The English Pokémon card rarity guide

[sturzflugbombardieru]

Flashfire

For Flashfire, as mentioned in the introductory post to the XY series above (“Introduction to the XY Series - Which Sequence Length Should I Use?”), I am going with the hypothesis that the secret rares (Mega Kanghaskhan EX and the two Mega Charizard EX) are printed on the same sheet as the regular Pokémon-EX, as the card stock and holofoil pattern seem the same. As mentioned in that introductory post, I am assuming 7.1 holos, 3.5 “regular” Pokémon-EX/secret rares and 1.4 full arts per box on average, which is also my guess for the box ratios in the next set, Furious Fists. As to how many secret rares were printed on the (likely 10x10) Pokémon-EX sheet, the raw data suggests secret rares are about one in every third box, as with most Black & White Series sets, so I am assuming each secret rare is printed 3 times on the sheet. The rarity table thus looks as follows:

The raw data for the holos, rares, Pokémon-EX/secret rares and full arts as given below, the dashed lines indicating where the transition from H16 to H15, etc., would occur:

Druddigon is a very good candidate for the H16 card. The two rares featured as holofoil cards in the theme decks (Meowstic and Heliolisk) don’t appear rarer than the other rares - unlike how the case seams to be in XY base set.

I reconstructed the reverse set, and the 30 RE2 cards are all commons. It looks as follows:

† Spritzee, Krokorok, Roselia, Startling Megaphone, Pineco, Barbaracle, Bergmite, Floatzel, Buizel, Ultra Ball, Sentret, Pokémon Center Lady, Flabébé (Aromatherapy), Litleo (Fire Mane), Avalugg, Geodude, Furfrou, Shinx, Protection Cube, Pidgey, Fiery Torch, Spheal, Shiftry, Duskull, Maractus, Luxio, Goomy, Blacksmith, Dusknoir, Caterpie, Weavile, Lysandre, Skrelp, Pyroar, Scraggy, Rapidash, Helioptile, Magnetic Storm, Buneary, Florges, Stunky (Smokescreen), Skuntank, Seedot, Floette (Flower Veil), Milotic, Flabébé (Razor Leaf), Torkoal, Pidgeotto, Stunky (Collect), Feebas, Carbink, Ponyta, Scrafty, Binacle, Dragalge, Sneasel (Icy Wind), Dusclops, Litleo (Combustion), Miltank, Roselia, Espurr, Druddigon, Spritzee, Forretress, Litleo (Fire Mane), Pidgeot, Sandile, Graveler, Fletchling, Shinx, Trick Shovel, Spheal, Pineco, Sentret, Durant, Scraggy, Buizel, Metapod, Bergmite, Pal Pad, Fletchinder, Goomy, Luxray, Skrelp, Goodra, Caterpie, Snorlax, Pidgey, Nuzleaf, Duskull, Geodude, Sealeo, Stunky (Collect), Heliolisk, Binacle, Butterfree, Helioptile, Furret, Stunky (Smokescreen), Roserade, Litleo (Combustion), Flabébé (Razor Leaf), Luvdisc, Sandile, Meowstic, Seedot, Qwilfish, Buneary, Lopunny, Floette (Petal Blizzard), Espurr, Sneasel (Scratch), Feebas, Sneasel (Icy Wind), Sacred Ash, Golem, Fletchling, Walrein, Pokémon Fan Club, Ponyta, Sliggoo †

Edit 2024/03/24: Changed sequence length from 216 to 360. This slightly affects pull rates for holos as well as full arts.

[sturzflugbombardieru]

Furious Fists

As mentioned in my last post, I am assuming the same box ratios for this set as for Flashfire, i.e. 7.1 holos, 3.5 Pokémon-EX/secret rares and 1.4 full arts. There are two secret rares in the set, Mega Heracross EX and Mega Lucario EX. To obtain a secret rare in about every third box, my guess is each one is printed 5 times on the (likely 10x10) Pokémon-EX sheet. The rarity table looks as follows:

As can be seen in the table, as in XY base set, the two rares featured as holos in the theme decks - Pangoro and Sylveon - appear to have lower pull rates than the other rares due to the raw data below; assigning them R4 rarity matches the raw data nicely:

The fact that the sample data only contains a single full art Battle Reporter is likely not relevant. A quick glance at the PSA population report shows 104 Battle Reporters compared to 107 Fossil Researchers (there are 168 Korinnas, but that is a “waifu” card), so I am assuming it is just a coincidence. (Generally I am sceptical about using the population report for estimating card rarities due to a card’s popularity influencing how often it is graded, but occasionally it can be useful.)

I reconstructed the reverse sheet, which looks as follows:

† Lickitung, Dedenne, Gothita, Clefairy (Moonblast), Hawlucha, Shroomish, Electivire, Vibrava, Fighting Stadium, Machop, Tyrantrum, Cubchoo, Gothorita, Mienfoo, Pikachu, Pangoro, Bellsprout, Thundurus, Lickilicky, Focus Sash, Poliwag, Drapion, Skorupi, Machoke, Golett, Maintenance, Sylveon, Shelmet, Hypno, Vigoroth, Fossil Researcher, Eevee, Flygon, Trapinch, Hitmonlee, Slakoth, Mountain Ring, Noivern, Magmar, Jynx, Watchog, Full Heal, Drowzee, Tornadus, Patrat, Hitmonchan, Machop, Sail Fossil, Slaking, Torchic, Gothitelle, Battle Reporter, Jaw Fossil, Makuhita, Weepinbell, Clauncher, Hitmontop, Gothita, Sparkling Robe, Leafeon, Noibat, Golurk, Energy Switch, Korrina, Poliwag, Accelgor, Electabuzz, Mienshao, Super Scoop Up, Clefairy (Moonlight), Victreebel, Shroomish, Magmortar, Pancham (Bad-Influence Evolution), Pancham (Comet Punch), Mienfoo, Skorupi, Scraggy, Combusken, Tool Retriever, Cubchoo, Blaziken, Bellsprout, Politoed, Tyrunt, Strong Energy, Golett, Pikachu, Lickitung, Poliwhirl, Training Center, Eevee, Poliwrath, Shelmet, Glaceon, Scrafty, Slakoth, Patrat, Breloom, Noibat, Amaura, Herbal Energy, Trapinch, Clawitzer, Magmar, Beartic, Clefable, Makuhita, Clauncher, Hariyama, Plusle, Raichu, Drowzee, Scraggy, Machamp, Torchic, Aurorus, Klefki, Electabuzz, Minun, Landorus †

The choice which reverse commons appear only once on the sheet is hardly a coincidence: the two Clefairy, Pancham of which there is a second, uncommon, variant in the set, and Plusle and Minun.

Edit 2024/03/24: Changed sequence length from 216 to 360. This slightly affects pull rates for holos and secret rares.

[amcgl58]

@sturzflugbombardieru This has been a very cool thread with lots of interesting data. Keep it up!

