In the February Q&A1 @smpratte asked a general question wondering how many boxes would it take to pull a complete set for modern Pokémon. I thought that was an interesting question and decided to run the numbers for Evolving Skies. I came up with an average of 190 boxes, which sounds crazy! So crazy I tried 3 different methods of confirming that estimate.
I thought some people may be curious about how I came up with that number.
Method 1: Analytic
I searched around for evolving skies pull rates and found a couple of groups that had opened 5k-10k packs and provided their pull rates. That was a small sample size, but I was just looking for an estimate.
I used the pull rates of the rarest 72 cards (cards 166-237) to calculate the number of packs that would need to be opened to have a 50% probability of opening the entire set. I came up with around 180. The low range (5% probability) was 120 boxes and the high range (95% probability) was 295 boxes.
I honestly didn’t believe this number and thought it was so high it couldn’t be accurate. Plus, it’s been a long time since my statistics classes.
Method 2: Simulation
I wrote a script to simulate opening Evolving Skies packs. I used the same pull rates for the rarest 72 cards. I ran the sim 5,000 times. The average was 190 boxes. The low range (5% quantile) was 120 boxes and the high range (95% quantile) was 290 boxes.
I still couldn’t believe the number was that high.
Method 3: Word of Mouth
I searched around to see if anyone else had attempted to open an entire set. I dug further into the source of the pull rates. Their spreadsheet states the entire set was completed after 130 boxes, which is within range of the simulation and analytic methods.
Conclusion
I still have a hard time with the number! I just don’t want to believe it. Any nerds feel free to take a crack at it and let me know if you come up with something different.
This insane rarity seems good for the hobby in the short term by keeping prices high, but bad for the individual and possibly the long term. I feel like modern Pokémon is just a lottery ticket that people are playing. Early WOTC is fun because you have a good chance of pulling the “big cards” from a set. I don’t really desire to open any of the modern sets when I don’t have any chance of getting the cards I’m interested in. The one exception being Celebrations because I knew I could pull the cards I wanted without spending 20K.
Does anyone still collect sets? It seems impossible. Curious if anyone else feels similar.
Help me understand this OP. Is the correct question not how many boxes does it take to complete a set but rather what is the average amount of boxes to complete a set?
Given there are no guarantees, all you can calculate is the latter. There would be a point above which you would statistically expect to have completed the set; but, again, no guarantees.
Assuming 72 rarest cards, one per box, all equally likely → 72*ln(72) + 72*0.5772156 + 0.5 = 350 boxesI think the assumption here is flawed though. Most likely your simulation numbers are accurate
This was such a good data point from the Q&A! 190 boxes is just insane. 190 Packs could get you most wotc sets. I agree buying singles is the way to go, but someone has to open all this product. Sets are really less unified, and just vehicles for hits.
As someone who used to love collecting master sets, its been painful to be forced to go a different way and quit going for each set and all of their 70 gigarare cards. This data just highlights how ridiculous it is now
@pkmnflyingmaster , I used the cumulative probability of the rarest cards. ∏1-(1-p)^n, where p is the pull rate of the card, n is the number of packs. I wasn’t 100% sure of that application which is why I ran the simulation as well.
@smpratte , I’m glad it was a valuable data point! Its nuts, at what point is buying the singles get boring? I don’t mind buying vintage cards, there is still an element of chase and they are out of print. Buying modern cards feels unsatisfying to me, especially when they are still in print. At this point it can be more impressive to see a complete modern set over a WOTC set, which seems weird.
@wisewailmer, Yeah, especially with the higher tier items. Some companies have learned that they can make more off the 1% vs 99%. You see this a lot with in-app purchase games. Majority of revenue is coming from a small group of fanatics. I wonder if modern Pokémon is the same? I’ve sold boxes to multiple people who say they have spent 20k+ on Pokémon packs per year. Easy to imagine vintage having a lot of room left to grow.
I have opened just over 100 celebrations packs and have pulled everything except 1 Rayquaza. Total cost invested is about 1000 bucks and I still have more product left in reserve, including 4 etb and 2 pokemon center etb and some other odds and ends. Definitely a fun set to pull about every card in. The other sets are just nuts. I would be disappointed with that many chase cards. IU simply can not get into it.
I have never followed the prices but occasionally see the buying bulk posts on the facebook. How do people make money off of modern bulk since there has to be piles of commons/uncommons everywhere for modern sets.
After opening a couple booster boxes, you have a decent pile of bulk. I cannot imagine the bulk from 190 Boxes.
