The English Pokémon card rarity guide

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Ex Power Keepers

This set concludes the Ex Series as far as main sets go. The set contains Pokémon-ex, Gold Stars and holofoil Energy Cards, the latter coming in the reverse slot. It seems they were printed 5 times each on the same sheet as the 91 reverses, making up a 121 card sheet, with the holofoil Energy Cards appearing approximately 1 in every 4 packs. The table below compares the observed data with this hypothesis; I can’t come up with any other one which would even remotely fit the data:

Since the holos/Gold Stars seem to have already been printed on a 121 card sheet for the last set, my working hypothesis from now on will be that all sheets, rather holofoil or not, will feature 121 cards, at least until we arrive at ultra-rare cards where parts of the illustration reach all the way to the card border. For these, 100 card (10x10) sheets seem to be used in some cases (see the video New Footage of Pokemon Cards Being Designed, Printed, Packaged & Shipped - YouTube at around 10 minutes showing Pokémon GX from Forbidden Light).

Both my own data as well as that provided on the Pokegym forums (PK EX/Stars Per Box | The PokeGym) points to the Pokémon-ex being 3 per box in this set. As to the Gold Stars, things are a bit more difficult to say. I observed 6 Gold Stars pulled from 15 boxes (I came across one more video on Youtube since my introductory post on the Gold Stars), but 4 of them came from one single box, meaning 12 of of 15 boxes contained none. The reported pulls on the Pokegym forums were about 1 Gold Star in 2 boxes. Based on this, I think the best guess is that the Gold Stars are printed on the same sheet as the holos, with each one (Flareon, Jolteon and Vaporeon) appearing twice on the sheet, yielding 2 x 3 / 121 * 9 = 0.446 Gold Stars per box. Unless they were printed in such a way that multiple can routinely appear in the same box, the large share of boxes with no Gold Star I observed would be coincidence. The rarity table looks as follows:

The raw data for the holos, rares and Pokémon-ex looks as follows (dashed lines indicating where the transition from H9 to H8, etc., would occur):

I have not yet looked at the commons or uncommons.

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POP Series 5

Thanks to the presence of two Gold Stars, Espeon and Umbreon, in the set, POP Series 5 is a lot more popular than the other POP Series, and there are more videos of pack openings on Youtube than for the other ones. The 5 uncommons and 6 commons appear to be printed on a single sheet just like in the earlier set; a model with each uncommon appearing 4 times on the sheet (leaving the other 101 positions for the commons) still fits the observed data very well.

A rare in every 10 packs still looks like a good estimate for the moment, although it may be a bit on the low side; I may end up revising it slightly (to 1 in 8) after looking at all 9 POP Series - unlike the main sets, I am looking at these only as I get to them. The big question is whether the Gold Stars are rarer than the other rares. Based on the data from 364 packs, they may be - or they may not be. Here are the rare pulls I observed:

For the moment I will go for a model where all rares have the same rarity (except for one printed 21 times on the sheet). Thus, the rarity table is identical to that for POP Series 4:

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Diamond & Pearl

This is the first set of the Diamond & Pearl Series. Instead of Pokémon-ex and Gold Stars, we now have Pokémon LV.X. For this first set, the pull rate is 1 per box. The number of cards per pack is increased to 10, the packs now featuring 3 instead of 2 uncommons. This is the first set since Ex Ruby & Sapphire to include “normal” (non-holofoil) Basic Energy Cards, which now include Darkness and Metal types. Unlike in previous sets, they are printed on the same sheet as the commons, which I was able to reconstruct. The rarity table looks as follows:

The raw data for the holos, rares and Pokémon LV.X is as follows (dashed lines indicating the transition from H8 to H7, etc.):

The commons/Basic Energy sheet looks as follows:

