The English Pokémon card rarity guide

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This set includes no less than 24 secret rares, thus unsurprisingly some cards have incredibly low pull rates - 1 in 1000 packs according to the model shown in the rarity table below; I even needed to add an extra color, black, to designate pull rates lower than 1 in 800, and change the font size in the cell:

In my model, all 24 secret rares have a pull rate of 1 in 1000 packs, being each printed 3 times on the 10x10 full art Trainers/secret rare sheet and thus taking up 72 slots on the sheet, leaving 28 for the full arts. This leads to 0.86 secret rares per box on average.

Of course, I could have modelled this differently, assuming all 3 full arts printed 10 times on the sheet, 22 secret rares 3 times and the remaining 2 secret rares only 2 times, which would give them pull rates of 1 in 1500 packs. The reason I modelled the set as I did - aside from keeping things as simple as possible - is because the video mentioned in earlier posts which shows how Pokémon cards are made shows part of this very same sheet. The upper part looks as follows (green denoting full arts, pink and red rainbow rares and yellow secret rare items and Energy cards):

The more or less regular pattern leads me to the conclusion that the upper five rows likely contain 14 full arts and 36 secret rares. If the same is assumed for the lower half, there would be 72 secret rares on the sheet, with each one likely printed 3 times, thus avoiding making two of them significantly rarer than the others.

The raw data - including that from Derium’s videos for the Pokémon-GX, full arts and secret rares - is shown at the bottom. The only noteworthy thing about it is that the two non-holo rares which appear as theme deck exclusive holos, Lunala and Solgaleo, appear to be significantly rarer than the others; my estimate is each of the two appears 3 times on the sheet.

The uncommons sheet looks as follows:

† Whimsicott, Vanillish, Aether Paradise Conservation Area, Hala, Sudowoodo, Mallow, Energy Recycler, Tentacruel, Choice Band, Altar of the Moone, Machoke, Gliscor, Komala, Slowbro, Brooklet Hill, Bewear, Lampent, Clefable, Mareanie, Field Blower, Gothorita, Sableye, Max Potion, Alolan Graveler, Sudowoodo, Rescue Stretcher, Hakamo-o, Energy Loto, Machoke, Glalie, Watchog, Multi Switch, Komala, Enhanced Hammer, Aqua Patch, Weepinbell, Fletchinder, Sliggoo, Bewear, Alomomola, Choice Band, Vanillish, Whimsicott, Mareanie, Hala, Aether Paradise Conservation Area, Tentacruel, Mallow, Alolan Graveler, Altar of the Sunne, Altar of the Moone, Gliscor, Brooklet Hill, Hakamo-o, Field Blower, Gothorita, Energy Recycler, Max Potion, Clefable, Lampent, Machoke, Slowbro, Watchog, Rescue Stretcher, Sudowoodo, Metang, Komala, Energy Loto, Aqua Patch, Vanillish, Enhanced Hammer, Alomomola, Mareanie, Fletchinder, Sableye, Multi Switch, Sliggoo, Bewear, Whimsicott, Aether Paradise Conservation Area, Alolan Graveler, Hala, Glalie, Weepinbell, Altar of the Moone, Mallow, Altar of the Sunne, Hakamo-o, Gliscor, Clefable, Metang, Choice Band, Field Blower, Sudowoodo, Lampent, Tentacruel, Max Potion, Machoke, Energy Recycler, Slowbro, Gothorita, Komala, Rescue Stretcher, Alomomola, Bewear, Brooklet Hill, Sliggoo, Energy Loto, Sableye, Mareanie, Aqua Patch, Enhanced Hammer, Glalie, Watchog, Weepinbell, Multi Switch, Fletchinder, Alolan Graveler, Altar of the Sunne, Metang, Hakamo-o †

Edit 2024/03/24: Changed sequence length from 180 to 360. This has no impact on pull rates.
Edit 2024/05/01: Added reconstruction of uncommons sheet

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Burning Shadows

For this set, as shown in my introductory post to the Sun & Moon series, I will be assuming 4.0 “regular” Pokémon-GX 1.1 full art Pokémon-GX and 1.3 full art Trainers/secret rares; on this last sheet, each of the 22 secret rares is assumed to be printed 3 times. This leads to the following rarity table:

For the non-holo rares, it appears Lycanroc and Alolan Ninetales, which are featured as theme deck exclusive holos, are artificially short-printed. The raw data for the various sheets is shown below (dashed lines indicating where the transition from H10 to H9, etc., would occur):

I reconstructed the commons and uncommons sheets. The commons sheet looks as follows (the dagger marks indicate it is unclear where it begins and ends):

† Magikarp, Croagunk, Pikachu, Pansear, Charmander, Alolan Rattata, Porygon, Panpour, Pansage, Espurr, Sawk, Noibat, Stufful, Mudbray, Tynamo, Oddish, Duskull, Morelull, Caterpie, Marill, Rhyhorn, Sandygast, Hoothoot, Tangela, Dewpider, Inkay, Ralts, Crabrawler, Sneasel, Venipede, Horsea, Cutiefly, Ledyba, Alolan Grimer, Riolu, Meowth, Alolan Vulpix, Wimpod, Togedemaru, Croagunk, Pansear, Magikarp, Mudbray, Alolan Rattata, Panpour, Caterpie, Porygon, Sawk, Oddish, Charmander, Marill, Pansage, Espurr, Pikachu, Noibat, Dewpider, Tangela, Rhyhorn, Riolu, Cutiefly, Tynamo, Duskull, Inkay, Stufful, Crabrawler, Morelull, Sandygast, Venipede, Horsea, Mudbray, Ledyba, Hoothoot, Alolan Vulpix, Ralts, Alolan Grimer, Sneasel, Charmander, Crabrawler, Meowth, Stufful, Pansage, Croagunk, Pikachu, Panpour, Cutiefly, Pansear, Magikarp, Alolan Rattata, Wimpod, Togedemaru, Sawk, Mudbray, Oddish, Duskull, Espurr, Morelull, Charmander, Porygon, Marill, Hoothoot, Rhyhorn, Ralts, Tangela, Tynamo, Crabrawler, Inkay, Ledyba, Caterpie, Sandygast, Venipede, Sneasel, Alolan Vulpix, Horsea, Noibat, Alolan Grimer, Riolu, Cutiefly, Dewpider, Togedemaru, Wimpod, Meowth †

And this is the uncommons sheet:

