Ultra Prism
Ultra Prism is the first set to introduce Prism Star cards, which appear in the reverse slot. As mentioned in the introductory post to the Sun & Moon series, the box ratios are assumed to be 3.0 “regular” Pokémon-GX, 0.8 full art Pokémon, 1.6 full art Trainers/secret rares and 3.0 Prism Stars.
When initially using a sequence length of 180 (instead of 360) packs to model this set, I came across the following problem, which was one of the reasons I opted to rethink the way I was modelling the sets (the other being that a sequence length of 180 packs just didn’t give me enough flexibility to get my models to fit the raw data well): As Ultra Prism is a “large” set which requires two 11x11 sheets to print the reverses, assuming 3.0 Prism Star cards per box would mean a sequence of 180 packs would contain 15 Prism Stars, leaving 165 - an odd number - for the reverses. The solutions for this problem are as follows:
- Change the box ratio for the Prism Stars to 3.2 or 2.8. I didn’t want to do this as my own compiled raw data and that from the Derium video don’t support this.
- Assume slightly different rarities for the two reverse sheets. Not impossible, but very messy for modelling.
- Assume 3 sheets were used to print the reverses and not 2. Was done in the past by WotC as it appears, but also not my favorite solution.
- Use the double sequence length (360 packs) in my model.
The last solution was what I went for, and I have since opted to use a sequence length of 360 in all XY, Sun & Moon and Sword & Shield series sets, eliminating this problem.
The rarity table looks as follows:
It is noteworthy that unlike for most other sets, the two non-holo rares which appear as theme deck exclusive holos (Empoleon and Garchomp) don’t seem to be short printed (see raw data at the bottom). As to how many secret rares are printed on the FT sheet, assuming each one is printed 3 times, leaving 49 slots for the full art trainers, fits the observed data well.
The raw data for the various card types is shown below:
The uncommons sheet looks as follows:
† Prinplup, Gardenia, Gabite, Manaphy, Grotle, Yanmega, Volkner, Cranidos, Alolan Dugtrio, Escape Board, Cherrim, Magneton, Oranguru, Drifblim, Pal Pad, Spiritomb, Gumshoos, Luxio, Looker, Shieldon, Order Pad, Monferno, Unidentified Fossil, Honchkrow, Lopunny, Turtonator, Mars, Electric Memory, Floatzel, Skuntank, Cynthia, Cosmoem, Bronzong, Fire Memory, Grotle, Purugly, Unit Energy LPM, Rotom, Drifblim, Gabite, Looker Whistle, Prinplup, Pokémon Fan Club, Cranidos, Oranguru, Missing Clover, Manaphy, Lillie, Magneton, Spiritomb, Alolan Dugtrio, Ancient Crystal, Cherrim, Gumshoos, Shieldon, Lopunny, Unit Energy GRW, Luxio, Escape Board, Honchkrow, Mt. Coronet, Rotom, Unidentified Fossil, Electric Memory, Looker, Yanmega, Pal Pad, Skuntank, Gardenia, Purugly, Floatzel, Missing Clover, Turtonator, Bronzong, Volkner, Cosmoem, Pokémon Fan Club, Gabite, Monferno, Fire Memory, Order Pad, Drifblim, Mars, Lopunny, Manaphy, Cynthia, Grotle, Escape Board, Alolan Dugtrio, Unit Energy LPM, Prinplup, Oranguru, Looker Whistle, Floatzel, Lillie, Magneton, Pal Pad, Luxio, Shieldon, Unidentified Fossil, Cherrim, Gumshoos, Ancient Crystal, Spiritomb, Rotom, Unit Energy GRW, Cosmoem, Looker, Yanmega, Purugly, Skuntank, Electric Memory, Turtonator, Mt. Coronet, Honchkrow, Monferno, Pokémon Fan Club, Cranidos, Fire Memory, Bronzong, Missing Clover †
Edit 2024/03/24: Edited text to reflect fact that all sets of this era are assumed to be using a sequence length of 360, and not 180 (for Ultra Prism, this was the assumption from the beginning).
Edit 2024/03/30: Added reconstruction of Uncommons sheet.