† Stunky, Clefairy, Potion, Marill, Seedot, Skorupi, Cleffa, Meditite, Glameow, Shinx, M Energy, Turtwig, Chimchar, Chatot, Duskull, Onix, Piplup, Hoothoot, Electabuzz, Wurmple, Magnemite, Gastly, Switch, Rhyhorn, Starly, Sneasel, G Energy, Azurill, Buizel, Cherubi, Mime Jr., Bidoof, Ponyta, Bonsly, Stunky, Combee, Buneary, Goldeen, Misdreavus, Machop, Clefairy, R Energy, Roselia, Energy Search, Chimchar, Glameow, Skorupi, Meditite, Marill, Seedot, Hoothoot, Magnemite, Electabuzz, Gastly, Turtwig, Starly, W Energy, Onix, Sneasel, Piplup, Cleffa, Wurmple, Duskull, Potion, Rhyhorn, Chatot, Shinx, Buizel, Cherubi, Buneary, Misdreavus, L Energy, Bonsly, Stunky, Combee, Bidoof, Chimchar, Mime Jr., Goldeen, Machop, Marill, Roselia, Ponyta, Switch, Azurill, Gastly, P Energy, Seedot, Meditite, Magnemite, Clefairy, Piplup, Sneasel, Skorupi, Turtwig, Cleffa, Onix, Glameow, Shinx, Wurmple, Chatot, F Energy, Duskull, Energy Search, Rhyhorn, Hoothoot, Cherubi, Electabuzz, Buizel, Bidoof, Mime Jr., Bonsly, Combee, Starly, Ponyta, Goldeen, D Energy, Buneary, Misdreavus, Roselia, Machop †

The reverses look like they were all printed on a single 121 card sheet, with 2 cards appearing on it twice.

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Mysterious Treasures

The only thing really mysterious about this set is how rare the secret rare (Time-Space Distortion) is. I saw one pulled from 10 boxes on Youtube. Just like Here Comes Team Rocket! in Ex Team Rocket Returns, it is impossible to say anything even semi-certain about this card’s rarity. There are two threads about it on the PokeGym forums, which I list for the sake of completeness, but no really conclusive information I was able to find:

• Space-Time Distortion? | The PokeGym
• Space-Time Distortion | The PokeGym

I am going to assume it’s a H2 card (printed twice on the holo sheet), the same assumption I made for Here Comes Team Rocket! and for some of the Gold Stars printed on holo sheets, but this is really not much more than a wild guess. If anyone has further information on the topic, I will gladly include it.

Pokémon LV.X still seem to be 1 per box (though a bit less consistently than in Diamond & Pearl). For the reverses, I just looked at one box, all 120 were probably printed on one sheet, with 1 card appearing twice. The rarity table looks as follows:

The raw data for the holos, rares and Pokémon LV.X looks as follows (dashed lines indicating where the transition from H7 to H6, etc., would occur):

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POP Series 6

The Pokémon Company - or the printing company - screwed up when producing these packs. Instead of inserting a rare every 10 packs (or whatever the distribution was supposed to be) they inserted one in every pack. The result is that the “rares” are actually the most common cards in the set.

As mentioned earlier, the commons/uncommons sheet is known. With that, the rarity table looks as follows:

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Secret Wonders

The two questions of interest for this set are the rarity of the Pokémon LV.X - since there are only two in the set, their pull rate is less than one per box - and the sheet layout for the reverses; since there are 130 of them, they will have required at least two sheets to print them.

My Youtube sample of 8 boxes yielded 4 Pokémon LV.X. I would guess they are either 1 in 2 boxes or 2 in 3 boxes. I will go with 1 in 2 for my model, since it best fits the observed data, even if 2 in 3 would meen the pull rate for the individual cards would be the same as for the Pokémon LV.X in the previous two sets.

The question of the reverses is a bit more complicated. The only sets so far to have used more than one sheet to print the reverses were the three e-series sets. As mentioned in the respective posts on this thread, it looks like Expedition and Aquapolis used three sheets and Skyridge used four. By printing 2-3 copies of each reverse, the pull rates of the individual cards were more balanced than if 1-2 copies had been printed on two sheets.