† Guzma, Whirlipede, Tormenting Spray, Simisage, Kirlia, Heatmor, Weakness Policy, Po Town, Rotom Dex, Simisear, Electabuzz, Lana, Metapod, Porygon2, Kiawe, Olivia, Bouffalant, Charmeleon, Rhydon, Noctowl, Mount Lanakila, Simisear, Dusclops, Acerola, Bodybuilding Dumbells, Seadra, Gloom, Lunatone, Wicke, Wishful Baton, Ribombee, Sophocles, Escape Rope, Rotom Dex, Seviper, Super Scoop Up, Simipour, Plumeria, Solrock, Guzma, Eelektrik, Wobbuffet, Whirlipede, Charmeleon, Seadra, Lunatone, Rhydon, Kiawe, Olivia, Kirlia, Ribombee, Po Town, Weakness Policy, Heatmor, Tormenting Spray, Lana, Seviper, Gloom, Acerola, Wobbuffet, Charmeleon, Porygon2, Simisear, Metapod, Dusclops, Noctowl, Simisage, Eelektrik, Bouffalant, Escape Rope, Wicke, Mount Lanakila, Wishful Baton, Solrock, Simipour, Bodybuilding Dumbells, Sophocles, Electabuzz, Super Scoop Up, Rotom Dex, Seadra, Plumeria, Lunatone, Olivia, Kirlia, Ribombee, Guzma, Whirlipede, Simisage, Weakness Policy, Porygon2, Po Town, Dusclops, Charmeleon, Tormenting Spray, Lana, Heatmor, Simisear, Kiawe, Mount Lanakila, Electabuzz, Noctowl, Simipour, Bouffalant, Eelektrik, Rhydon, Bodybuilding Dumbells, Metapod, Wishful Baton, Acerola, Gloom, Escape Rope, Solrock, Ribombee, Sophocles, Seviper, Wicke, Wobbuffet, Seadra, Plumeria, Super Scoop Up †

Edit 2024/02/25: Added info that my model for Ultra Prism does in fact use a sequence length of 360 packs instead of 180, though that for Burning Shadows continues to use 180.
Edit 2024/03/24: Increased sequence length from 180 to 360; changed box ratios for full art Pokémon and full art Trainers/secret rares from 1.0 and 1.4, respectively, to 1.1 and 1.3, respectively. Also removed a bunch of unnecessary information from the text.
Edit 2024/04/06: Added reconstruction of uncommons sheet.

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Shining Legends

I made a mistake when summarizing the data for this set, thinking at first the reverse/holo Basic Energy cards were printed separately from the other reverses, and even went back to my post on Generations and edited it assuming it would be the same case there. Then I realized however that the pattern printed on the non-energy reverses is deceptive and the actual holofoil pattern is the same for them and the Basic Energy cards. So I undid my edit on Generations.

To be sure about my theory that all reverses were printed on the same sheet is plausible, I speed-watched two Youtube videos by Derium counting how many reverse energies he got. They were large openings, one of 501 packs, the other of “501 or 502”. Assuming each reverse Basic Energy is printed once on the sheet, the expected number is 9 / 121 * 501 = 37.26. In the two openings I counted 29 and 37, respectively. The first number is suspiciously low, but I am assuming it is not statistically relevant. The fact that the packs come from various sources of product and not from booster boxes, when you usually get 36 reverses in sequence from the sheet, ought to lead to higher uncertainty. (It is also possible I missed one or two when speed watching the videos.) Anyway, I will be assuming only one sheet was used for all the reverses.

The set features holos, “regular” Pokémon-GX, full art Pokémon-GX, one full art Trainer, secret rares and 6 Shining Pokémon, but no non-holo rares; all of these cards come in the rare slot. Going by holofoil pattern, I will assume the sole full art Trainer (Pokémon Breeder) and all secret rares were printed on one sheet. This includes the “Test Tube Mewtwo”, aka “MewTube” secret rare, which while having the layout of a regular Pokémon-GX is textured like the other secret rares.

For the pull rates, I have three of the four sources I used for the main sets back in my introductory post on the Sun & Moon Series, namely my own data from Youtube videos (1), that posted on E4 by @burpies (Pull Rates in Sun & Moon - Sword & Shield Sets) (2) and the two videos by Derium (4). It is possible (2) includes the data from (4). Here are the “box ratios” for the various types of cards (I am calculating box ratios for the sake of comparison with other sets even though Shining Legends was not sold in booster boxes):

My own sample is the smallest of the three by far; it is also an outlier. In my model I am going to go with 4.0 “regular” Pokémon-GX, 1.0 full art Pokémon, 1.4 full art Trainers/secret rares and 3.2 Shining Pokémon per “box”. The first three are also consistent with other Sun & Moon series sets, while the ratio for the Shining Pokémon is based solely on the data above.

The rarity table looks as follows (the box ratios nbox are grayed out as there are no booster boxes):

As can be seen, the model leads to the full art Pokémon-GX having exactly half the pull rates as the “regular” ones, which is kind of neat. For the full art Trainer/secret rare sheet, the three sources of data suggests secret rares take up around 62.5 to 67.3 slots on the 10x10 sheet. I am thus assuming Pokémon Breeder to be printed on the sheet 35 times, and the five secret rares 13 times each.

The raw data for the holos, full art Trainer/secret rares and Shining Pokémon is as follows (the “regular” and full art Pokémon-GX are assumed to all have the same pull rate):

It is certainly interesting that “MewTube” appeared more often than the other secret rares, but I don’t think the sample size is large enough to conclude that this is meaningful, so I am modelling all secret rares with equal pull rates.

Edit 2024/03/24: Changed sequence length from 180 to 360. This has no impact on pull rates.

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Crimson Invasion

There aren’t many mysteries regarding the pull rates for this set. The number of “regular” Pokémon-GX appears to be reduced to 3.0 per box, and I am modelling the set to include 1.2 full art Pokémon and 1.2 full art Trainers/secret rares per box on average. On the latter sheet, I am assuming each of the 13 secret rares is printed 5 times, which fits the raw data well and leads to 0.78 secret rares per box on average. The only artificial rarity differences I think are likely are for the non-holo rares, where I would guess Hydreigon and Kommo-o, those ones featured as theme deck exclusive holos, are prnted 4 times each on the sheet, the other ones 6 or 7 times. The rarity table looks as follows:

The raw data for the holos, rares, Pokémon-GX, full art Pokémon and full art Trainers/secret rares looks as follows:

The uncommons sheet looks as follows:

† Psychic Memory, Staravia, Piloswine, Lusamine, Hakamo-o, Haunter, Devoured Field, Zweilous, Gastrodon, Sea of Nothingness, Miltank, Cinccino, Gladion, Lairon, Alolan Graveler, Emolga, Mawile, Grumpig, Peeking Red Card, Diggersby, Hakamo-o, Counter Catcher, Fighting Memory, Counter Energy, Accelgor, Lusamine, Staravia, Kakuna, Dashing Pouch, Psychic Memory, Piloswine, Devoured Field, Zweilous, Miltank, Sea of Nothingness, Counter Energy, Gladion, Cinccino, Lairon, Emolga, Alolan Graveler, Fighting Memory, Gastrodon, Counter Energy, Mawile, Grumpig, Staravia, Counter Catcher, Diggersby, Accelgor, Kakuna, Lusamine, Haunter, Dashing Pouch, Hakamo-o, Miltank, Peeking Red Card, Piloswine, Zweilous, Cinccino, Grumpig, Emolga, Gladion, Staravia, Alolan Graveler, Mawile, Psychic Memory, Lairon, Fighting Memory, Devoured Field, Gastrodon, Kakuna, Accelgor, Sea of Nothingness, Haunter, Counter Catcher, Hakamo-o, Diggersby, Piloswine, Counter Energy, Miltank, Zweilous, Gastrodon, Peeking Red Card, Cinccino, Alolan Graveler, Devoured Field, Emolga, Grumpig, Lusamine, Lairon, Mawile, Dashing Pouch, Gladion, Staravia, Accelgor, Kakuna, Miltank, Psychic Memory, Haunter, Fighting Memory, Hakamo-o, Sea of Nothingness, Diggersby, Alolan Graveler, Piloswine, Peeking Red Card, Gastrodon, Zweilous, Haunter, Cinccino, Grumpig, Emolga, Counter Catcher, Mawile, Diggersby, Fighting Memory, Dashing Pouch, Lairon, Kakuna, Accelgor †

Edit 2024/03/24: Changed sequence length from 180 to 360; this has no impact on pull rates.
Edit 2024/04/06: Added reconstruction of uncommons sheet.