[sturzflugbombardieru]

Phantom Forces

This set is generally similar to the last two, except that it contains two “Team Flare Hyper Gear” holos with a red border, which will have required a separate sheet to print them, and that of the three secret rares, one of them, Dialga EX, is textured and was printed on the same sheet as the full arts, as can be seen from the miscuts below. The other two, Mega Gengar EX and Mega Manectric EX, are assumed to be printed on the same sheet as the “regular” Pokémon-EX.

The observed box ratios from 28 boxes opened on Youtube were 6.14 “normal” holos, 0.86 Team Flare Hyper Gear holos, 3.50 Pokémon-EX/secret rares and 1.57 full arts/secret rares.

I will model them as follows: 6.1 “normal” holos, 0.9 Team Flare Hyper Gear holos, 3.5 Pokémon-EX/secret rares and 1.5 full arts/secret rares. This is similar to the last two sets, except:

• The number of cards from the full art sheet increases by 0.1 per box. This is reasonable as the sheet now not only includes full arts, but a secret rare as well. The increase seems to come at the expense of the holos.
• There are two holo sheets (yellow borders and red borders). I assigned them ratios 6.1 and 0.9 per box based on the raw data. The boxes contain either 0, 1 or 2 “Team Flare Hyper Gear” cards. A ratio of 6.0 and 1.0 per box would make more sense as it would give all holos basically the same rarity, and the sample size isn’t large enough to rule this out by any means in my opinion, but 6.1 and 0.9 just fits the observed data better.

That leaves it to be determined how many times the secret rares were printed on the sheets. I chose to model Mega Gengar EX and Mega Manectric EX as EX3 cards (printed 3 times each on the Pokémon-EX sheet) and Dialga-EX as a FA7 card (printed 7 times on the full art sheet). This gives all of them the exact same rarity, and all secret rares together a ratio of about 1 in 3 boxes. (The sample data yielded 1 Gengar, 1 Manectric and 4 Dialga, but that is not statistically relevant in my opinion.)

The rarity table looks as follows:

As in XY base set and Furious Fists (but not Flashfire), the two rares featured as theme deck exclusive holos, Galvantula and Talonflame, appear to have lower pull rates than the others, so I am modelling them as R4 cards, which best fits the raw data.

Here is the raw data for the holos, rares, Pokémon-EX and full arts (the latter two including secret rares):

As to the Team Flare Hyper Gear cards, Head Ringer appeared 13 times and Jamming Net 11 times.

The reverse sheet looks as follows:

† Bunnelby, Hand Scope, Goodra, Mystery Energy, Robo Substitute, Crobat, Purrloin, Finneon, Pyroar, VS Seeker, Gulpin, Zubat, Lysandre’s Trump Card, Regigigas, Chansey, Roller Skates, Swalot, Karrablast, Spearow, Feraligatr, Xerosic, Whismur, Goomy, Manectric Spirit Link, Roggenrola, Murkrow, Shauna, Musharna, Fletchling, Yanma, Heliolisk, Double Colorless Energy, Totodile, Alomomola, Professor Sycamore, Munna, Dedenne, Steel Shelter, Gliscor, Poochyena, Exploud, Chandelure, Gligar, Klefki, Joltik, Venonat, Venomoth, Helioptile (Quick Attack), Bronzor, Honchkrow, Frillish, Diggersby, Gourgeist, Roggenrola, Zweilous, Bunnelby, Target Whistle, Yanmega, Karrablast, Krabby, Mightyena, Litwick, Swadloon, Gigalith, Sewaddle, Sliggoo, Totodile, Tierno, Leavanny, Munna, Purrloin, Spiritomb, Litleo, Fletchinder, Heatran, Murkrow, Fearow, Wobbuffet, Trick Coin, Talonflame, Chansey, Kingler, Bronzong, Dimension Valley, Yanma, Slurpuff, Venonat, Girafarig, Lampent, Gulpin, Jellicent, Helioptile (Tail Rap), Croconaw, Dedenne, Enhanced Hammer, Furfrou, Diancie, Gligar, Loudred, Boldore, Goomy, Pachirisu, Skarmory, Lumineon, Frillish, Gengar Spirit Link, AZ, Hydreigon, Deino, Litwick, Liepard, Swirlix, Galvantula, Bronzor, Golbat, Pumpkaboo, Sewaddle, Battle Compressor, Litleo, Escavalier, Blissey †

The RE2 cards are 19 reverse commons.

Edit 2024/03/24: Changed the sequence length from 216 to 360. this affects the pull rates of the holos (both yellow border and “Team Flare Hyper Gear” red border)

[sturzflugbombardieru]

Primal Clash

As I wrote in my introductory post on the XY series, I am assuming 5.6 holos, 4.0 “regular” Pokémon-EX and 2.4 full arts/secret rares per box for this set as well as for the following two (Roaring Skies and Ancient Origins). The secret rares I am assuming to be printed on thee same sheet as the full arts, and as to the Ancient Trait cards, I see no reason why they would require a separate sheet. Here is the rarity table for Primal Clash:

It is notable that the holos are very hard to come by - rarer than the “regular” Pokémon-EX, and that’s not taking into account that these all have a full art version as well. I haven’t looked at all the previous sets in detail to check where else this may be the case; the last time it was so pronounced was for the early Ruby & Sapphire series sets if I am not mistaken. The raw data for the holos is as follows:

For the rares, as in recent sets the two which appear as theme deck exclusive holos, Groudon and Kyogre, are rarer than the others; I am assuming they aree R3 cards, all the others being R5. The raw data is as follows:

The raw data for the Pokémon-EX is as follows:

For the full arts and secret rares, the best agreement with the observed data - slightly less than 0.3 secret rares per box on average - is to assume each one appears 3 times on the sheet (0.29 secret rares per box, as opposed to 0.38 per box if each one was printed 4 times on the sheet):

Two sheets were required for the reverses; I did not investigate them. I did, however, reconstruct the commons sheet - it looks as follows, and the choice of the 4 C4 cards is not random:

† Bunnelby, Weedle, Zigzagoon, Shroomish, Spheal (Ball Roll), Mudkip, Feebas, Slugma, Bunnelby, Lotad, Meditite, Bidoof, Horsea, Chinchou, Tynamo, Nidoran f, Tentacool, Torchic, Hippopotas, Surskit, Barboach, Zigzagoon, Treecko, Vulpix, Rhyhorn, Volbeat, Spheal (Ice Ball), Staryu, Clamperl, Bunnelby, Illumise, Solrock, Mudkip, Trapinch, Nosepass, Spinda, Horsea, Skitty, Tangela, Treecko, Honedge, Meditite, Drilbur, Shroomish, Marill, Corphish, Weedle, Barboach, Spheal (Ball Roll), Bidoof, Chinchou, Electrike, Tentacool, Rhyhorn, Tynamo, Torchic, Staryu, Lotad, Solrock, Drilbur, Nosepass, Volbeat, Spinda, Mudkip, Feebas, Illumise, Hippopotas, Slugma, Nidoran f, Trapinch, Spheal (Ice Ball), Torchic, Marill, Surskit, Zigzagoon, Treecko, Shroomish, Tangela, Bidoof, Clamperl, Meditite, Tentacool, Vulpix, Corphish, Tynamo, Weedle, Barboach, Honedge, Electrike, Drilbur, Skitty, Rhyhorn, Spheal (Ball Roll), Lotad, Bidoof, Staryu, Volbeat, Nosepass, Spinda, Mudkip, Chinchou, Solrock, Clamperl, Nidoran f, Tangela, Illumise, Slugma, Torchic, Marill, Surskit, Corphish, Horsea, Trapinch, Vulpix, Spheal (Ice Ball), Honedge, Hippopotas, Electrike, Feebas, Skitty, Treecko †

