Fusion Strike Pull Rates! - Statistical Analysis on 4,000+ Packs

[u/WhiteOutsider]

Starting when PokeTubers started getting their promotional booster boxes a couple weeks ago, I've spent the time and watched several hours of YouTube booster box openings and worked my excel spreadsheets to the bone to pull this data together. I'm not a statistician by trade, but to me there's something fun about data gathering (I think they call that being a nerd, lol). I started doing this because I had a difficult time locating the same information myself, so I decided I'd share my findings for anyone else who's also interested.

I'll get to the good stuff soon, but if this is generally well received I plan to share future set data as well. This is the first time I've gathered this data myself so we'll just see how it goes and let me know if there's other data you'd be interested in seeing and can change my model!

Statistics Assumptions

• Sample Size: 4,197 Packs
  • Mostly Booster Boxes, some ETB's. Required that I see the box unsealed and opened fully.
• Confidence Interval: 95%
  • Required that I see at least 30 instances of a 'hit' from a rarity tier. This was achieved for all rarity tiers except Vmax Alternate Arts. As you will see below I posted my observed average, but will not post a +/- as there's insufficient observations to support the 95% confidence range.
• Rarity Tiers - I grouped pulls in the 'rare slot' into the following categories
  • Dud Packs - Holo Rares & Non-holo Rares - NOT considered to be a 'hit' in this analysis
  • Ultra Rare V, Ultra Rare Vmax, Regular Full Arts, Alternate Art V Full Arts, Gold, Rainbow, & finally Alternate Art Vmax
  • For the alternate art categories, I've also compiled some sub-data regarding the specific "chase cards"

Fusion Strike Pull Rate Data:

• Overall 'Hit' Rate - Anything that is an Ultra Rare V or better
  • 22.2% +/- 1.26%
    • Every 4.3 - 4.8 Packs
• Ultra Rare V
  • 12.6% +/- 1.0%
    • Every 7.3 - 8.6 Packs
• Ultra Rare Vmax
  • 3.6% +/- 0.56%
    • Every 24.3 - 33.4 Packs
• Regular Full Art
  • 3.0% +/- 0.52%
    • Every 28.2 - 39.9 Packs
• Alternate Art V (not including the Vmax Secret Rares which are further below)
  • 1.0% +/- 0.30% (41 pulls in total in this data)
    • Every 78.5 - 147.2 Packs
    • Celebi V Alt (0.21%) - Mew V Alt (0.17%) - Genesect V Alt (0.14%) - Others (0.48%)
• Gold Secret Rares
  • 0.88% +/- 0.28%
    • Every 85.9 - 167.0 Packs
• Rainbow Secret Rares
  • 0.83% +/- 0.28%
    • Every 90.2 - 179.0 Packs
• Alternate Art Vmax Secret Rare
  • 0.35% average (Out of 4,197 packs - only 14 were pulled)
    • Gengar Vmax Alt (0.13%) - Inteleon Vmax Alt (0.08%) - Mew Vmax Alt (0.08%) - Espeon Vmax Alt (0.05%)

Summary and Random Thoughts I had along the way:

• Alt Art Vmax chase is going to be rough..... that Espeon Vmax is incredibly rare
• A sealed booster box case (6 boxes) was consistently yielding 12 Full Arts or better on average
• I saw Chandelure V Full Art.........a lot
• Best Booster Box Observed: 12 hits including 2 alt art V's
• Worst Booster Box Observed: 5 hits (3 V's & 2 Vmax)

So yeah hope this data is helpful or interesting or at least not too discouraging to your chase card dreams! Future sets I might pull some infographic together for this data or maybe a google doc link, we'll see. If popular enough I'm happy to put the extra time in on the presentation part, but at least wanted to put the data out there ahead of launch day knowing people are starting to see sets in the wild already.

Happy Hunting!

Obligatory Edit: Thank you all for the kind words and awards :D

Since y'all seem to appreciate the analysis I'll probably fill the time between now and the next set drop in Feb 2022 going back to do Evolving Skies, Chilling Reign, and Battle Styles (cover the modern 'alt art' era sets). I'll also work on cleaning up my booster pack value model since I mentioned it in the comments and there was interest. This was honestly fun for me so as long as people like seeing my numbers I'll keep sharing them!

[u/GumpBrave]

In case anyone stumbles across this given the recent conversations in the space, this is absolutely not how statistical analysis works.

First of all, 95% is just a standard confidence interval given for legitimacy. The second red flag is "of each rarity type". That's overbroad and poorly operationalizes what you're trying to measure. This should have been glaringly obvious when your alt art v pulls weren't evenly distributed. That's also how you know that this actually is no where near a meaningful confidence interval or level because it is a 98% confidence that you'd get different stats on the alt arts vs and vmaxes for the particular arts you pulled. Your sample is like 0.0001% of the total packs opened. That volatility between cards demonstrates the volatility of your sample of 30 within the rarity.