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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.

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Forbidden Light

For Forbidden Light, the rarity table looks as follows:

The total number of full art Pokémon, full art Trainers and secret rares in the model is smaller for this set (2.2) than for earlier Sun & Moon series sets (2.4); this is supported by the raw data. In the model I am assuming each secret rare is printed 4 times on the FT sheet, taking up 60 of 100 slots in total, which leads to a somewhat low box ratio for secret rares of 0.72. This also fits the raw data more or less, as the ratio of secret rares to total number of cards from that sheet in the samples looked at is 65.3 for my own data, 61.9 for that of @burpies and 58.8 from the Derium video.

The two non-holo rares which are featured as theme deck exclusive holos, Alolan Exeggutor and Lycanroc, are short printed, as can be seen from the raw data presented at the bottom.

The raw data for the various types of cards is as follows:

The uncommons sheet looks as follows:

† Gogoat, Mesprit, Unidentified Fossil, Uxie, Mysterious Treasure, Azelf, Spewpa, Dedenne, Amaura, Lady, Araquanid, Klefki, Frogadier, Heliolisk, Floette, Poipole, Mesprit, Ultra Space, Metal Frying Pan, Hoopa, Judge, Magneton, Gogoat, Bonnie, Gabite, Tyrunt, Sliggoo, Frogadier, Eneporter, Doublade, Hawlucha, Braixen, Azelf, Crasher Wake, Uxie, Unit Energy FDFa, Amaura, Fossil Excavation Map, Diggersby, Ultra Recon Squad, Heliolisk, Spewpa, Zygarde, Mysterious Treasure, Araquanid, Unidentified Fossil, Dedenne, Gogoat, Floette, Magneton, Klefki, Uxie, Lady, Hoopa, Lysandre Labs, Mesprit, Ultra Space, Braixen, Doublade, Judge, Araquanid, Metal Frying Pan, Spewpa, Tyrunt, Bonnie, Frogadier, Eneporter, Gabite, Sliggoo, Zygarde, Hawlucha, Amaura, Unit Energy FDFa, Uxie, Poipole, Crasher Wake, Azelf, Ultra Recon Squad, Fossil Excavation Map, Lysandre Labs, Dedenne, Gogoat, Unidentified Fossil, Mesprit, Floette, Heliolisk, Diggersby, Lady, Braixen, Mysterious Treasure, Metal Frying Pan, Bonnie, Magneton, Sliggoo, Frogadier, Spewpa, Klefki, Gabite, Hoopa, Crasher Wake, Doublade, Judge, Azelf, Tyrunt, Ultra Recon Squad, Amaura, Eneporter, Araquanid, Ultra Space, Poipole, Hawlucha, Unit Energy FDFa, Braixen, Fossil Excavation Map, Zygarde, Doublade, Diggersby, Heliolisk, Magneton, Hoopa, Lysandre Labs †

Edit 2024/03/24: Changed sequence length from 180 to 360; this has no impact on pull rates.
Edit 2024/03/29: Added reconstruction of uncommons sheet

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Celestial Storm

Based on the information compiled in the introductory post for the Sun & Moon series, I am assuming the following box ratios for this set: 4 “regular” Pokémon-GX, 0.8 full art Pokémon-GX, 1.4 full art Trainers & secret rares, and 2 Prism Star cards.

As I did for Sun & Moon Base Set, I chose not to model all secret rares having the same pull rate, even though assuming each one of the 15 cards printed 4 times on the sheet would yield 0.84 secret rares per box, not an outlandish number. Still, I think a model where 8 of them are printed 3 times on the sheet and the remaing 7 are printed 4 times better fits the raw data, both in terms of secret rares per box (0.73 according to this model) as well as in terms of the ratio between full art Trainers and secret rares. The raw data displayes the following ratios of secret rares / (full arts + secret rares): 53.5% (data compiled by me), 55.4% (data from @burpies) and 56.4% (data from Derium video); in the model, this ratio is 52.0%.

The rarity table looks as follows:

As with most other sets of this era, the two non-holo rares which are featured as theme deck exclusive holos, Sceptile and Swampert, are short printed. The raw data for the various holos, etc. is shown below:

For this set, I also reconstructed the uncommons sheet - it looks as follows:

† Metang, Apricorn Maker, Hiker, Lure Ball, Oricorio (Captivating Salsa), Swalot, Copycat, Huntail, Grovyle, Energy Switch, Lombre, Mawile, Acro Bike, Last Chance Potion, Lisia, Torkoal, Oricorio (Zappy Pom-Poms), Illumise, PokéNav, Scyther, Energy Recycle System, Marshtomp, Sableye, Kecleon, Hustle Belt, Volbeat, Combusken, Minun, Tate & Liza, Cacturne, Weepinbell, The Masked Royal, Oricorio (Captivating Salsa), Pupitar, Fisherman, Super Scoop Up, Masquerain, Bill’s Maintenance, Plusle, Pelipper, Solrock, Life Herb, Sky Pillar, Torkoal, Lure Ball, Rainbow Energy, Gorebyss, Nuzleaf, TV Reporter, Dunsparce, Last Chance Potion, Swalot, Underground Expedition, Minior, Combusken, Lisia, Beast Ball, Switch, Grovyle, Lanturn, Shelgon, Hustle Belt, Oricorio (Zappy Pom-Poms), Tropius, Hiker, Energy Switch, Rainbow Brush, Apricorn Maker, Donphan, Scyther, Hau, Metang, Huntail, Minun, Copycat, Loudred, Energy Recycle System, Shrine of Punishment, Acro Bike, Super Scoop Up, Weepinbell, Friend Ball, Mawile, Illumise, Plusle, PokéNav, Vigoroth, Fisherman, Pupitar, Kecleon, TV Reporter, Life Herb, Gorebyss, Sableye, The Masked Royal, Minior, Volbeat, Pelipper, Sky Pillar, Dunsparce, Tate & Liza, Bill’s Maintenance, Cacturne, Lombre, Lanturn, Switch, Loudred, Masquerain, Hau, Underground Expedition, Shelgon, Beast Ball, Rainbow Brush, Tropius, Marshtomp, Solrock, Donphan, Vigoroth, Nuzleaf, Friend Ball, Rare Candy †

Note that the 3 U1 cards (Rainbow Energy, Rare Candy, Shrine of Punishment) are rarer than all the non-holo rares.