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

[sturzflugbombardieru]

Double Crisis

This small special set contains 34 cards - 6 holos, 12 uncommons, 14 commons and 2 full art Pokémon-EX. All except the full arts also come as reverses. Each pack contains 7 cards: 3 commons, 2 uncommons, 1 reverse and 1 holo or full art. As to the ratio for the full arts, I only looked at quite a small sample of 116 packs; it included 14 full arts. There are definitely a good deal more videos available on Youtube, but it would be time-consuming to watch them all and the uncertainty would still be large. In my model I will be assuming one full art in nine packs on average, whch is just a rough guess. That would lead to the following rarity table (the defined sequence lenght of 360 is arbitrary, I chose it to match the main series sets):

The raw data for the holos looks as follows:

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

[randox]

Amazing work OP. Great insights - thanks for doing this!

[sturzflugbombardieru]

Roaring Skies

I am assuming 5.6 holos, 4 “regular” Pokémon-EX and 2.4 full arts/secret rares per box, and as the raw data showed 0.29 secret rares per box, I am assigning each of the two FA6 rarity, meaning each one is printed six times on the 10x10 full art/secret rare sheet.

The only artificial rarity differences are for the non-holo rares, where Zapdos and the variant of Articuno with Find Ice as its first attack - the two cards featured as Theme Deck exclusive holos - appear to have R5 rarity based on the raw data.

The rarity table looks as follows:

Here is the raw data for the holos, rares, Pokémon-EX and full arts/secret rares:

The reconstructed reverses sheet has all reverse commons, as well as every other reverse uncommon Pokémon (by set number) appearing twice on it:

† Electrike, Swablu, Dustox (Psybeam), Inkay, Dunsparce, Manectric, Spearow, Electrode, Dratini, Dustox (Δ Plus), Tropius, Fletchling, Exeggcute, Beautifly, Altaria (Song of Echoes), Swellow (Δ Plus), Wingull, Reshiram, Gligar, Zapdos, Natu (Δ Plus), Shedinja, Fearow, Dragonite (Max Wind), Natu (Peck), Taillow, Pelipper, Nincada, Swellow (Clutch), Togepi, Hawlucha, Fletchinder, Unfezant (Quick Attack), Xatu, Deoxys, Voltorb, Pidove, Winona, Bagon (Leer), Victini, Unfezant (Δ Evolution), Klefki, Salamence, Inkay, Altaria (Δ Evolution), Wurmple, Banette (Δ Evolution), Shelgon, Togetic, Latios Spirit Link, Absol, Bagon (Continuous Headbut), Gliscor, Healing Scarf, Manectric, Dunsparce, Talonflame, Pikachu, Jirachi, Swablu, Altaria (Song of Echoes), Dratini, Mega Turbo, Silcoon, Shuppet, Sky Field, Cascoon, Togekiss (Powerful Slap), Exeggutor, Articuno (Find Ice), Spearow, Electrike, Dragonair, Meowth, Natu (Δ Plus), Wide Lens, Dustox (Psybeam), Revive, Nincada, Tranquill, Exeggcute, Togekiss (Δ Evolution), Fearow, Hawlucha, Steven, Togepi, Wally, Wingull, Carbink, Unfezant (Quick Attack), Fletchling, Bagon (Leer), Tropius, Binacle, Taillow, Ninjask, Pidove, Double Dragon Energy, Pelipper, Dragonite (Δ Plus), Gligar, Rayquaza Spirit Link, Voltorb, Gallade Spirit Link, Switch, Natu (Peck), Trainers’ Mail, Articuno (Δ Plus), Binacle, Exeggutor, Ultra Ball, Meowth, Togetic, Skarmory, Wurmple, Shuppet, Pikachu, Banette (Tool Concealment), Zekrom, Cascoon, Bagon (Continuous Headbut) †

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

[sturzflugbombardieru]

Ancient Origins

The box ratios for this set are identical to those for Roaring Skies, but there are a few interesting observations nevertheless. Here is the rarity table:

There is nothin in particular to say about the holos; the raw data looks as follows:

As to the rares, were it not for the observations made in various other sets, I would have likely concluded that the fact that Metagross (with Magnetic Wrap) and Regirock, the two featured as Theme Deck exclusive holos, appear slightly fewer times than the others in the raw data was just coincidence. As it is, I am modelling them as R8 cards - just slightly less common than the other rares. (This is calculated as (43 + 45) / 670 * 121 / 2 = 7.95.) This is the raw data:

There isn’t anything special about the raw data for the “regular” Pokémon-EX:

That for the full arts and secret rares is interesting, though. With 17 cards in total (15 full arts and 2 secret rares) assumed to be printed on a 10x10 sheet, that means 15 FA6 and 2 FA5 cards. Is it reasonable to assume the two FA5 cards are the secret rares? The raw data below doesn’t really support this, with the observed number of secret rares being 0.29 per box. Not certain by any means with this sample size, but I would actually guess that the two FA5 cards are actually full arts and not secret rares, making these two full arts the rarest cards in the set! They are probably also not any of the three Primal Pokémon-EX (marked green below).

(Side note: The situation is somewhat similar to Neo Revelation, though there I went with the guess that it was indeed the two secret rares - Shining Magikarp and Shining Gyarados - printed the fewest times on the holo sheet.)