From a Youtube sub-sample of four boxes, it is apparent that those reverses which appear fewer times on the sheet are reverse commons. It is however not possible to tell from the sample data if two or three sheets were used to print them, as printing most the reverses twice and 18 reverse commons once on two sheets, or printing most of the reverses three times and 27 reverse commons twice on three sheets would yield the exact same share of reverse rare holos, rares, uncommons and commons (see table below):

In order to determine which option - two sheets or three sheets - was most likely used, the best way is to look at the reverses in Legends Awakened, the next “large” set to require more than one sheet to print them. For Legends Awakened, it is also apparently some or all reverse commons which are printed fewer times on the sheets. If two sheets were used, 36 of the 48 reverse commons would only be printed once, the other reverses twice. If three sheets were used, all 48 commons and 4 other cards - I am hypothetically assuming they are reverse uncommons - would be printed twice, the other reverses three times. The table below shows that the first option - 2 sheets - fits somewhat better:

As a final piece of evidence, while developing this method of analyzing the reverses I have already looked at two later “large” sets: Boundaries Crossed, and BREAKThrough, which both also seem to have used two and not three sheets.

Thus, assuming 1 Pokémon LV.X in 2 boxes and the reverses printed on two sheets, the rarity table looks as follows:

The raw data for the holos, rares and Pokémon LV.X is as follows (dashed lines indicating where transition from H6 to H5, etc., would occur):

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Digression: Mapping the Great Encounters Booster Box

I hadn’t planned to write much about Great Encounters, since there isn’t that much to say about the set. But when doing my usual analysis of the reverses, I noticed that the “extra” spaces left on the reverse sheet after printing all 102 reverses once didn’t seem to be filled out according to rarity, e.g. only with reverse commons or reverse uncommons. That prompted me to do what I had already done for some XY era sets, namely to reconstruct the reverses sheet. It is possible to do so if you note down in which position in a box (L1-L18, R1-R18) the packs are in, and what the pack art is. Even though it is time-consuming, I decided to do it, and also note down which rares came with which reverses (a thing I unfortunately hadn’t thought of doing when looking at the XY era sets); the idea being that it would give insight into the pattern in which holos were inserted into packs. Here is the result (broken into two images for easier viewing):

The left column contains the reconstructed 121 card sheet sequence. A rather random group of 19 cards appears on the sheet twice. The blocks of green and yellow are sequences of cards I observed in order in more than one box, the white ones I observed in order only once. Then, for twelve boxes, the pack art and the position in the box is noted. The packs seem to come in the sequence C(resselia) - Di(alga) - P(alkia) - Da(rkrai). They are in order to some degree, but have been shuffled around somewhat in the box. This meens it is practically impossible to map a box without weighing or opening most of the packs.

I marked the packs containing a holo in red, those containing a Pokémon LV.X in dark red. Note that they follow a pattern: 5 non-holo rares, 1 holo or better, 2 non-holo rares, 1 holo or better, 1 non-holo rare, 2 holo or better. A Pokémon LV.X can take the place of one in 12 holos, though is not always in the same position. Unless these are all different print runs and the Pokémon LV.X are strictly every 36th pack in a single print run, this will lead to some boxes having 0 or 2 Pokémon LV.X (not observed here except for one “error” box).

Boxes 1, 3, 4, 6, 7, 10, 11 and 12 all received 36 reverses in sequence from the sheet. Boxes 2 and 9 consist of two, box 8 of three part-sequences. That is one way how “error boxes” can be created, since not only the reverses, but also the rares/holos/etc. are from two or more part-sequences; thus box 8 lacks a Pokémon LV.X. As to the reverse Cacnea from box 5 that doesn’t fit in the sequence, it likely got inserted in the stack, possibly when handling the cards, before the cards were inserted in packs; this is because it came from a Darkrai pack.

The only really uncertain part of the reconstruction is that Latios and Slowpoke - possibly due to someting about their position on the sheet - seem to have a tendency to get flipped around, so both appear first in the sequence twice; it isn’t possible to say which comes first.

That the reconstruction is correct is confirmed by looking at the rares: If I eliminate all the holos and Pokémon LV.X, the boxes contain 24 rares in sequence - or, in the cases of boxes 2, 8 and 9, two or three part-sequences; combining all these together yields a sequence of 102 and one of 18, so nearly the complete 121 card rare sheet.