As to my method of reconstructing the uncommons sheet, I intend to make a special post about that at a later time. Basically, I noticed that instead of looking at individual packs and trying to piece together sequences of 3 uncommons, I could look at complete boxes. In this set (and in Evolutions, which I analyzed the same way) cards are inserted from two sheets of uncommons into packs alternatingly, yielding two sequences of 54 uncommons each, making it relatively easy to reconstruct the uncommons sheet with the data from just a small number of boxes (3 in this case).

Edit 2024/03/24: Changed sequence length from 180 to 360 (no impact on pull rates); added reconstruction of uncommons sheet.

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Dragon Majesty

For this special set, I can rely on my own compiled data (1) as well as that provided by @burpies (2) in order to model the “box ratios” (the set was not sold in booster boxes, but they are practical for comparing with other sets). (Derium did not make a large opening video for this one.) Here is the data:

The two samples are relatively consistent between each other (of course they may be partially relying on the same Youtube videos); at least they are more consistent than those for Shining Legends. The only big difference is the ratio between full art Trainers (FAT) and secret rares, which are assumed to be printed on the same sheet; interestingly, it is wildly different in the two samples. My model is based on the following three assumptions:

• A “hit” (Pokémon-GX, full art or secret rare) in every fourth pack
• A Prism Star card in every tenth pack
• Reasonably similar pull rates between full art Pokémon and full art Trainers. This (and the fact that it is a “rounder” number, double that of the full art Pokémon) led me to modelling 2.4 full art Trainers/secret rares per “box” and not 2.6; if I assume 36 of 100 slots on this sheet taken up by full art Trainers (which my own sample would suggest), they still have higher pull rates than the full art Pokémon.

The rarity table is given below. Note that this set contains reverse Basic Energy cards, assumed to be printed on the same sheet as the other reverses, for a total of 65 reverses:

The raw data for the holos, Pokémon-GX, full art Trainers/secret rares and Prism Star cards is given below (the full art Pokémon are assumed to have identical pull rates):

Two concluding remarks:

• The difference in observed pulls for the two Prism Star cards is noteworthy, but I am assuming no artificial rarity differences as I can’t say whether or not it is statistically significant.
• I did not look at the reverses, so I don’t know if the reverse Basic Energy cards are RE1 or RE2 cards.

Edit 2024/03/24: Changed sequence length from 180 to 360, which has no impact on pull rates.
Edit 2024/05/05: Fixed error in rarity table (total number of reverses in 65, not 69)

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Lost Thunder

For this set, as mentioned in my introductory post on the Sun & Moon series, I am assuming 3.6 “regular” Pokémon-GX, 1.1 full art Pokémon-GX and 1.3 full art Trainers/secret rares; on this last sheet, I am assuming each of the 22 secret rares to be printed 3 times, taking up 66 of the 100 slots on the 10x10 sheet, or 66.0%.

Interestingly, while this agrees well with the samples from @burpies and Derium (see the introductory post for their raw data), which show 65.2% and 63.2% secret rares respectively, my own sample is kind of an outlier with only 56.1% of the cards from that sheet being secret rares. Again, this shows it is necessary to be very carefull even with comparatively large samples.

The rarity table looks as follows:

The two rares which appear as theme deck exclusive holos, Entei and Raikou, appear to be short-printed (R2).

The raw data for the holos. rares, Prism Star cards, Pokémon-GX, full art Pokémon and full art Trainers/secret rares is as follows:

I also reconstructed the uncommons sheet, which I figured out is actually not that difficult if you take into account the sequence in which the pack are inserted in a box. It looks as follows:

† Vespiquen, Mina, Alolan Dugtrio, Pinsir, Choice Helmet, Morty, Stantler, Quilava, Girafarig, Carbink, Shiinotic, Kecleon (Unit Color 1), Aether Foundation Employee, Kirlia, Mantine, Ariados, Fairy Charm P, Professor Elm’s Lecture, Trumbeak, Pupitar, Lampent, Grovyle, Adventure Bag, Xatu, Sableye, Brionne, Electropower, Delibird, Bayleef, Sudowoodo, Counter Gain, Gogoat, Moomoo Milk, Fairy Charm G, Ninjask, Magearna, Lost Blender, Silcoon, Kahili, Dedenne, Heracross, Fairy Charm F, Skiploom, Pinsir, Grovyle, Custom Catcher, Fairy Charm Dr, Hitmontop, Faba, Electabuzz, Spell Tag, Cascoon, Wait and See Hammer, Net Ball, Kecleon (Unit Color 3), Sightseer, Whitney, Flaaffy, Kahili, Sudowoodo, Choice Helmet, Mantine, Girafarig, Mixed Herbs, Stantler, Morty, Carbink, Shiinotic, Fairy Charm P, Gogoat, Shuckle, Alolan Dugtrio, Professor Elm’s Lecture, Mina, Kirlia, Aether Foundation Employee, Quilava, Pupitar, Counter Gain, Ariados, Moomoo Milk, Vespiquen, Heracross, Pinsir, Memory Energy, Kecleon (Unit Color 1), Lampent, Sableye, Electropower, Xatu, Bayleef, Dedenne, Adventure Bag, Skiploom, Grovyle, Brionne, Trumbeak, Ninjask, Fairy Charm Dr, Mantine, Wait and See Hammer, Fairy Charm G, Silcoon, Faba, Sightseer, Delibird, Cascoon, Lost Blender, Custom Catcher, Hitmontop, Magearna, Fairy Charm F, Mixed Herbs, Flaaffy, Electabuzz, Kecleon (Unit Color 3), Net Ball, Whitney, Shuckle, Spell Tag, Memory Energy †

Edit 2024/03/24: Changed sequence length from 180 to 360, and slightly edited pull rates for full art Pokémon-GX as well as full art Trainers/secret rares.
Edit 2024/03/27: Added reconstruction for uncommons sheet

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Team Up

Since the last update to this thread, I have made a few changes. First of all, I decided that the sequence length used in my models of 180 packs was unsatisfactory for modelling the Sun & Moon series sets, so I changed it to 360. I am thus able to adjust box ratios for different types of cards in increments of 0.1 per box, instead of 0.2. I made use for this for Burning Shadows as well as Lost Thunder, and am doing so for Team Up as well. I also updated the introductory post for the Sun & Moon series with the new models for each set. Furthermore, I decided to go back to the first four XY Series sets (XY Base Set, Flashfire, Furious Fists and Phantom Forces) and changed the sequence length from 216 packs to 360; this has a small effect on the pull rates as well.

The second change I made was that I realized that when reconstructing uncut sheets, looking at complete boxes instead of individual packs means it is actually relatively easy to reconstruct uncommons sheets (I intend to make a special post about that in the future), so I added the info on the uncommons for Celestial Storm and Lost Thunder.