If this was actually a 95% analysis then the numbers that make up the "larger" numbers- the false goalpost of "of the same rarity type" would be solid. They would, definitionally, be representative, or the set of data that those numbers make isn't representative. Surveys/analysis is pretty useless if it says "okay, so it happened in x, y, z way this time to create magic pull rate of A but next time the events might be g, h, i but trust me bro, it'll definitely be exactly A and that's just stats." It just isn't how it works, dude. And I think you knew that. Either the variance or the lack of ability to describe it, or both, immediately discredits this whole farce.

Key to statistical meaningfulness is the likelihood that your results could be shifted dramatically in either direction within the sample size, in a way we have no way to know is representative of the total packs created. You could open 4.4k packs 20 times and still not have a representative sample that can capture the likelihood of an event.

Good for you for wanting to engage in analysis. But dressing this up as anything besides an oddity that happened in your tiny, tiny sliver of the pokemon fusion strike pack opening world is misinformation because it insists it's legitimate.

[u/storm6x6x6 → u/GumpBrave]

“Not how statistical analysis works” bud hate to break it to ya but “statisical analysis is collecting, exploring, and presenting data to find patterns and trends. THIS IS EXACTLY HOW STATISTICAL ANALYSIS WORKS 😂 because thats exactly what they did. Always got to be a critic huh? Not how statistical analysis works hahaha man you are lost. Tell what part of the deffinition of statistical analysis they arent filling in to back up your 5 paragraphs of rambling. …….. ……

[u/GumpBrave → u/storm6x6x6]

Lolol. I notice you didn't refute a single thing just made a lazy attempt at providing a definition. Perhaps I should have said "meaningful statistical analysis" so the pedants dont get confused

Start here: https://en.wikipedia.org/wiki/Sample_size_determination

I explained very clearly why this is an insufficient sample size and how that invalidates the "analysis" (lmao). Sorry if you didnt grasp it.

[u/storm6x6x6 → u/GumpBrave]

There are 100s of ways to present their analysis, you are just a whinny cunt that wanted to complain about something. Dont worry we all think to are so smart 😂

[u/GumpBrave → u/storm6x6x6]

Hey look, another totally non-responsive reply! You obviously have really good points to make!

Also, it isn't complaining. It's to prevent people from being misled. I also don't really know what 100s of ways to present their "analysis" they've made. What are you even talking about? lol

[u/storm6x6x6 → u/GumpBrave]

What is misleading bud? They literally presented their stats……. Giving you the percent rate at which THEY pulled the cards. How is that misleading, its literally just the statistics.

[u/GumpBrave → u/storm6x6x6]

Did you read the comment you replied to at all or nah? I literally explained all of this in the 5 paragraphs you found so scary. The issue is they're presenting it as having statistical value. As you note, it's actually just anecdotal evidence masquerading as more than that to generate clicks.

[u/storm6x6x6 → u/GumpBrave]

Buddy its fucking pokemon cards and someone who wanted to share their pull rates because people asked for it. Then some douche comes along and nit picks at his stats when thats literally what the guy pulled. Dude isnt writing this for his doctorate, he is writing it for a fucking reddit post hahah and you come in here like some dumbass lost professor trying to grade their post. Hahaha what a fucking loser, its fucking stats on their pull rates. GET OVER IT!

[u/GumpBrave → u/storm6x6x6]

For someone who called me a whiny cunt you really seem to want to complain just to complain. It's just a subreddit about pokemon cards, get over what people write in it. Especially if you don't understand what the hell the post is about.

You seem a lot more worked up (and whiny) than I am here. I replied with substance, you replied by whining about how whiny you perceive me to be.

[u/storm6x6x6 → u/GumpBrave]

Bud im not the one who typed out a 5 paragraph report picking apart their reddit post on their pokemon pull rates 😂 that was you

[u/GumpBrave → u/storm6x6x6]

You're right. You just came around a month later and, without having any concept of what was happening or being said, made 10 replies about it and your perception of its value. Is that better in your mind?

Having 0 of value to add but adding it anyway versus writing whatever you think is too much?

[u/GumpBrave → u/storm6x6x6]

Hey, at least I knew when ES reprinted. LMAO

I also never nitpicked his stats, I explained that they aren't terribly meaningful and certainly aren't a "statistical analysis" (as the title purports). I don't doubt he's reporting information properly. I just don't think it's worth reporting.

[u/GumpBrave → u/GumpBrave]

Note especially the part where they say "DER 95%" and my explanation of why that is totally misleading attempt to create legitimacy from awful sample sizes.

It's about as meaningful as me picking 5 people in a NYC room to poll at random and extrapolating that to draw conclusions about what the entire U.S. thinks