So, to conclude:

• For sets with only 1 reverse sheet, a box usually contains 36 reverses in sequence (or fewer if other cards appear in the reverse slot), but often it contains two or more part-sequences.
• Rares - and likely also holos and ultra-rares - are inserted in sequence as well.
• The holos, etc. are inserted in a simple pattern, though not simply every third pack (this seems to be the pattern used for the initial print run of Sun & Moon, making the boxes somewhat mappable).
• Since the packs are partially shuffled before being inserted in boxes, the boxes are generally unmappable unless the packs are weighed or opened.

I will go over the card rarities for Great Encounters in my next post.

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Great Encounters

Great Encounters, like the first two Diamond & Pearl era sets, has one Pokémon LV.X per box on average. The rarity table looks as follows:

I talked about the reverses in my previous post. The selection of RE2 cards appears random and includes one reverse rare holo (Pachirisu), two reverse rares, six reverse uncommons and ten reverse commons.

For the holos, they would all fit 11 times on a 121 card sheet and I have no reason to assume there were any artificial rarity differences introduced. Since there are only 11 of them, they are actually marginally more common than some of the non-holo rares.

As mentioned in my previous post, I was able to nearly completely reconstruct the rares sheet, and feel confident I identified the five R5 cards - their choice is obviously not random.

I did not look at the uncommons, but I reconstructed the commons sheet. Interestingly, Lunatone is only printed twice on the sheet, making it rarer than the other commons. I would guess this is by mistake, since Solrock appears three times on the sheet. The commons sheet looks as follows:

† Mankey, Cacnea, Slowpoke, Porygon, Koffing, Kakuna, Torchic, Whismur, Feebas, Treecko, Lunatone, Togepi, Clamperl, Ekans, Volbeat, Zigzagoon, Solrock, Luvdisc, Illumise, Igglybuff, Slugma, Mudkip, Caterpie, Glameow, Makuhita, Unown L, Weedle, Snubbull, Krabby, Houndour, Treecko, Porygon, Buizel, Mankey, Drowzee, Jigglypuff, Baltoy, Torchic, Wingull, Swablu, Koffing, Tangela, Slowpoke, Zigzagoon, Lunatone, Makuhita, Clamperl, Whismur, Caterpie, Ekans, Togepi, Feebas, Slugma, Cacnea, Luvdisc, Glameow, Unown L, Solrock, Kakuna, Mudkip, Igglybuff, Houndour, Weedle, Krabby, Porygon, Baltoy, Volbeat, Drowzee, Snubbull, Buizel, Illumise, Makuhita, Jigglypuff, Wingull, Caterpie, Koffing, Zigzagoon, Mankey, Treecko, Slowpoke, Swablu, Torchic, Tangela, Clamperl, Glameow, Krabby, Weedle, Ekans, Whismur, Mudkip, Cacnea, Slugma, Porygon, Feebas, Kakuna, Baltoy, Togepi, Unown L, Volbeat, Krabby, Igglybuff, Solrock, Illumise, Luvdisc, Snubbull, Torchic, Treecko, Makuhita, Zigzagoon, Wingull, Caterpie, Drowzee, Jigglypuff, Mudkip, Tangela, Baltoy, Glameow, Houndour, Weedle, Buizel, Swablu †

As to Pokémon LV.X, my Youtube sample yielded 6 Cresselia, 4 Dialga, 2 Darkrai and 2 Palkia.

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POP Series 7

There is little to write about this set. I am still assuming rares to be 1 in 10 packs, just like in POP Series 1 to 5 (I will reassess once I have looked at all the POP Series). Uncommons look like they were printed 4 times each on the commons/uncommons sheet, leaving 101 spaces for the 7 commons. The rarity table looks as follows:

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Majestic Dawn

Looking at the reverses, a sample of four boxes yielded 15% reverse rare holos, 18% reverse rares, 31% reverse uncommons and 37% reverse commons. If a 121 card sheet is assumed, with 25 “extra” spaces once the 96 reverses have all been positioned on it once, these extra spaces don’t look like they were filled in by rarity, e.g. 25 commons/25 uncommons etc. Just like in the last set (Great Encounters), they may very well be quite a random selection. I didn’t go through the trouble of trying to reconstruct the reverses sheet, though it probably would be possible to do so.