Now, to Team Up. The rarity table looks as follows:

For the holos, the raw data looks as follows - the sample size is to small to say anything about individual card rarities:

For the non-holo rares, it appears that Blastoise and Charzard, which appear as theme deck exclusive holos, are short-printed - pretty heavily, likely as R2 cards; also, I feel confident from the raw data that Galvantula is the sole R5 card:

There is nothing remarkable about the Prism Star cards or about the “regular” Pokémon-GX (like for earlier sets, I am also using the data from Derium’s videos):

For the full art Pokémon sheet, I am assuming it also includes the alt arts, as the holofoil used appears to be the same as for the other full arts. I can see no pattern of alt arts being rarer that other full arts:

For the full art Trainers/secret rares sheet, my estimate is that all these cards are printed 4 times each on the sheet and thus have the same rarity. I can see no pattern of secret rares (highlighted in red) being rarer than full art Trainers:

Finally, a word on the uncommons. I reconstructed the sheet - the 23 C2 cards are the 22 Trainers, plus Jynx - but as for some other sets (though interestingly not for Celestial Storm or Lost Thunder), I noticed certain parts of the sheet have a tendency for the cards there to get flipped around. Here it seems to be the sequence where Kakuna is followed by Rapidash (underlined below), and often either one or the other card seems to go missing - so there I might have gotten the sequence wrong:

† Spiritomb, Heliolisk, Jasmine, Judge Whistle, Cosmoem, Persian, Lavender Town, Nidorino, Dangerous Drill, Hitmonchan, Dragonair, Unidentified Fossil, Rapidash, Evelyn, Nanu, Farfetch’d, Alolan Graveler, Brock’s Grit, Pupitar, Electrocharger, Charmeleon, Water Memory, Omanyte, Kangaskhan, Heliolisk, Sabrina’s Suggestion, Torracat, Jynx, Hitmonlee, Dana, Kabuto, Nita, Nidorina, Doublade, Flaaffy, Morgan, Spiritomb, Viridian Forest, Tentacruel, Ingo & Emmet, Wartortle, Tauros, Persian, Metal Goggles, Golduck, Grass Memory, Kakuna, Rapidash, Return Label, Kangaskhan, Cosmoem, Hitmonchan, Jasmine, Dragonair, Torracat, Brock’s Grit, Pokémon Communication, Flaaffy, Omanyte, Tauros, Lavender Town, Wartortle, Heliolisk, Buff Padding, Kabuto, Fairy Charm UB, Charmeleon, Unidentified Fossil, Farfetch’d, Tentacruel, Evelyn, Pupitar, Kakuna, Nidorino, Judge Whistle, Nanu, Hitmonlee, Doublade, Dangerous Drill, Alolan Graveler, Omanyte, Water Memory, Golduck, Dana, Spiritomb, Viridian Forest, Rapidash, Electrocharger, Hitmonchan, Grass Memory, Persian, Farfetch’d, Cosmoem, Dragonair, Ingo & Emmet, Charmeleon, Morgan, Flaaffy, Jynx, Kangaskhan, Nidorina, Sabrina’s Suggestion, Alolan Graveler, Nita, Tauros, Torracat, Kabuto, Nidorino, Fairy Charm UB, Wartortle, Pupitar, Pokémon Communication, Hitmonlee, Metal Goggles, Golduck, Doublade, Tentacruel, Return Label, Nidorina, Kakuna, Buff Padding †

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Detective Pikachu

For this set, each booster pack consists of 3 holofoil commons and 1 holofoil rare. This leads to the following rarity table:

As to the raw data for the holos, despite the fact that a very small sample showed Mewtwo appearing the fewest times, I am assuming there are no artificial rarity differences between cards:

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Unbroken Bonds

For this set, as described in my introductory post on the Sun & Moon series, I am assuming 3.6 “regular” Pokémon-GX, 1.1 full art Pokémon-GX and 1.3 full art Trainers/secret rares. This set no long er contains Prism Star cards. As to the composition of the full art Trainers/secret rares sheet, this is the third and final Sun & Moon set for which my model assumes different rarities for the secret rares (the other two being Sun & Moon Base Set and Celestial Storm) as this model seems to best fit the raw data: each of the 6 full art Trainers printed 5 times on the sheet, 10 of the 20 secret rares 4 times and the other 10 3 times. (Alternatively, another model would be the 6 full art Trainers and 16 secret rares printed 4 times and the remaining 4 secret rares 3 times, but that would yield 0.99 secret rares per box on average, which appears to be a bit much.) The rarity table looks as follows:

Note that the two non-holo rares which are featured as theme deck exclusive holos, Mewtwo and Zeraora, appear to be short-printed. I also feel confident enough from the raw data (presented further below) to assume that Butterfree, Meowstic, Persian, Purugly, Raichu and Wigglytuff are the 6 R4 rares.

The raw data (including that compiled from Derium’s 1,080 pack opening, and TheGameCapital’s 2,592 pack opening) is shown below. The “overlap” are the cards in one case opened by TheGameCapital on Youtube which I included in my sample. I subtracted the pulls from that case so as to not count them twice.

The reconstructed uncommons sheet looks as follows:

† Beast Bringer, Hitmontop, Gliscor, Frogadier, Rhydon, Wartortle, Cleffa, Porygon2, Ultra Forest Kartenvoy, Golbat, Metapod, Torracat, Poliwhirl, Gloom, Dodrio, Raticate, Weepinbell, Fearow, Charjabug, Pyukumuku, Togetic, Fairy Charm L, Krokorok, Graveler, Hitmontop, Chatot, Molayne, Frogadier, Welder, Lairon, Gliscor, Triple Acceleration Energy, Energy Spinner, Rhydon, Green’s Exploration, Tyrogue, Happiny, Metal Core Barrier, Tentacruel, Ultra Forest Kartenvoy, Dusk Stone, Haunter, Lt. Surge’s Strategy, Electromagnetic Radar, Cleffa, Giovanni’s Exile, Graveler, Porygon2, Martial Arts Dojo, Fairy Charm L, Poliwhirl, Devolution Spray Z, Metapod, Koga’s Trap, Dust Island, Pyukumuku, Fire Crystal, Weepinbell, Surprise Box, Torracat, Energy Spinner, Charjabug, Chip-Chip Ice Axe, Samson Oak, Janine, Raticate, Triple Acceleration Energy, Fairy Charm Ability, Tyrogue, Stealthy Hood, Chatot, Electromagnetic Radar, Frogadier, Beast Bringer, Power Plant, Lairon, Green’s Exploration, Wartortle, Gloom, Haunter, Cleffa, Happiny, Dust Island, Golbat, Tentacruel, Pokégear 3.0, Molayne, Giovanni’s Exile, Dusk Stone, Raticate, Lt. Surge’s Strategy, Samson Oak, Porygon2, Dodrio, Metapod, Fearow, Graveler, Metal Core Barrier, Fire Crystal, Devolution Spray Z, Togetic, Koga’s Trap, Power Plant, Charjabug, Torracat, Surprise Box, Chatot, Lairon, Martial Arts Dojo, Fairy Charm Ability, Chip-Chip Ice Axe, Tyrogue, Janine, Pokégear 3.0, Triple Acceleration Energy, Tentacruel, Stealthy Hood, Happiny, Welder, Haunter, Krokorok †

