The English Pokémon card rarity guide

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 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.





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Burning Shadows

In modelling the rarities in this set, the two main questions are what are the rates at which cards from the full art Pokémon (FP) and full art Trainer/secret rare (FT) sheets are inserted into packs, and how many of the 100 slots on the FT sheet are taken up by secret rares. For the first question, here is the data from the various samples again, as presented a few posts further up in the introductory post for the Sun & Moon series:

As can be seen, in my model I went with 1.0 full art Pokémon and 1.4 full art Trainers/secret rares, though 1.1 and 1.3 may be a better guess. However, I am trying to keep my models as simple as possible and consistent between sets, so I am continuing to use (at least for the moment) the assumption that the box ratios result from integer numbers divided by a sequence length of 180 packs in total, i.e. they come in increments of 0.2. Thus I may be modelling the pull rates for full art Trainers and secret rares too high, and for full art Pokémon too low.

For the second question, the raw data can be useful, but first it needs to be said that even for large samples it isn’t always that reliable when it comes to looking at how many spaces on a sheet were taken up by a specific type of card. For example, we know from photos the Radiant Collection uncommons/ultra rares sheet for Generations features 28 ultra rares and 72 uncommons, but the raw data from my sample yielded 30.7% ultra rares and 69.3% uncommons.

For samples (1), (2) and (4) the ratio secret rares / (secret rares + full art Trainers) is 64.0, 67.1 and 64.9, respectively. I thus think a model in which each of the 22 secret rares appears 3 times on the sheet, and the remaining 34 slots are filled out by the full art trainers, is the best guess. This leads to the following rarity table:

Interestingly, despite the fact it may be off somewhat, the model leads to pretty similar pull rates for full art Pokémon and full art Trainers. 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):

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I reconstructed the commons sheet, which 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 †

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 Modern 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 thee “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):

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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.

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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:

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