Thus, for this set, all that is to be done is to present the rarity table (shown below - the Pokémon LV.X appear at a rate of 1 per box) and the raw data:

The raw data for the holos, rares and Pokémon LV.X looks as follows (dashed lines indicating where the transition from H9 to H8, etc., would occur):

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Legends Awakened

This is a “large” set where the reverses (139 in all) do not all fit on one sheet. I already showed in my post on Secret Wonders that the best-fitting assumption is that two sheets were used to print them, all reverses except 36 commons being printed twice. However, it is of course possible that the RE1 reverses weren’t all selected according to rarity, as was observed for the last two sets - Great Encounters for sure, Majestic Dawn likely.

The set also has 7 Pokémon LV.X, more than any previous set, so the number of Pokémon LV.X per box was increased to 2.

Here is the rarity table:

The raw data for the holos, rares and Pokémon LV.X looks as follows (dashed lines indicating where transition from H8 to H7, etc., would occur):

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Digression: an overview over POP Series pull rates

Next set up in this series is POP Series 8. Since this set, just like POP Series 9, differs somewhat from the earlier POP series as far as pull rates/sheet composition go, this seems like a good place to provide an overview over all 9 POP series.

For POP Series 1-7, my assumption has been that the commons and uncommons are printed on one sheet, with 20 spaces on the sheet reserved for the uncommons and the rest for the uncommons (this is definitely true for POP Series 6, where the commons/uncommons sheet is known). For the rares, I am assuming no difference in rarity between “regular” rares, Pokémon-ex and Gold Stars, though I can’t rule out that there may be some. With the exception of POP Series 6, which features a rare in every pack (making the rares more common than the commons), my estimate has been that rares are generally 1 in 10 packs. The following table shows what I have observed from Youtube videos:

As can be seen, both assumptions (1 rare in 10 packs, uncommon to common ratio of 20:101) fit the data well.

For POP Series 8 and 9, two things change:

• Each pack includes a Basic Energy Card, for a total of three cards per pack. Thus there will have been a separate sheet for Basic Energy Cards printed.
• Both rares and uncommons always appear as the middle card of the pack, never as the last one. Thus uncommons can’t have been printed on the same sheet as the commons. They may or may not have been printed on the same sheet as the rares.

The observed data for these two sets looks as follows:

About every other pack seems to contain a rare or uncommon. What is somewhat remarkable is that POP Series 8 seems to feature more rares than POP Series 9. I can’t say if it’s statistically significant, but I am assuming it is not. If rares and uncommons were printed on the same sheet - and I will be going with this hypothesis in my model -, my best guess would be these sheets included 40 rares and 81 uncommons - nice, round numbers that fit the observed data relatively well.

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POP Series 8

Based on the assumptions mentioned above, the rarity table for POP Series 8 looks as follows:

“U” denotes a combined uncommons/rares sheet, which I am assuming contains 40 rares and 81 uncommons. “E” contains the 8 Basic Energies. As can be seen, the rares are slightly more common than for POP Series 1-5 and POP Series 7.

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Stormfront

Stormfront, the last Diamond & Pearl Series set, introduces two types of cards also featured in the Platinum Series sets, namely secret rares which are reprints from earlier sets (in this case Charmander, Charmeleon and Charizard from Base Set) and Shining Pokémon (shiny holographic subset). Both appear to have a rarity of about one per box (the Shining Pokémon appear in the reverse slot). Pokémon LV.X, just like in Legends Awakened, are two per box.

The reverse sheet is known (see Uncut Sheets). Of the 95 reverses, 72 are printed once on the sheet and 23 (all uncommon Pokémon and Special Energies) are printed twice. The final three spots on the 121-card-sheet are taken up by the 3 Shining Pokémon, meaning their actual rarity is 1 in 40.3 packs (slightly less than one per box) . I looked at the reverses from one Youtube box opening video and they were 36 cards in sequence from the sheet.

As to the secret rares, my guess is they are printed on the holo sheet, each appearing 4 times on the sheet, which would give them an actual rarity of almost 1 per box: (4 x 3 / 121) * 10 / 36 = 1 in 36.3 packs. The rarity table looks as follows:

The Pokémon LV.X are the easiest to pull in any set so far, as they come two per box and there are only five of them in total.