Edit 2024/04/26: added additional sample (TheGameCapital) to raw data; added note on alternative composition for full art Trainers/secret rares sheet

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Unified Minds

For this set, the box ratios for the full art Pokémon and the full art Trainers/secret rares appear similar to those in Unbroken Bonds, which is not surprising as the number of these cards is very similar for both sets. Thus I am going with 1.1 full art Pokémon and 1.3 full art Trainers/secret rares in my model. For the “regular” Pokémon-GX, there are more per box on average (also not surprising as there are 17 “regular” Pokémon-GX in the set as opposed to 14 in Unbroken Bonds) and I am assuming 4.6 per box on average. As to the composition of the FP (full art Trainers/secret rares) sheet, my estimate is each of the 22 secret rares is printed 3 times on it, 2 full art Trainers are printed 5 times and the remaining 4 are printed 6 times. This results in 0.86 secret rares per box on average. The rarity table looks as follows:

The two non-holo rares which are featured as theme deck exclusive holos, Dragonite and Necrozma, appear to be short-printed (R2). Based on the raw data further below, I feel fairly confident as to which 9 rares are R4 cards.

I reconstructed the uncommons sheet and the 23 U1 uncommons are a mixture of Trainers and Special Energy Cards. The sheet looks as follows:

† Carracosta, Audino, Yanmega, Jynx, Dragonair (Tail Whap), Dhelmise, Heracross, Coach Trainer, Cresselia, Cherish Ball, Tauros, Tirtouga, Tranquill, Recycle Energy, Thundurus, Dragonair (Twister), Steenee, Doublade, Channeler, Azelf, Blue’s Tactics, Fraxure, Basculin, Munchlax, Reset Stamp, Eelektrik, Dedenne, Lurantis, Giant Bomb, Bug Catcher, Mesprit, Komala, Pokémon Research Lab, Lumineon, Normalium Z, Hapu, Magneton, Sableye, Swadloon, Flyinium Z, Blizzard Town, Wynaut, Type: Null, Poké Maniac, Lapras, Karate Belt, Grimsley, Pyukumuku, Archen, Yanmega, Ear-Ringing Bell, Blaine’s Quiz Show, Oranguru, Weakness Guard Energy, Stadium Nav, Gabite, Cherish Ball, Tag Switch, Elgyem, U-Turn Board, Carracosta, Great Potion, Bibarel, Tornadus, Jynx, Slumbering Forest, Relicanth, Blue’s Tactics, Lampent, Musharna, Dragonair (Tail Whap), Tirtouga, Giant Hearth, Vigoroth, Audino, Thundurus, Recycle Energy, Breloom, Komala, Dhelmise, Cresselia, Dragonair (Twister), Basculin, Misty’s Favor, Noctowl, Tranquill, Eelektrik, Reset Stamp, Heracross, Type: Null, Steenee, Azelf, Dedenne, Lumineon, Gabite, Tauros, Munchlax, Magneton, Bibarel, Doublade, Oranguru, Lurantis, Mesprit, Sableye, Lapras, Relicanth, Fraxure, Elgyem, Pyukumuku, Vigoroth, Unidentified Fossil, Tornadus, Swadloon, Wynaut, Archen, Lampent, Breloom, Dark City, Musharna, Misty’s Favor, Noctowl †

The raw data for the holos, rares and various types of ultra rares is given below. It includes that compiled from Derium’s 1,080 pack opening, and TheGameCapital’s 2,592 pack opening. The “overlap” are the cards in one case opened by TheGameCapital on Youtube which I included in my sample. I subtracted the pulls from that case so as to not count them twice.

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Digression: How to reconstruct an uncommons sheet

When I started off reconstructing uncut sheets of commons from Youtube videos, I was initially only looking at individual packs. A sheet of commons - almost always 11x11 cards, the only exception I encountered was Neo Destiny which was 10x11 - can be pieced together by looking at the sequences of between 4 and 7 cards from packs and looking for overlaps. But for uncommons, this is much more difficult as each pack only contains between 2 and 3 uncommons. I was able to figure out which uncommons appeared how many times on the sheet for some sets - Gym Heroes (where my hypothesis turned out to be correct when an image of the uncut sheet surfaced), Neo Genesis, Neo Destiny and Expedition Base Set - but it was time-consuming and I wasn’t able to reconstruct the entire sequence of cards on the sheet.

However, later on I noticed that for those sets where all the reverses fit on one sheet, it is possible to reconstruct the reverses sheet as the packs in a complete box contain 36 reverses in sequence. It is also possible to tell if the stacks of packs have been “cut” and restacked based on the sequence of pack arts.

So I tried this method for the uncommons, and it was quite successful: For all the sets I looked at - most of the Sun & Moon series sets, plus Evolutions - there are two stacks of uncommons being inserted into packs alternatingly, so a box of 36 packs yields two 54 (18 x 3) card sequences. Given the total number of cards on the sheet is 121, that meens if you find 2-3 videos where you can see the uncommons from all the packs, the pack arts and the position in the box they came from, it is fairly easy to reconstruct the sheet, though occasionally the cards seem to get shifted around during cutting/stacking so sometimes it is necessary to observe some parts of the sequence from more than one box.

The following image (taken from an Excel table) shows the principle:

That shows the uncommons from three boxes of Lost Thunder. The Lugia (L) and Blacephalon (B) packs form one sequence, the Zeraora (Z) and Celebi (C) a second one. R18 designates the 18th pack on the right side, L11 the 11th on the left etc., going front to back.

For the commons, at least for Evolutions which I briefly looked at this way it is similar, except here not two but three different sequences are used, being inserted every third pack instead of every other.

(And as a final note, those reverse sheets I reconstructed are likely all backwards, as I did not take into account that the packs seem to be filled into boxes back to front. This has no impact on card rarities, of course.)

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Hidden Fates

Next up for discussion is Hidden Fates, one of the most popular special sets of all times. Before going into the details of pull rates, we need to look into the different kinds of cards, and different kinds of sheets they were likely printed on:

• Commons, uncommons, rares, rare holos, and reverses: These are present just as in the main expansions. For the reverses, note that just like previous special sets, Hidden Fates includes reverse holo Basic Energies. Also, just like Dragon Majesty, the total number of reverses is 65, meening the 121 card sheet should include 56 printed twice and 9 printed once. I wouldn’t be surprised if these 9 were the 9 Basic Energies, but did not attempt any statistical analysis counting how many reverse Basic Energies appear in Youtube samples.
• “Regular” Pokémon-GX: also the same as in other sets.
• Full art Pokémon-GX: There is only one (Moltres, Zapdos & Articuno GX), which I assume is printed on its own sheet.
• Full art Trainers and secret rares: In am assuming a sheet for the main set including the two full art Trainers (Giovanni’s Exile and Jessie & James) and the rainbow rare Moltres, Zapdos & Articuno GX. As the full art trainers from the Shiny Vault come in the reverse slot, they can’t have been printed on the same sheet. (Extremely random side note: I am already thinking about how the cards in the “god packs” from Pokémon 151 were printed, it is a very interesting question.)
• “Baby shinies”: These cards from the Shiny Vault will have been printed on their own sheet. Due to the uniformly yellow borders, there is no reason to assume the cards were spaced on the print sheet, so I am assuming an 11x11 sheet, just as I did for the Prism Star cards.
• Shiny Pokémon-GX, full art Trainers from the Shiny Vault, and full-gold cards (Tapu Koko GX, Tapu Lele GX, Tapu Bulu GX, Tapu Fini GX). Here is where things get really interesting.
  -As I personally don’t collect modern English cards (kind of ironic given I am writing this elaborate guide) I don’t have any on hand to check if there are any differences in texture or holofoil pattern which would preclude these being printed on the same sheet. Any information on this topic would be very welcome! For now, I am assuming there isn’t - the texture and holofoil pattern for the Shiny Pokémon-GX seems very similar to that of the rainbow rares which are generally printed on the same sheet as full art Trainers and other secret rares, and the full-gold cards appear generally the same as those featured in Ultra Prism and Dragon Majesty which I am also assuming to be printed on the same sheet as full art Trainers, rainbow rares and other secret rares.
  -Due to the observed pull rates (see below) however, I have come to the conclusion that these cards were not all printed on the same sheet; I am assuming one sheet for the Shiny Pokémon-GX and another for the full art Trainers and gold cards.

Now, to the pull rates. For these, I have three main sources: my own Youtube samples (1), data on 1,480 packs by Derium (4) and the thread by @burpies Pull Rates in Sun & Moon - Sword & Shield Sets (2). The latter source, for all its merits, unfortunately does not distinguish between full art Trainers from the main set and those from the Shiny Vault, so the data is not completely comparable. (There is also a post on Reddit by “cardzard.com”, based on 2,350 packs, which arrived at a pull rate of 1/4 for baby shinies, 1/9 for Shiny Pokémon-GX, 1/73 for Shiny Vault full art Trainers, and 1/57 for full-gold cards.)

Here is the data:

From left to right, the columns show:

• number of packs in the sample
• holos (only looked at in my own sample)
• “regular” Pokémon-GX
• full arts from the main set (greyed out as it doesn’t correspond to a single sheet)
• full art Pokémon from the main set (Moltres, Zapdos & Articuno GX)
• full art Trainers from the main set (greyed out as it doesn’t correspond to a single sheet)
• secret rares from the main set (Moltres, Zapdos & Articuno GX) (greyed out as it doesn’t correspond to a single sheet)
• combined full art Trainers/secret rares from the main set
• “baby shinies”
• Shiny Pokémon-GX (assumed to be on a sheet of their own)
• full art Trainers from the Shiny Vault (greyed out as it doesn’t correspond to a single sheet)
• full-gold cards from the Shiny Vault (greyed out as it doesn’t correspond to a single sheet)
• combined full art Trainers/full-gold cards from the Shiny Vault (assumed to be on a sheet of their own)
• full art Trainers (all) (for comparison only, greyed out as it doesn’t correspond to a single sheet)

At the bottom, the model I am assuming for “box” ratios is shown (Hidden Fates wasn’t sold in boxes, but the ratio of cards per 36 packs is simply very usefull for comparing with other sets). The philosophy behind the model is that it appears that there is about a 1 in 3 (12 in 36) chance in getting a premium card in the reverse slot, and a 2 in 5 (14.4 in 36) chance of getting one in the rare slot. This latter ratio is what is standard for the Sword & Shield series. Everything else in the model is basically just chosen to best fit the raw data.

Now, why am I assuming the Shiny Pokémon-GX were printed separately from the full art Trainers and the full-gold cards from the Shiny Vault? Well, it has to do with sheet composition. There are 35 of the former, and 14 of the latter, so the most intuitive way to print them on one sheet would be for 47 of these 49 cards to be printed twice and the remaining two 3 times on a 10x10 sheet. Depending on whether these two cards were Shiny Pokémon-GX or other cards, the Shiny Pokémon-GX would make up 70-72% of the cards on the sheet, and should make up approximately that amount of the pulls (though previous experience writing this guide indicates uncertainty tends to be high in this regard). Assuming the full art Trainers and full-gold cards all only printed once and the rest of the sheet filled out with Shiny Pokémon-GX would lead to 86% of the sheet being taken up by Shiny Pokémon-GX.

Looking at the available data, my own sample yields 82% Shiny Pokémon-GX, Derium’s 76% and cardzard.com’s (from Reddit) 1 / 9 / (1 /9 + 1 / 57 + 1 / 73) = 78%. Were it only for Derium’s data, I would say it’s within the margin of error, but all in all the only way I could see all these cards printed on the same sheet would be if some of Shiny Pokémon-GX were printed on the sheet 3 times and some of the full art Trainers/full-gold cards only once. All in all, a strange way of composing a sheet which I am not fond of assuming in my model, which is why I am assuming two sheets.

For the rarity table below, I have designated the baby shinies as SPa, the Shiny Pokémon-GX as SPb and the Shiny Vault full art Trainers and full-gold cards SPc:

A note on rainbow rare Moltres, Zapdos & Articuno GX: I have no indication it is significantly rarer than the two full art Trainers; I am arbitrarily assuming it has FT33 rarity.

The raw data for the various types of cards is shown below:

I’ll conclude with two observations regarding individual card rarities: Looking at the raw data for Shiny Pokémon-GX, it looks like Charizard GX is not among the rarer cards. However, observed data can be very random, as is shown by Naganadel GX: In my own sample, it’s the most common Shiny Pokémon-GX, while in Derium’s it’s among the rarest ones.

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Cosmic Eclipse

For Cosmic Eclipse, the data is not quite as good as for the earlier sets, particularly as Derium didn’t do a large 1,000+ pack opening like he did for other sets of the era. Based on the compiled data (see introductory post on the Sun & Moon series) I am assuming the pull rates are slightly worse than for previous sets, with 4.6 “regular” Pokémon-GX, 1.0 full art Pokémon and 1.2 full art Trainers/secret rares per box on average. For the latter sheet, which includes 32 different cards in total (9 full art Trainers and 23 secret rares) I am assuming most of them are printed 3 times on the sheet and 4 of them, which I am assuming are all full art Trainers, 4 times.

There are also 12 “character rares” in the set which appear in the reverse slot. At this point it is appropriate to say something about how reverses appear to be inserted into packs in “large” sets like Cosmic Eclipse where two sheets are required to print them:

The picture above is from one of my Excel sheets, showing the reverses as they appeared in a box, the position of the pack in the box, and the pack art (Blastoise/Dialga/Solgaleo/Cleffa). Those cards I marked in green and red are sequences I observed in other boxes as well. Thus it looks like cards are inserted altenatingly from each of the two sheets, and that the character rares (marked in black) are inserted separately and were thus printed on a separate sheet, which due to the cards’ plain yellow borders I am assuming was a 11x11 sheet. I did not attempt to reconstruct the entire reverse sheets, but it would likely be possible to do so.

