10^8 = 200,000,000 lbs of weight gained during Halloween.
Hmm, that’s an interesting question!
Start with the $2.7 billion. We want to know the total calories that represents, so we need to figure out the avg cost per candy and the avg calories per candy. For simplicity, I assume the avg candy costs $2.70, and the avg calories per candy is 1000. (Remember “Candy” is an avg of individual bars all the way up to bags)
$2.7 billion ÷ $2.70 = 100 million units of candy
100 million candy × 1000 calories = 100 billion calories consumed
Next, we want to know how much total weight is gained (Assuming 3500 calories per 1lb). We can simply divide the total 100 billion calories by 3500 to get the total pounds of weight gained by Americans. I can estimate that: 10×10^10 ÷ 3.5×10^3 = 10÷3.5×10^7 = 2.8×10^7 or about 28 million lbs.
If we assume 300 million Americans, that’s an avg of about .1 lbs of weight gain per person from Halloween candy, which seems pretty reasonable to me.
Thanks Victor!
Hi Victor –
Please find my estimation below:
(1) Total number of candies consumed
$2.7bn candies purchased
÷ $1.3 average price per candy (*)
x 95.0% consumption (**)
= ~2.0bn candies consumed
(2) Avg. number of candies needed for a person to gain 1 pound
3,500.0 calories per pound
÷ 250.0 calories per candy (***)
= 14.0 avg. number of candies needed to gain a pound
(3) Total pounds gained (aggregated) = (1) / (2)
~2.0bn candies consumed
÷ 14.0 avg. number of candies needed to gain a pound
= ~142.0mm of pounds (aggregated)
Overall, this makes sense to me as it implies, assuming a population of ~320mm people, a weight gain of less than 0.5 pounds. However, this number is likely to be much higher as candy consumption in Halloween is skewed towards kids and select adults (vs. overall population), which is concerning to me mainly given (1) rising obesity / lifestyle related diseases in the U.S. population, coupled with (2) number of times this occurs in a year (i.e., likely not a “once a year” situation for those kids / select adults, given other holidays / birthdays / etc).
Caveats / :
– Price: Candy price / selection can vary significantly across states / cities and does not take into account the effect of promotion (which often occurs around Halloween)
– Calories per candy: Assumed a calorie range in-line with item considered for pricing (standard, non premium chocolate bar) for consistency purposes but this ratio can vary with actual mix (i.e., hard candy, chocolate bar, etc)
– For my per capita estimation, as mentioned above, assumes everyone consumes candy on Halloween, however the data is skewed with kids and certain adults consuming considerably more candy
Sources:
(*) Per http://www.candywrapperarchive.com/candy-collector/candy-prices-over-the-years; Assumes a standard-size non premium candy bar (Baby Ruth, Butterfinger, etc)
(**) Assumes 1 out of 20 pieces of the candy purchased not consumed; many reasons might exist ranging from kids not liking a particular flavor to parents throwing candy away (or “taxing” their kids’ candies) to limit consumption, among other
(***) Assumes average calorie count for a standard-size non premium chocolate bar (midpoint of range of 200-300 calories in popular chocolate bars similar to the ones assumed for pricing)
Given:
$2.7B sales of candies
Calculation:
Candies can be bought at Retail price (eg. CVS) or Bulk Price ( eg. Sam’s Club)
Assume $ sales at: Retail -$1.2B, Bulk – $ 1.5B
# of candies at Retail – 2.5 B, Bulk – 7.5 B (given that more candies will be bought at Bulk price)
Total candies bought: 10B
Assume half split between low calorie (40/candy) and high calorie (100/candy)
# of calories across low calorie candy – (40 *5B) – 200B
# of calories across low calorie candy – (100 *5B) – 500B
Total # of calories – 700B
Calories per pound increase – 3500
Total pounds put on – (700B/3500) = 200M
Assume 30% candy is wasted
Total pounds Americans put on ~130M
Every American will gain 2 ponds.
ANSWERS
– calories in $2.7B candy spend: $2.7T
– net weight gained: ~767MM lbs.
– reasonable?: Conservatively estimating 300MM people in the U.S., this suggests each person gains around 2.5lbs. from Halloween candy consumption. This seems on the high end, but not completely outside a spectrum of reasonability if we assume all the candy is consumed at once and processed by our bodies normally.
REASONING
To figure out the net weight gained by Americans, we need to determine the weight gained by consumption and subtract out the weight lost by Trick-or-Treating/chaperoning.
WEIGHT GAINED: 770MM lbs.
We need to break down $2.7B total candy spend into a number of calories to convert to lbs. gained. To find the number of calories, we need to divide total spend by the cost/bag of candy, multiply by the # pieces/bag, and multiply by the # of calories/piece. Assuming a bag of candy costs $10 and has 50 pieces, each of which contain 200 calories, we are essentially dividing by 10 and multiplying by 10,000, yielding a total calorie gain of 2.7 trillion calories. Knowing that 3,500 calories are roughly 1 lb., it seems as though that we’ll gain ~770MM lbs. This would translate to a little over 2.5lbs./person if we estimated 300MM people in the U.S.
WEIGHT LOST: < 3MM lbs. 🙁
To estimate this number, we need to determine how many people participate in Halloween, how many miles they walk, and how many calories they burn per mile. Assuming children aged 5-16 participate (roughly 15% of total U.S. pop assuming even population distribution across an avg. life expectancy of 80 yrs., despite our candy-gorging habits) with an 80% participation rate, that's 36MM kids walking. Assuming adults only chaperone children aged 5-12 (roughly 10% of total U.S. pop), with a 40% participation rate (half that of children b/c assuming one parent stays home to give out candy), that's 12MM parents walking. Total people walking is 48MM, and let's say they walk about 2 miles on average, burning 100 calories per mile. This yields a total calorie burn of 9.600B, resulting in a weight loss of a little less than ~3MM lbs.
For the sake of accuracy in terms of deriving (estimating) how much additional weight America gains, I would
1) categorize the candies on basis of their calories (high, mid, low- along with average unit calories for each groups)
2) assuming that higher the calories higher the unit price (b/c more ingredients are added), I would estimate average unit price for each category
3) I would then assume m/s % (based on unit) for each category. If I don’t have enough data I would distribute the m/s %s evenly (33.33%) across the 3 category
4) Once I have unit prices and m/s%, I would use them to derive quantities sold for each category ($2.7bn * corresponding m/s % / corresponding unit price)
5) multiply corresponding average unit calories defined in step 1 to derive how much calories $2.7 bn worth of candies are worth
6) I could just take the easy path and divide the total calories by 3,500 to derive how much weight that translates into.
However if I wanted to be more accurate I would take few steps further and measure how much calories an average person (or average person from multiple categories of people) take in & burn per day. Assuming everyone gets the same mix of candies & the candies are consumed within 7 days (I’m just taking this from personal experience), I would calculate how much of the calories are left unburned which ultimately will be the actual weight America will put on.
p.s. apologies for not having an actual number
Let’s give it a try ☺
The average Candy portion is sold $1.30 (http://www.candywrapperarchive.com/candy-collector/candy-prices-over-the-years/)
but for Halloween, most people anticipate on the purchase and get deals/bulk, let’s say it brings the average to $1.10
the 2.7 billion dollars get us 2.45 billion candy bars
If we say the average candy portion is 220cal
(snickers is 215, M&M’s are 230) the entire Halloween candy represents 540 billion calories of pleasure.
With the given fattening rate of 1 pound gained every 3500 cal, and given that everything is eaten, Halloween candy would add around 154,285,714 pounds to the american population
155 billion pounds = 70 million kg
As Victor’s children tax rate shows however, everybody in the US doesn’t get an equal split… ☺
If we assume:
that all parents somehow get their hands on 33% of the candy (tax or simple racket)
that all children of 15 and under go trick or treating (roughly 20% of the population)
that anyone older than 15 is considered an adult, therefore getting their share from the 33% of taxed candy
Our 64 million children would gain 46.2 million kg
0.72 kg per child?
Assuming $10 bags and 70 pieces per bag and 70 cals per piece = 1.323 trillion calories and 378 million pounds gained
For a (very) quick estimation of the weight gained by the happy trick-or-treaters (or just those who love bite-sized candy), we can do an order-of-magnitude estimation. Because this is “quick-and-dirty”, we’ll only use multiples of 10, or if a number is between two orders, use the geometric average (3).
To convert from money spent to weight gained, we can use the following conversion:
Weight Gained =(((Money Spent/Cost per 1lb Bag) / (Weight per piece) )* (Calories Per Piece)) / (Calories per Pound Gained)
The first operation (Money Spent/Cost per 1lb Bag) gives an approximate number of bags of candy purchased. The second (dividing by Weight per piece) tells how many pieces of candy were purchased. The third (multiplying by calories per piece) tells how many calories were purchased, and the final step converts these purchased calories to weight gained.
Estimates for these quantities are:
Money Spent on Candy: Known $2.7B, but simplify as 3E9
Cost per 1lb Bag: $10, or 1E1
Weight per Piece: 0.03lb – [there are certainly more than 10 pieces in a pound (0.1lb/piece), but somewhere less than 100 (0.01lb/piece), so that’s how we end up with 0.03lb/piece.]
Calories per Piece: 100, or 1E2 [Some candy will have more, some less, but it’s probably around 100 – 10 is too low, 1000 is too high, 30 also seems too low]
Calories per Pound Gained: Known 3500, but simplify to 3E3
Then our estimation is nice and simple:
Weight gained = (3E9 * 1E2) / (1E1 * 3E-2 * 3E3) = (3/9) E (9) = 3E8
Or, 300M pounds, roughly one pound per person in the US. This is just an order of magnitude estimation, so the real number could be anywhere between 30M-1B, if we tweak the numbers a bit.