I more or less reconstructed the reverses sheet, on which all reverse commons and all but two reverse uncommons appear twice. I say “more or less” because it appears this is another one of those sets where cards in certain positions on the sheet have a tendency to get flipped around. This is the same thing I noticed with the commons in the HeartGold & SoulSilver set. Again, the “flipping” positions are spaced 11 cards appart, so they would be right above each other on the sheet. I have underlined them in the sheet sequence below:

† Cottonee, Dangerous Energy, Golurk (Dig Out), Sableye, Jolteon, Gardevoir, Forest of Giant Plants, Inkay, Larvesta, Golett, Ampharos Spirit Link, Ralts, Flash Energy, Malamar, Metang, Goodra, Porygon-Z (Θ Stop), Vileplume, Meowth, Ariados, Registeel, Porygon-Z (Cyber Crush), Gloom, Virizion, Unown, Magikarp, Persian, Vespiquen (Θ Double), Hex Maniac, Entei (Θ Double), Vespiquen (Intelligence Gathering), Entei (Burning Roar), Eevee, Oddish, Bellossom, Metagross (Magnetic Warp), Relicanth, Beldum, Quagsire, Level Ball, Regirock, Flareon, Baltoy (Θ Stop), Goomy, Spinarak, Volcarona (Solar Birth), Sceptile Spirit Link, Baltoy (Slap), Porygon, Kirlia, Lysandre, Wooper, Vaporeon, Golurk (Θ Stop), Golett, Combee, Eco Arm, Tyranitar Spirit Link, Golurk (Dig Out), Gyarados (Berserker Splash), Whimsicott, Paint Roller, Gyarados (Θ Double), Rotom, Hex Maniac, Inkay, Larvesta, Energy Recycler, Dangerous Energy, Ariados, Cottonee, Sliggoo, Unown, Magikarp, Sableye, Level Ball, Kirlia, Gloom, Faded Town, Flash Energy, Vespiquen (Intelligence Gathering), Beldum, Porygon2, Quagsire, Malamar, Metang, Lucky Helmet, Whimsicott, Baltoy (Slap), Forest of Giant Plants, Ralts, Flareon, Eevee, Ace Trainer, Eco Arm, Meowth, Oddish, Paint Roller, Sliggoo, Persian, Sceptile Spirit Link, Porygon, Vaporeon, Bellossom, Ampharos Spirit Link, Energy Recycler, Regice, Spinarak, Goomy, Porygon2, Volcarona (Θ Stop), Tyranitar Spirit Link, Baltoy (Θ Stop), Rotom, Relicanth, Metagross (Θ Double), Faded Town, Wooper, Combee, Claydol, Ace Trainer †

The middle one (Goomy/Spinarak) particularly could just as well have been printed on the sheet the other way around. Still, the reconstruction should be basically correct.

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

[sturzflugbombardieru]

Digression: XY Break Series Box Ratios

I decided to do a quick introductory post on the box ratios for the next five main series sets (BREAKThrough, BREAKPoint, Fates Collide, Steam Siege and Evolutions) because box ratios vary quite significantly between sets, and because we have now arrived at a point where there are different reliable ressources available concerning pull rates. Aside from my own samples from Youtube videos (at least 1,000 packs for each set), they are:

• A video done by Danny Phantump nearly two years ago iin which he explores the pull rates for all sets from XY Base Set to Fusion Strike (for link see below). To my understanding the data he compiled for the XY era is, just like mine, not first-hand data.
• Derium did videos for most sets where he opens 1,000 packs, generally giving a summary of the pulls at the end of the video. For the XY BREAK Series, he did one for each set except Fates Collide. I am assuming the total number of packs in each video is actually 1,008 (28 boxes) though it would not make much of a difference for the observed box ratios if it were exactly 1,000.

In the table below, I compare the data of these two sources with that I compiled myself, and add how I am going to model the sets. The working hypothesis is that the smallest increment is 1 in 180 packs, i.e. all box ratios are multiples of 0.2 per box. The sequence length I am assuming is 360 packs, but due to the large differences between the various samples I did not see any instance where using the finer increment makes sense. I am also assuming the full arts and secret rares are printed on the same sheet. Here is the data:

The data from Derium’s videos and that compiled by me is in pretty good agreement except that Derium got notably fewer full arts/secret rares in his BREAKThrough opening. This is indeed very strange, and the only possible explanation I can think of is that different print runs may have had slightly different ratios - maybe the full art sheet was accidentally underprinted somewhat. The data from Danny Phantump tends to show slightly lower box ratios in general.

I decided to model the sets as best fits my own compiled data, namely 2.4 full arts/secret rares in each set (just as in the three previous sets) and a varying number of “regular” Pokémon-EX which roughly scales with the total number of Pokémon-EX in the sets but doesn’t seem to follow any exact rule. As to the BREAK cards, I will talk about them when I cover the individual sets.

Edit 2024/03/24: Minor changes to text, no changes to model.

[sturzflugbombardieru]

BREAKthrough

Here is the rarity table for BREAKthrough:

Based on my own sample data, I am assuming 3.2 Pokémon-EX and 2.4 full arts/secret rares per box, though the data from Derium’s 1,000 pack opening video shows only about 2 full arts per box on average (see introductory post above). As to the BREAK cards, I decided to go with 2.8 per box - my sample yielded 2.90, Derium’s video 2.71. For the secret rares I am assuming each one is printed 6 times on the 10x10 full art sheet, the odds of pulling any secret rare thus being the same as in the previous three sets. Finally, I am assuming the BREAK cards (denoted with SP for “special” in the rarity table) are printed on a 10x10 sheet like the other ultra rares.

Below is the raw data for the holos, rares, Pokémon-EX, full arts/secret rares and BREAK cards; for the latter three, I included the data from Derium’s video as well. The only artificial rarity differences are for the regular rares, where the two cards which are featured as theme deck exclusive holos, Raichu and Noivern, seem to be slightly short-printed.

The reverses will have required two sheets to print them; a model with most reverses appearing twice on the two sheets except for the reverse rare holos and 18 of the 21 reverse rares fits the sample data nicely:

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

[sturzflugbombardieru]

BREAKpoint

Here is the rarity table for BREAKpoint:

Based on my own sample, which matches the data from Derium’s 1,000 pack opening video pretty well, I am going with 3.6 “regular” Pokémon-EX, 2.4 full arts/secret rares and 2.4 BREAK cards per box. I am assuming the odds of getting a secret rare are the same as in the previous few sets. Since the set includes only a single secret rare, Gyarados EX, that would mean it was printed 12 times on the full art sheet and is actually more common than the full arts.

The raw data for the holos, rares, Pokémon-EX and full arts/secret rares is shown below, that for the latter two including the pulls from the Derium video. (I am assuming the five BREAK cards all have the same rarity as they fit 20 times each on a sheet.)

For the rares I would guess the two ones which are featured as theme deck exclusive holos, Greninja and Luxray, are slightly short printed. I did not investigate the reverses.

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

[sturzflugbombardieru]

Generations

This guide is largely based on analyzing pack opening videos on YouTube. I followed the strategy of only looking a complete box openings for main series sets, not just because of the possibility that loose packs can be weighed for earlier sets and possibly otherwise tampered with, but because the degree of randomness is higher for loose packs. A box can be assumed to usually contain 36 packs in a row from the packaging line, leading to very “sharp” statistics. In the case of the EX series sets, the contents of a booster box is so predictable that you can usually tell whether a Gold Star will take the place of a Pokémon-ex or of a holo in a box.

For the special sets that don’t come in booster boxes, I don’t have this option, so for most sets I relied on videos of ETBs being opened. The degree of randomness is higher, and so is the uncertainty regarding the pull rates.

Generations is a special case, since the ETBs were only released very late, and most of the videos available on YouTube are from loose packs. For this reason I am using a triple sample to analyze the pull rates:

• 170 packs from ETBs
• 516 packs from large openings of loose packs
• the summary of a 500 pack opening by Derium. This sample only includes data on the ultra rares, not on the holos.

Before looking at the results, let’s look at the contents of a Generations pack. Each pack contains 4 commons/Basic Energies (they were printed on the same sheet), 2 uncommons, 1 reverse, 1 common from the Radiant Collection, 1 uncommon or ultra rare from the Radiant Collection, and the rare slot, which can be either a non-holo rare, a holo rare, a Pokémon-EX or a full art (Articuno or Zapdos). A photo exists of the Radiant Collection uncommons/ultra rares sheet; each uncommon is printed 6 times on the sheet, each ultra rare 4 times:

Back to the samples from YouTube. For the sake of comparison with sets that came in booster boxes, I am giving the ratios as “box” ratios, i.e. pulls per 36 packs. Based on the values shown below, the estimate for my model is 3.80 holos, 7.40 Pokémon-EX and 0.80 full arts per 36 packs, making for a total of 12 “hits” per 36 packs:

An alternative model would be to go back to the 216 pack sequence length instead of the 180 pack one and assume 3.75 holos, 7.50 Pokémon-EX and 0.75 full arts per 36 packs. This would be kind of neat as it would mean the odds of getting a Pokémon-EX from the main set are twice as high as getting a holo.

The rarity table thus looks as follows, with SPa denoting the Radiant Collection uncommons/ultra rares sheet, and SPb the Radiant Collection commons sheet.

The ratios per box are provided solely for comparison with other sets.

Some things need to be said about the individual sheets. The raw data for the holos and Pokémon-EX is given below (for the rares and full arts my assumption is that they are all printed on their sheets an equal number of times, and the data doesn’t suggest anything to the contrary):

For the Radiant Collection, the raw data is shown below for both sheets:

The raw data for the uncommons/ultra rares sheet is interesting because it can be compared to the actual sheet. With the high degree of randomness prevalent outside of booster boxes, the cards known to be the least common (the seven ultra rares) don’t all appear the fewest times in the sample; two uncommons - Slurpuff and Swirlix - appear fewer times than some of these ultra rares. The upshot from that is to be cautious with data on individual cards from special sets when the sample isn’t coming from booster boxes (and to be cautious with data on individual cards in general).

A word on the commons from the main set: The small number of cards in total (meaning the individual ones appear up to 5 times on the sheet), the fact that there are only 4 commons per pack, and a tendency I observed for cards to get flipped around and appear outside of the sheet order means reconstructing the commons sheet to my own satisfaction of accuracy would be too time-consuming. I do however have an approximate idea how the sheet looked and am very confident each Basic Energy card appeared 3 times on it. I am also relatively confident that the only common to appear only 4 times on the sheet is Clefairy.

For the reverses, I am assuming the reverse Basic Energies are printed on the same sheet as the other reverses. The patterns on the other cards (Energies for the Pokémon, Pokéballs for the Trainers) are not part of the actual holofoil, but printed on. I did not look at the reverses myself, but the number of reverse Basic Energies shown in the summary of Derium’s video is consistent with these reverses appearing only 1 time on the 121 card sheet. As to the other 8 reverses to which this also applies, I don’t know which ones they might be.

As a final note, there are some error packs where the Radiant Collection uncommon/ultra rare is accidentally replaced by a non-holo rare from the main set. Not knowing how prevalent this error is, I did not make a separate rarity table for it. But it does have an interesting implication: With the ETBs only being released very late, they may have come from a later print run. Having accidentally “disposed” of some non-holo rares in packs, that may have left an overhang of “hits” and let to the ratios being changed, explaining why the sample of ETB packs shows a slightly higher ratio of “hits”. This is pure speculation, however, and the observed outcome is not necessarily statistically relevant.

Edit 2024/02/17: Added some text explaining why the reverse Basic Energies are in my opinion printed on the same sheet as the other reverses.
Edit 2024/03/24: Changed sequence length from 180 to 360. This has no impact on pull rates.

[wisewailmer]

Great job on all the work putting this together!

[sturzflugbombardieru]

Fates Collide

After Generations, back to a set that is relatively unremarkable. The box ratios based on my sample and the data provided by Danny Phantump (see introductory poast on the XY BREAK Series) are estimated to be 5.2 holos, 4.4 “regular” Pokémon-EX and 2.4 full arts/secret rares, as well as 2.4 BREAK cards. I am assuming the odds of pulling a secret rare are the same as in the other sets going back to Primal Clash, and the sole secret rare (Alakazam EX) is thus printed 12 times on the full art sheet, making it less rare than the full arts. The rarity table looks as follows:

Lugia and Zygarde, the two rares which are featured as theme deck exclusive holos, account for 49 / 693 = 8.56 / 121 of the rares in the sample (see raw data below). I am assuming them to be R5 cards according to my tendency of being cautious when assuming artificial rarity differences, though R4 would also be a possibility. Given the fact that the entire set has only 5 holos, this makes these two cards rarer than any of those. Another noteworthy thing about the set is the large number of uncommons compared to that of commons.

The raw data for the holos, rares, Pokémon-EX and full arts/secret rares is given below, the dashed line indicating where the transition from H25 to H24, etc., would occur (the BREAK cards are assumed to all have the same rarity):

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

[sturzflugbombardieru]

Steam Siege

This is not everyone’s favourite set by any means, however it did feature some pretty nice cards in my opinion. The box ratios are assumed to be 7.2 holos, 2.4 “regular” Pokémon-EX and 2.4 full arts, as well as 2.4 BREAK cards (in the reverse slot). The relatively low number of ultra rares contributed to the sets unpopularity. With two secret rares, and assuming the overall odds of getting one remains the same, they are assumed to be printed 6 times each on the full arts sheet. The rarity table looks as follows:

The raw data for the holos, rares, Pokémon-EX, full arts/secret rares and BREAK cards is given below; for this set, I also looked at the summary of Derium’s 1,000 pack opening (he did not do one for Fates Collide apparently):

The two non-holo rares featured as theme deck exclusive holos, Volcanion and Hoopa, account for 28 / 666 = 5.09 / 121 rares in the sample; I am thus assuming them both to be R3 cards. This makes them rarer than the holos, which is significant as Volcanion was a very playable card back then. As to the rarest cards in the set, these are now secret rares again since the set includes more than one of them.

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

[sturzflugbombardieru]

Digression: Different Pull Rates for Different Print Runs?! - Be Carefule even with Large Sample Data!

The next set up is Evolutions, for which there is a huge amount of info available online due to its popularity and the large quantities printed. I will discuss some aspects about this set here, but the main info about the set itself will be in a separate post, as usual.