Here is the rarity table:

As usual, the two rares which are featured as theme deck exclusive holos, Kyogre and Groudon, appear to be short-printed (see raw data further below). As to the full art Trainers and secret rares, it is worth noting this set includes no less than 28 cards with a pull rate of 1:1000, at least according to this model.

The raw data for the various holos etc. looks as follows:

Unlike the previous few sets, I did not look at the uncommons, but I reconstructed the commons sheet. It looks as follows:

† Onix, Wailmer, Palpitoad, Kricketot, Aipom, Woobat, Ducklett, Swirlix, Alolan Grimer, Slugma, Chinchou, Cosmog (Unaware), Pancham, Drilbur, Tangela, Eevee (Follow My Tail), Duskull, Tympole, Flabébé (Petal Blizzard), Alolan Sandshrew, Ponyta, Sunkern, Cosmog (Ascension), Psyduck, Trapinch (Dig), Oddish, Rufflet, Piplup, Alolan Vulpix, Rockruff, Stufful, Rowlet (Skill Dive), Phantump, Magnemite, Lillipup, Trapinch (Nest Building), Sneasel, Spheal (Body Slam), Alolan Meowth, Ralts, Passimian, Jangmo-o (Gnaw), Rowlet (Hide and Seek), Skrelp, Pikachu, Teddiursa, Nosepass, Litleo, Flabébé (Floral Invitation), Spheal (Rollout), Natu, Palpitoad, Jangmo-o (Raging Claws), Deerling, Golett, Dewpider, Aipom, Onix, Tepig, Alolan Sandshrew, Snorunt, Koffing, Drilbur, Swirlix, Kricketot, Woobat, Ducklett, Helioptile, Cosmog (Unaware), Slugma, Wailmer, Pawniard, Togedemaru, Trapinch (Dig), Flabébé (Petal Blizzard), Tangela, Duskull, Tympole, Piplup, Cosmog (Ascension), Ponyta, Crabrawler, Carvanha, Chinchou, Azurill, Rufflet, Oddish, Ralts, Sandygast, Spheal (Body Slam), Cottonee, Rowlet (Skill Dive), Phantump, Alolan Grimer, Magnemite, Eevee (Lead), Flabébé (Floral Invitation), Sneasel, Natu, Trapinch (Nest Building), Spheal (Rollout), Passimian, Rowlet (Hide and Seek), Lillipup, Skrelp, Pikachu, Stufful, Pawniard, Litleo, Koffing, Nosepass, Snorunt, Rockruff, Deerling, Teddiursa, Golett, Dewpider, Helioptile, Carvanha, Tepig, Togedemaru †

This concludes the Sun & Moon series. The upcoming Sword & Shield series will be a good deal less complex as there won’t be the issue of the full arts being printed on two separate sheets, which made modelling the sets quite tricky.

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Digression: A very short introduction to the Sword & Shield series

As mentioned in my last post, modelling pull rates of Sword & Shield series sets is a good deal less complex than for the Sun & Moon series, as the full arts now appear to all feature the same holofoil pattern and texture, and thus I am assuming they were all printed on the same sheet. Special cards like the Amazing Rares, Radiant Pokémon and Trainer Gallery cards which come in the reverse slot aside, the following ultra-rare sheets are assumed to exist: “regular” Pokémon-V, full arts (including Pokémon-VMAX and Pokémon-VSTAR), and secret rares (which, unlike the full arts, have a glittery card texture). That the Pokémon-VMAX were printed on the same sheet as the full arts can be seen from the following miscut from Evolving Skies, featuring Dracozolt VMAX and Espeon V full art:

I am assuming the same thing for the Pokémon-VSTAR. The box ratios I observed from Youtube videos are shown below (the number of packs ranges from 1,224 and 6,946):

“Special” denotes the Amazing Rares and Radiant Pokémon and TG1, TG2 and TG3 the “regular” Trainer Gallery cards, Pokémon-V/VMAX/VSTAR from the Trainer Gallery and the black and gold cards from the Trainer Gallery which feature a glittery card texture and which I thus assume were printed on a separate sheet. Here are two interesting miscuts of Trainer Gallery cards:

The first shows Pokémon-V and Pokémon-VMAX from the Trainer Gallery were printed on the same sheet. The second shows the gold and black Pikachu-VMAX from the Trainer Gallery appears to have been printed next to another gold and black card, which underlines the assumption that this type of card was printed on a separate sheet. One other note: I haven’t looked at the Radiant Pokémon in detail yet so I’m not completely ruling out they may have been printed on the same sheet as some Trainer Gallery cards.

Back to the table above: “Sum 1” denotes the number of holo or better per box in the samples, and it varies between 14.23 and 14.54. “Sum 2” is the number of “hits” - in this context, Pokémon-V or better, ignoring any cards which come in the reverse slot, and it varies between 7.82 and 8.19. I feel very confident in modelling the first to always be 14.4 per box (2 in 5 packs), which means the sequence length of 10 boxes (as opposed to 6 boxes used to model Gen I-V sets) comes in handy. As to the second, I am strongly inclined to assume the number of “hits” per box is generally 8, and the number of holos per box 6.4.

So much for the introduction, the next post will be about Sword & Shield Base Set.

[sturzflugbombardieru]

Sword & Shield

After a bit of a break (lots of other stuff going on), I am back.

According to what I wrote in my introductory post on the Sword & Shield series above, I am assuming 6.4 holos and 8.0 “hits” (Pokémon-V or better) for this set. Based on the raw data, I am assuming the “hits” break down into 5.2 Pokémon-V, 2.0 full arts (including Pokémon-VMAX) and 0.8 secret rares. As to the ratio of Pokémon-VMAX to full arts, it is a bit more tricky to determine. I have two samples, one compiled by myself from various Youtube videos, and one from a single 1000 pack (or more likely, 1008 pack) opening by Youtuber Derium. In my sample, the ratio is 31.0 : 69.0; in Derium’s, it is 37.9 : 62.1. This means the four Pokémon-VMAX are likely either printed 8 or 9 times each on the 10x10 sheet, taking up either 32 or 36 slots. In my model, I am assuming they are printed 8 times each, but this is just a guess.

The raw data for the various types of cards from the two samples is shown at the bottom of this post, as usual. There appear to be no artificial rarity differences for the Pokémon-V, Pokémon-VMAX, full arts or secret rares. For the non-holo rares, the three cards which were featured as theme deck exclusive holos - Rillaboom, Cinderace and Inteleon - appear to be short-printed, just as was the practice in earlier sets. Much more interesting is the situation for the holo rares. Here it appears that three cards are short-printed: Rillaboom, Inteleon and Cinderace Rhyperior. Short printing Rhyperior is so absurd that the likeliest explanation in my view is that this was a mistake and one of the two holo Cinderace cards was meant to be short printed - after all, one card is red and the other is reddish brown. (It is true that unlike Rillaboom and Inteleon, there is no non-holo version of Cinderace in the Build & Battle Boxes, but that does not explain why Rhyperior would be short printed).

Here is the rarity table:

I did not look at the uncommons, commons, reverses or Basic Energy Cards (note that with Fairy Energy discontinued, there are only 8 Basic Energy cards). Below, the raw data for the various types of cards is shown: