Expect to pay $215 to fill out your 2018 World Cup sticker album
Professor Paul Harper of the university of Cardiff recently calculated that it would cost 773 pounds ($1,100) to fill out the 2018 Panini world cup sticker album assuming the collector didn’t trade any of her repeats with anyone else. If 10 friends swap with each other, the cost could go down to 247 pounds ($352) according to the professor’s calculations. Panini, the manufacturer of the sticker album, released an official statement saying professor Harper overestimates the true cost by assuming the collectors live in a bubble and don’t trade with strangers.
I’ve recently started filling out my sticker album and I wanted to calculate for myself how much I should expect to pay to complete it. I wrote a program to simulate sticker collection under various swapping scenarios and I think the true cost is closer to $290. I’ll walk you through how I set up the simulation and my findings below.
The set up
The Panini world cup sticker album has been released every four years since the 1970 tournament in Mexico. Collectors buy stickers in packs and trade their repeated stickers in order to complete the album. This year, the album consists of 682 stickers. Each pack costs $1 and carries 5 stickers.
My simulation makes the following assumptions:
- Every sticker is equally likely to appear in any pack.
- Collectors can only exchange their repeated stickers in mutually beneficial trades*
- Each collector starts off with a random subset of 25 stickers.
In my simulation there are 10 friends that are trying to complete the album. At every time step, the 10 friends will trade with each other. After the trading among friends is done, each person has the opportunity to trade with k complete strangers. I ran the simulation for the following values of k {0, 2, 5, 10}. If the player cannot make a trade with his friends or strangers, he buys a pack of stickers. The simulation terminates when all 10 friends complete the album.
To summarize, here are the parameters my simulation takes and the values I’m using:
- Number of friends trading = 10
- Number of stickers in the album = 682
- Number of stickers in each pack = 5
- Number of strangers each player can trade with in each round = {0, 2, 5, 10}
- Number of stickers the strangers have purchased prior to trading = 100
Results
For all scenarios, I ran the simulation 100 times and then studied the distribution of the money spent by the 10 friends. Therefore, each distribution is based off 1000 points.
Scenario 1: No trading with strangers
In this scenario, the 10 friends can only trade with each other. To me, this is the scenario for which professor Harper computed a cost of $352. Over the 100 simulations, I’m finding the average cost is $326 but there’s a lot of noise. The cost can be as low as $199 and as high as $1218. I’m suspecting that what’s happening is that some unlucky friend is left being the only one collecting the album and she needs to resort to buying packs until she’s done.
Scenario 2: Can trade with 2 strangers after trading with friends
In this scenario, the results are less noisy. The collectors spend an average of $215 dollars but it can range from $146 to $498.
Scenario 3: Can trade with 5 strangers after trading with friends
The average cost in this scenario is $181. The distribution’s range is tightening around the mean.
Scenario 4: Can trade with 10 strangers after trading with friends
In this scenario, the average cost to complete the album is $135.
Conclusion
It’s common sense that trading with strangers will help you complete the album faster at a lower cost but my simulation gives insight into this relationship by quantifying by how much costs are expected to decrease as a function of the number of strangers you trade with. What I find most compelling is that frequently trading with just two strangers can reduce your cost by 30% as compared to only trading with the same 9 friends. Moreover, the added benefit of frequently trading with one more stranger decreases as the number of strangers increases. The takeaway is that you only need to break out of your bubble a little bit to get the biggest reduction in costs.
Ultimately, I think there is truth in both professor Harper’s and Panini’s arguments. Panini is right that the cost of the album is as high as you want it to be. If you don’t want to be buying a lot of packs, you should be trying to trade with as many strangers as possible. However, Harper is right when he notes that the prize of the album keeps increasing over time as Panini increases the number of stickers in the album as well as the price of stickers. Expecting people to frequently trade with upwards of 10 strangers in order to keep the price under $100 seems a bit unreasonable given that Panini is deliberately making the album more expensive.
I hope this gives you a better idea of what it can cost to complete the world cup album but this analysis is by no means exhaustive. I invite you to check out the code I used for this simulation and modify the assumptions as you see fit. Collecting the stickers is a ton of fun, especially when you get that sticker you’ve been dying to get, so I hope I haven’t turned you away from starting your collection. If you’re in Chicago, I’d love to trade with you!
Appendix:
*I’ve also simulated scenarios where the collectors only make one-for-one trades. The key takeaways are the same but the distributions are less noisy.