Before I get started, here a reminder of the assumptions I have been working with:

• No differences in pull rates between different types of product (booster boxes, ETBs, blisters, various merchandise). There is no reason for the Pokémon Company to do this, and it would be an unnecessary risk to their reputation. The only instance where I suspected this potentially not to apply was Generations, where the ETBs had slightly better pull rates than “loose boosters from various sources” in my samples. But, it must be stressed that for most other sets (including all main series sets) I have no data to support this assumption, as I only looked as booster boxes.
• No differences in pull rates between print runs. There are exceptions to this, namely Neo Destiny and EX Ruby & Sapphire. This digression will look into if Evolutions might be an exception as well.
• Box ratios (i.e. how many rares, holos, Pokémon-EX etc. per box) are “round” numbers such as X in 6 boxes or Y in 10 boxes. This is not really founded on any argumentation - there is no reason against one set featuring cards inserted at a rate of 1 in 193 packs and the next 1 in 182, but it is just a way of modelling the sets in a way that keeps things simple. I am currently working with the assumtion I am dealing with 1 in 360 packs for sets starting with XY (see my post further back: “Digression: What Kind of a Sequence Length to Model the XY Series?”) and plan to continue using this assumption for the Sun & Moon, Sword & Shield and Scarlet & Violet Series.

Now back to Evolutions. There are a handful of huge openings on YouTube, mostly with recaps of the pulls (one video from Derium doesn’t, I watched it but did not count the BREAK cards). There is also the statistics provided in two video by Danny Phantump (one of them from 2022 on pull rates in general, one from early 2024 on Evolutions), and that compiled from my own sample of various videos. It is shown in the table below:

(As to the date, my own sample is mostly from 2016-2017.)

The first thing you can see is that for the huge 9000 pack opening by Derium from 2020 (5), and for Danny Phantump’s recent statististics on Evolutions (7), the pull rates have dropped significantly. I must say that I am somewhat mistrustful about the data in (7) as it is such an outlier. Particularly for the “regular” Pokémon-EX though, it is impossible to deny the decline between (1)-(4) and (5) seams significant. Maybe pull rates for later print runs were in fact lower?

It is impossible to say for sure. The upshot of this post is that even large (>1000 packs) sample data has significant uncertainty. It is important to keep this in mind when modelling the rarities of Sun & Moon series and later sets.

The second question is to the box ratios for Evolutions. I think 4.4 “regular” Pokémon-EX and 2.0 BREAK cards is a very good estimate, the question is how many full arts per box on average. Should I go with 2.4, as I wrote earlier when discussing XY BREAK series box ratios, or 2.2? The first would be consistent with earlier sets. The argument for 2.2 would be that there are no secret rares in the set (they were printed on the same sheet as the full arts in earlier sets) and thus purely in terms of full arts, 2.2 would better match the number of full arts in the earlier sets (starting with Primal Clash my models have assumed 88 / 100 * 2.4 = 2.11 full arts per box).

I have decided to stick with 2.4 for the moment as it fits 3 of the 4 early samples best (2.47, 2.37 and 2.32) and there is only one outlier (2.18).

Edit 2024/03/23: Edited assumption about sequence length (now assumed to be 360 packs starting with XY Base Set)

[sturzflugbombardieru]

Evolutions

Based on what I wrote earlier, in the model I am going with 4.4 “regular” Pokémon-EX, 2.4 full arts and 2.0 BREAK cards (the latter in the reverse slot) per box. I reconstructed the commons sheet (which has the 9 Basic Energy cards on it), the uncommons sheet (which has the 5 secret rares on it) and the reverses sheet. The rarity table for Evolutions looks as follows:

For the rares sheet, it appears from the raw data (see below) that Mewtwo, which features as a theme deck exclusive holo, is slightly rarer than the others; based on the raw data my guess is it is a R11 card, but that is somewhat uncertain. (The other theme deck exclusive holo is Pikachu; it is a C5 common.) The raw data for the holos and rares is as follows, the dashed lines indicating where the transition from H10 to H9, etc., would occur:

Thanks to the large openings on Youtube mentioned in the last post, I have a lot of data on the Pokémon-EX, full arts and BREAK cards coming from the recap of these videos which greatly exceeds the sample size I analyzed myself: 13,176 packs for the first two, and 12,168 for the BREAK cards. I am not breaking the data down between the five samples below, so here is the summary:

For the Pokémon-EX, Pidgeot EX, Slowbro EX, Venusaur EX and Blastoise EX are good candidates for the 4 EX9 cards, but I wouldn’t consider it to be completely certain.

The data on BREAK cards is included for the sake of comparison with what according to the model at least should be the same rarity for all four cards.

As to the reconstructed sheets, the commons sheet looks as follows:

† Magnemite, Pikachu, Machop, Weedle, Doduo, Staryu, Onix, Fairy Energy, Voltorb, Tangela, Poliwag, Seel, Magikarp, Lightning Energy, Caterpie, Gastly, Diglett, Rattata, Charmander, Psychic Energy, Pikachu, Growlithe, Machop, Nidoran m, Ponyta, Drowzee, Electabuzz, Vulpix, Sandshrew, Onix, Magikarp, Fighting Energy, Staryu, Tangela, Rattata, Weedle, Voltorb, Poliwag, Gastly, Magnemite, Seel, Charmander, Diglett, Drowzee, Caterpie, Doduo, Pikachu, Machop, Growlithe, Onix, Nidoran m, Poliwag, Grass Energy, Rattata, Vulpix, Electabuzz, Magikarp, Gastly, Sandshrew, Weedle, Tangela, Ponyta, Doduo, Staryu, Seel, Charmander, Magnemite, Water Energy, Growlithe, Machop, Voltorb, Diglett, Caterpie, Poliwag, Pikachu, Ponyta, Nidoran m, Vulpix, Darkness Energy, Magikarp, Weedle, Electabuzz, Drowzee, Staryu, Metal Energy, Growlithe, Gastly, Charmander, Rattata, Caterpie, Magnemite, Voltorb, Sandshrew, Poliwag, Diglett, Seel, Nidoran m, Ponyta, Doduo, Pikachu, Staryu, Onix, Weedle, Machop, Tangela, Vulpix, Fire Energy, Voltorb, Charmander, Diglett, Gastly, Caterpie, Drowzee, Magikarp, Electabuzz, Rattata, Growlithe, Nidoran m, Vulpix, Sandshrew, Ponyta †

The reverses sheet looks as follows:

† Kakuna, Misty’s Determination, Porygon, Fire Energy, Gastly, Devolution Spray, Doduo, Switch, Poliwag, Charizard, Tangela, Nidorino, Pidgeot Spirit Link, Pikachu, Water Energy, Zapdos, Energy Retrieval, Brock’s Grit, Onix, Drowzee, Ninetales, Professor Oak’s Hint, Rattata, Pokédex, Staryu, Lightning Energy, Nidoking, Full Heal, Vulpix, Venusaur Spirit Link, Seel, Poliwrath, Chansey, Ponyta, Potion, Voltorb, Psychic Energy, Mew, Maintenance, Charmander, Double Colorless Energy, Diglett, Gyarados, Beedrill, Switch, Machop, Haunter, Fighting Energy, Machamp, Magnemite, Charmeleon, Nidoran m, Sandshrew, Raichu, Arcanine, Growlithe, Metapod, Machoke, Darkness Energy, Hitmonchan, Magikarp, Onix, Poliwhirl, Caterpie, Magneton, Dewgong, Gastly, Magmar, Misty’s Determination, Metal Energy, Clefairy, Revive, Poliwag, Mewtwo, Koffing, Doduo, Starmie, Professor Oak’s Hint, Pikachu, Kakuna, Fairy Energy, Porygon, Slowbro Spirit Link, Electabuzz, Dugtrio, Drowzee, Brock’s Grit, Electrode, Staryu, Rattata, Vulpix, Poliwhirl, Machoke, Super Potion, Charmander, Raticate, Nidorino, Ponyta, Weedle, Voltorb, Sandshrew, Seel, Haunter, Blastoise Spirit Link, Tangela, Machop, Farfetch’d, Nidoran m, Charmeleon, Magmar, Weedle, Diglett, Growlithe, Grass Energy, Koffing, Charizard Spirit Link, Caterpie, Metapod, Magikarp, Magnemite, Electabuzz †

The uncommons sheet look as follows (the secret rares are underlined):

† Misty’s Determination, Revive, Haunter, Brock’s Grit, Slowbro Spirit Link, Kakuna, Energy Retrieval, Blastoise Spirit Link, Switch, Nidorino, Pidgeot Spirit Link, Porygon, Full Heal, Poliwhirl, Pokédex, Potion, Magmar, Venusaur Spirit Link, Metapod, Charizard Spirit Link, Double Colorless Energy, Machoke, Koffing, Kakuna, Charmeleon, Professor Oak’s Hint, Nidorino, Super Potion, Brock’s Grit, Maintenance, Switch, Magmar, Devolution Spray, Pokédex, Porygon, Pidgeot Spirit Link, Metapod, Imakuni’s Doduo, Haunter, Blastoise Spirit Link, Misty’s Determination, Poliwhirl, Revive, Slowbro Spirit Link, Super Potion, Charmeleon, Venusaur Spirit Link, Energy Retrieval, Nidorino, Double Colorless Energy, Charizard Spirit Link, Kakuna, Full Heal, Machoke, Potion, Maintenance, Poliwhirl, Brock’s Grit, Professor Oak’s Hint, Metapod, Switch, Koffing, Revive, Here Comes Team Rocket!, Magmar, Surfing Pikachu, Misty’s Determination, Porygon, Devolution Spray, Nidorino, Slowbro Spirit Link, Pokédex, Haunter, Energy Retrieval, Kakuna, Pidgeot Spirit Link, Blastoise Spirit Link, Switch, Machoke, Full Heal, Venusaur Spirit Link, Potion, Metapod, Professor Oak’s Hint, Double Colorless Energy, Super Potion, Charmeleon, Charizard Spirit Link, Poliwhirl, Maintenance, Haunter, Flying Pikachu, Koffing, Misty’s Determination, Revive, Nidorino, Devolution Spray, Brock’s Grit, Slowbro Spirit Link, Magmar, Energy Retrieval, Blastoise Spirit Link, Pidgeot Spirit Link, Poliwhirl, Full Heal, Porygon, Pokédex, Kakuna, Potion, Venusaur Spirit Link, Machoke, Super Potion, Charizard Spirit Link, Charmeleon, Double Colorless Energy, Devolution Spray, Metapod, Professor Oak’s Hint, Koffing, Maintenance, Exeggutor †

Note that due to the proximity of Here Comes Team Rocket! and Surfing Pikachu, it is possible to get two secret rares in one pack.

Also, note that the sheet contains a handful of repeated sequences of two cards. That means that looking at the individual packs alone, it would not be possible to reconstruct the complete sheet (for example, it would not be possible to tell if the sequence Kakuna - Energy Retrieval - Blastoise Spirit Link is followed by Switch or by Pidgeot Spirit Link). It is possible to look at the sequence the packs come in a box, though, and that allowed me to reconstruct the complete sheet rather easily. I may make a special post on how exactly I did this in the future.

This concludes the XY series. The next step for the Sun & Moon series will be determining which box ratios to use in my model based on the data I have compiled, and based on large opening videos on Youtube like the ones I used for analyzing recent sets.

Edit 2024/03/23: Added reconstruction of complete uncommons sheet.
Edit 2024/03/24: Changed sequence length from 180 to 360. This has no impact on pull rates.

[sturzflugbombardieru]

Digression: Sun & Moon Series Box Ratios

(Note: I significantly re-wrote this post, changing the sequence length used in the models from 180 to 360 packs.)

Advance note: This topic has already been looked into by E4 member @burpies on a different thread: Pull Rates in Sun & Moon - Sword & Shield Sets. It is great work, and very useful for the models I am developing.

Before looking at the individual sets of the Sun & Moon series, it is a good idea to try and establish what the box ratios - i.e. the number of different types of cards per box on average - are. The assumption I am making is that there is at least some consistency between the sets. For the moment I will focus only on the main sets, of which there are 12, and ignore the special ones. The sets feature the following types of ultra rares:

• “Regular” Pokémon-GX
• Full arts, both of Pokémon-GX and Supporter cards; starting with Team Up, this includes alt arts.
• Secret rares; this includes both rainbow rares and gold-bordered cards featuring items and Energies. One set, Ultra Prism, also features two gold Pokémon-GX, Solgaleo-GX and Lunala-GX.
• Some sets feature “special” cards inserted in the reverse slot, namely all the sets from Ultra Prism to Team Up which feature Prism Star cards, and Cosmic Eclipse which features “Trainer Rares”.

For the XY Series sets starting from Primal Clash, full arts and secret rares appear to have been printed on the same sheet due to evidence from miscuts, as is the case for Black & White Series sets starting with Boundaries Crossed. (For the early XY Series sets, secret rares are assumed to be printed with the regular Pokémon-EX with the exception of the silver Dialga EX card from Phantom Forces.) As to how secret rares and full arts were printed for the Sun & Moon Series, there is a video about how Pokémon cards are produced as evidence (couldn’t find the original, this is from a reaction to it):

If you look at the image, it appears that - unless this is just a test print, which I doubt - at least for Guardians Rising, there is a sheet which contains secret rares (both rainbow rares & items/energies) and full art Trainers, but no full art Pokémon. And this does make sense as if you look at the full art Pokémon, you will notice they reflect the light in lines in a way the full art trainers and secret rares don’t. For more details, see this thread: Question regarding card texturing - Guardians Rising. Many thanks to @ratequaza for the insight provided!

So for the rare slot, I will be assuming five different sheets: non-holo rares, holos, “regular” Pokémon-GX, full art Pokémon-GX (including alt arts) and full art Trainers/secret rares (including gold cards from Ultra Prism).