The raw data for the holos, rares and Pokémon LV.X looks as follows (dashed lines indicating where transition from H10 to H9, etc., would occur):

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Platinum

Like Stormfront, Platinum contains secret rares which are reprints from earlier sets (Electabuzz, Hitmonchan and Scyther - the “Haymaker” trio from the early days of the TCG), as well as Shining Pokémon (Lotad, Swablu and Vulpix). Pokémon LV.X, just like in the previous two sets, appear to be about two per box; for the secret rares, I am making the same assumption as for Stormfront, namely that they are printed four times each on the holo sheet.

For the reverses, there are two conceivable variant. There are a total of 121 reverses which would exactly fit onto one sheet, but with the addition of the three Shining Pokémon, a second sheet must have been required. The variants are:

• One sheet for the reverses, one for the Shining Pokémon, with the latter being one per box.
• Two sheets, containing 115 of the reverses and all three Shining Pokémon printed twice, and six reverses printed once; the Shining Pokémon would have a rarity of 6 / 242 * 36 = 0.89 per box if both sheets were printed in equal quantities.

The first variant is more elegant, and it appears to be the one that was chosen. I observed some footage on Youtube and noted down the position of the packs and the pack art (Dialga, Palkia, Giratina and Shaymin) - see figure below. The overlapping sequences (marked in yellow) make it look like all the reverses in the boxes were coming from one single sheet (if two sheets were used, I would expect them to be inserted alternatingly, or in some similar pattern). Also, the orange marking denotes the place a Shining Pokémon was inserted in pack L2 (featuring Palkia artwork) of the first box, interrupting the sequence.

The rarity table looks as follows (SP denoting the Shining Pokémon):

The raw data for the holos, rares and Pokémon LV.X looks as follows (dashed lines indicating where the transition from H7 to H6, etc., would occur):

As to the Shining Pokémon, I saw 4 Lotad, 3 Swablu and 3 Vulpix pulled - which obviously has no statistical significance whatsoever.

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I’m not sure which DP set with the shinies it was, but I think there’s a picture of the reverse holo sheet around.

Also, the other day there was an Evolving Skies reverse sheet which I thought might interest you since those modern sets are huge now. It seems like cards were repeated rather quickly on that sheet.

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Thanks for the tip on the Evolving Skies sheet, this is extremely interesting! I will definitely look at the images in detail.

As to the picture of the sheet, I know their is one of the Stormfront sheet, which I looked at. The shinies are on the same sheet as the reverses in this set.

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POP Series 9

This is the final POP Series set. As I explained in my post further back about the POP Series in general, POP Series 8 and 9 differ from the earlier seven in pack collation. Aside from containing Basic Energy cards, the uncommons are printed on a separate sheet from the commons, a I am assuming they are printed on the same sheet as the rares. The rarity table is identical to that of POP Series 8:

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Rising Rivals

Rising rivals continues to feature Pokémon LV.X and secret rare reprints (in this set Pikachu, Flying Pikachu and Surfing Pikachu), but instead of the Shining Pokémon there is a Rotom subset with six cards. Since these feature a cracked ice holofoil pattern, they will have been printed on a separate sheet.

The general rarity distribution is two Pokémon LV.X, two Rotom subset cards and one secret rare per box. My guess, just as for Stormfront and Platinum, is that the secret rares were printed on the holo sheet.

As to the reverses, they all fit on one sheet. In my Youtube sample, I observed a very high proportion of reverse uncommons:

My guess (model) is most of the cards are printed once on the sheet, with 19 of the 32 reverse uncommons being printed twice. I would explain the difference between observed pulls and the model by the fact that there seems to be a cluster of reverse uncommons on the sheet, and a lot of the boxes I watched being opened happened to contain cards from this part of the sheet.

This shows that the method of trying to say something about reverse sheets based on observed samples has its limitations. However, it is still useful as the other sets I looked at so far didn’t have such a cluster where multiple packs in a row all contain reverse uncommons.

These things said, the rarity table looks as follows (“SP” denoting the Rotom subset):

As can be seen, the Pokémon LV.X from this set are the most difficult so far to pull.

The raw data for the holos, rares and Pokémon LV.X looks as follows (dashed lines indicating where the transition from H9 to H8, etc., would occur):

As to the Rotom subset, the card I observed the most of was Wash Rotom.

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Supreme Victors

For this set, the Pokémon Company significantly increased the pull rates for the Pokémon LV.X. This, as well as the presence of Charizard G LV.X, are possible reasons why this set seems to have been very popular. There are a ton of box opening videos on Youtube, and this is the first set for which I have at least 1000 packs (28 boxes) in my sample.

Nevertheless, I am not certain what the exact ratio for Pokémon LV.X is in this set. The sample yields 3.75 per box (19 boxes with 4, 8 with 3, 1 with 5). Contemporary discussion on the Pokegym forums (SV Box Ratios? | The PokeGym) isn’t really conclusive either. Boxes with 3 Pokémon LV.X seem to be common, as are such with 4 of them. Even though the latter seem to be a bit more prevalent, in my model I am going to assume 3.5 Pokémon LV.X per box (21 per case). This means the individual cards have the same average pull rate as in the next set, Arceus (3 Pokémon LV.X per box, with 6 different ones in the set; Supreme Victors contains 7 different Pokémon LV.X).

As to the reverses, I would assume two sheets were used, with all of the reverse uncommons, rares and rare holos, the three Shining Pokémon and one reverse common printed twice, and the remaining 44 reverse commons printed once. A comparison with observed data looks as follows:

The three secret rare reprints of the Legendary Birds I would guess to be printed 5 times each on the holo sheet; this would make them very close to 1 per box. The rarity table looks as follows:

The raw data for the holos, rares and Pokémon LV.X is shown below (dashed lines signifying where the transition from H8 to H7, etc., would occur). For the rares, I felt confident enough for the first time giving an estimate on which ones have which rarity based on observed pull rates alone; it looks very much like the R3 cards are the 12 Pokémon SP as well as the Legendary Birds (different versions from the secret rare reeprints). (The information I provided for the rares in Great Encounters was based on a near-complete reconstruction of the rares sheet.)

The commons sheet, which I reconstructed, looks as follows (dagger marks signifying that it isn’t clear where the sheet begins and ends):

† Mudkip, Zubat, Beldum, Mime Jr., Surskit, Doduo, Pachirisu, Geodude, Kricketot, Croagunk, Whismur, Buizel, Roselia, Cherubi, Meditite, Gible, Bulbasaur, Starly, Chingling, Sandshrew, Bidoof, Rhyhorn, Nincada, Buneary, Goldeen, Meowth, Magnemite, Turtwig, Chatot, Drifloon, Seel, Growlithe, Chimchar, Shinx, Combee, Piplup, Shroomish, Mankey, Mime Jr., Roselia, Cherubi, Starly, Magnemite, Pikachu, Geodude, Skorupi, Chingling, Corphish, Bulbasaur, Doduo, Sandshrew, Mudkip, Gible, Baltoy, Magikarp, Beldum, Pachirisu, Chimchar, Nincada, Shroomish, Shinx, Drifloon, Piplup, Meowth, Zubat, Whismur, Combee, Kricketot, Feebas, Bidoof, Mankey, Surskit, Buneary, Growlithe, Seel, Chatot, Meditite, Paras, Beldum, Skorupi, Mime Jr., Gible, Magnemite, Zubat, Turtwig, Cherubi, Whismur, Geodude, Bidoof, Shroomish, Kricketot, Surskit, Drifloon, Corphish, Mudkip, Growlithe, Roselia, Baltoy, Pachirisu, Mankey, Doduo, Pikachu, Magikarp, Nincada, Buizel, Croagunk, Starly, Buneary, Paras, Piplup, Feebas, Sandshrew, Shinx, Bulbasaur, Combee, Meowth, Rhyhorn, Goldeen, Chimchar, Pikachu, Corphish †

It is noteworthy that the 14 C2 cards are basically every third common card according to set numbering, with the exception of Mudkip which is a C3 card.