For the box ratios, there is quite a lot of data around, and I will present data from four different sources here in summary along with how I preliminarily intend to model the sets. I say preliminarily because I won’t rule out something changing when I get around to covering them individually. The sources are:

(1) my own data, compiled from Youtube videos. These are all from complete booster boxes.

(2) the data presented by E4 member @burpies in this thread mentioned at the beginning of this post. The data comes from large openings on Youtube, with the packs being from both booster boxes and other sources.

(3) the data compiled by Youtuber and card store owner Danny Phantump: https://www.youtube.com/watch?v=4TCjfoHoUqk. I am not sure what exactly the source is.

(4) a number of large box openings by Youtuber and card business owner Derium, typically 1,000 packs. They are not necessarily all from booster boxes.

(5) large openings by Youtuber and card business owner TheGameCapital (only for Unbroken Bonds and Unified Minds). For both these sets, there is a slight overlap with my own sample, as he opened one case on camera and I included the pulls in my sample.

From this, I compiled this large table:

Here are some general remarks about the data:

• The columns for full art (FA), full art Trainer (FAT) and secret rare (SR) are in grey because these are not actual sheets. The information is nevertheless important for the purpose of comparing it with Danny Phantump’s data (3).
• I converted the data from @burpies (2) from pack odds to box ratios; the rounding error caused by this is negligeable.
• For Sun & Moon base set, the data from @burpies (2) is identical to that from Derium’s videos (4) so it is obviously compiled from them.
• I can’t be completely sure exactly how many packs were opened in Derium’s videos (4); it seems to generally be 28 boxes (1008 packs), though for Forbidden Light there is mention of 27.7 boxes which would be exactly 1000 packs, and for Unbroken Bonds and Unified Minds it is mentioned that it is in fact 30 boxes (1080 packs). The 2999 (and not) packs for Team Up come from the fact that one pack was shown left sealed as it had an unusual error on the outside.
• For Sun & Moon and for Team Up the Derium data (4) contains the pulls from two different videos, for Guardians Rising from three.
• There is no video by Derium for Cosmic Eclipse.
• Parts of the data are really consistent, such as the ratios for “regular” Pokémon-GX for the earlier sets, but there are also some big outliers, such as the ratio for “regular” Pokémon-GX in Cosmic Eclipse in (3).

For the sequence length which defines the increments for box ratios, I will continue to use 360 in my model, i.e. all box ratios are in steps of 0.1, though this is nothing more than a hypothesis. (In an earlier version of this post, I was using a sequence length of 180, but I ended up running into trouble when it came to accurately modelling the raw data.)

The next step is to look at the combined full art Trainer/secret rares sheet and try to figure out how many slots on the sheet were taken up by secret rares for the various sets, and thus how many secret rares there are per box on average. In the end, this number should be in good agreement with the raw data presented above for the different sets. In order to keep things simple, I tried to go with all secret rares being printed on the sheet an equal number of times - 3 (FT3), 4 (FT4) or 5 (FT5) times - wherever it was possible to do so and get a result that fits the raw data. Where this did not yield a good fit, I instead went with the assumption that all full art trainers are printed on the sheet an equal number of times. The models I am using are shown in the table below:

As can be seen, I am assuming all secret rares are printed on the sheet the same number of times for all sets except three:

• For Sun & Moon Base Set, I am assuming 10 secret rares printed 4 times on the sheet and 4 of them 5 times. That leaves 40 slots for the 4 full art Trainers, each of which would be printed 10 times on the sheet (FT10).
• For Celestial Storm, I am assuming 8 secret rares printed 3 times on the sheet and 7 of them 4 times. That leaves 48 slots for the 8 full art Trainers, each of which would be printed 6 times on the sheet (FT6).
• For Unbroken Bonds, I am assuming 10 secret rares printed 3 times on the sheet and 10 of them 4 times. That leaves 30 slots for the 6 full art Trainers, each of which would be printed 5 times on the sheet (FT5). (Alternatively, it would be possible to model this set with all 6 full art trainers and 16 of the secret rares printed 4 times on the sheet, and the remaining 4 secret rares 3 times. With 1.3 cards from that sheet per box on average, that would however yield 0.99 secret rares per box, which seems too much for me when I consider the observed data.)

In general, these models also lead to fairly similar pull rates for the individual full art Trainers and full art Pokémon, even if they are not printed on the same sheet.

Edit 2024/02/25: Added that the sequence length used to model Ultra Prism is 360 packs and not 180, and that this may me the case in a later revision for Burning Shadows as well.

Edit 2024/03/10: Added the data from Derium’s videos of large Team Up openings.

Edit 2024/03/24: Rewrote post, I am now assuming a sequence length of 360 pack for all sets. This affects the pull rates of Burning Shadows, Lost Thunder, Team Up and Unbroken Bonds.

Edit 2024/04/26: Added further source of data for Unbroken Bonds and Unified Minds (videos by TheGameCapital); changed preliminary model for Unified Minds; added note on alternative model for Unbroken Bonds.

[sturzflugbombardieru]

Sun & Moon

As mentioned in the introductory post to the Sun & Moon series, in my model I am assuming 5.6 holos, 4.0 “regular” Pokémon-GX, 1.0 full art Pokémon and 1.4 full art trainers/secret rares per box on average. The latter sheets are labelled “GX”, “FP” and “FT” in the tables. From this set onwards, one Basic Energy Card is included in each pack, bringing the total number of cards to 11. I am including it in the table (the sheet is labelled “E”), but not in the sum of cards (“set”) on the right; the master set for Sun & Moon including reverses thus includes 289 cards and not 298. Here is the rarity table:

It is a very large set, and the rarest cards (10 of the secret rares) have the second-lowest pull rate (1 in 642.9 packs) of any set up to this point (Plasma Freeze still holds the record according to my model, with 1 in 720). As mentioned in my introductory post, I am assuming each full art Trainer to be printed 10 times on the FT sheet, and 10 of the secret rares to be printed 4 times and 4 of the 5 times on the same sheet.

The raw data for the various sheets is shown below, with the dashed lines indicating where the transition from H8 to H7, etc., would occur:

Two observations:

As we will see in later sets, the practice of making the non-holo rares which were theme deck exclusive holos slightly rarer than the others was very much still a thing during the Sun & Moon era, but for this set I see no conclusive evidence for it. There are three theme decks featuring exclusive holo versions of Decidueye, Incineroar and Primarina. Decidueye and Primarina did appear the fewest times in the sample, but not by much, and Incineroar appeared very frequently, so I am guessing there are no artificial rarity differences.

For the secret rares, the ones with the higher observed pull rate are all rainbow rares and not Items/Energies. If this is replicated in the other two sets for which I am assuming different pull rates for different secret rares (Celestial Storm and Unbroken Bonds - see introductory post for the Sun & Moon series), it may be estimated to be significant.

Edit 2024/03/24: Changed sequence length from 180 to 360; this has no impact on pull rates. Made minor edits to text.