Was searching for something else and forgot about this from this Reddit post: Reddit - Dive into anything
Are Arcanine and Gyarados potentially printed on a separate sheet?
I don’t think they’ve had any noticeable pull rate difference but the only way you’d get an error like the picture would be if they were on the same sheet.
The regular Pokémon-ex have a different texture, the full arts too as far as I know. So they should be printed on a different sheet.
Next Destinies
This set marks a milestone in the evolution of the Pokémon TCG, since it introduces the “standard” set composition of having some “regular” ultra rares (in this case, Pokémon-EX), some full arts of the same Pokémon (though in later sets occasionally some cards were availabe only as a “regular” ultra rare or as a full art, and beginning with Boundaries Crossed full art Trainers were added as a standard feature), and some secret rares. The box ratios for the next three sets are fairly simple. I looked at a relatively large sample on Youtube, and these are the results:
Basically, a box usually contains two regular Pokémon-EX and one full art, and the secret rares are assumed to be one in three boxes. Due to holofoil pattern and texturing - the full arts in this set are the first textured cards - four separate sheets must have been used for holos, Pokémon-EX, full arts and secret rares.
As to the full arts, I am still assuming they were printed on 10x10 sheets. For the Pokémon-EX, I am assuming the same. Here is an image of a miscut Pokémon-EX from the Black & White Series, the red lines showing where the cards should have been cut:
By contrast, I see no reason why the secret rares with their standard yellow borders shouldn’t have been printed on an 11x11 sheet. Note that the secret rares for these sets differ from those in Boundaries Crossed and later Black & White Series sets, the latter being fully textured.
The rarity table for Next Destinies looks as follows:
The secret rares are the rarest cards in the TCG up to this point, with a pull rate even lower than the Gold Stars from the Ex Series. The raw data for the holos, rares, Pokémon-EX, full arts and secret rares looks as follows (dashed lines indicating where the transition from H13 to H12, etc., would occur):
Despite the large sample, I can’t say anything definitive about individual card rarities, though my guess is Reshiram and Zekrom are among the R5 rares.
Dark Explorers
As mentioned in my last post, Dark Explorers has the same box ratios as Next Destinies. The secret rares have higher pull rates as there are only 3 of them in the set as opposed to 4. The rarity table looks as follows:
And here is the raw data for the holos, rares, Pokémon-EX, full arts and secret rares (dashed lines indicating where the transition from H14 to H13, etc., would occur):
Nothing definitive can be said about individual card rarities.
Dragons Exalted
Again, the box ratios seem to be the same as those for the previous two sets. Here are the rarity table, as well as the raw data for the holos, rares, Pokémon-EX, full arts and secret rares (dashed line indicating where the transition from H10 to H9, etc., would occur):
Due to the quite large sample (43 boxes) I feel confident enough from the raw data to assume that Probopass is likely the sole R6 rare. As to the rest of the raw data, I wouldn’t draw any conclusions. That the regular print of Registeel EX appeared somewhat less often than the other five Pokémon-EX I would assume to be coincidence. Since the set has four secret rares, they have the same low pull rates as those in Next Destinies.
Dragon Vault
Before we get to the rather complex analysis of the rarities in the later Black & White Series sets, it’s time to look at the first mini-set ever released (not counting the POP Series): Dragon Vault. It contains 21 holographic cards (of which 1 secret rare, Kyurem). They were all printed on the same sheet. The simplest guess would be that each of the 20 regular cards appeared on the sheet six times and Kyurem once, but a quick look at some raw pull data observed on Youtube showed that some of the more desirable cards like Rayquaza and Haxorus seem to appear less often than the two Dratini and the two Axew, for example. For this reason, I reconstructed the sheet. Five cards appear seven times on the sheet, ten six times, five five times (Latias, Latios, Rayquaza, Haxorus and Druddigon being the “rares”) and Kyurem once. This leads to the following rarity table (the sequence length being one pack since there is only one sheet):
The sheet sequence is shown below. There are some repeated sequences of three cards, but I was able to unambiguously reconstruct the sheet:
† Fraxure (Grit), Dratini (Wrap), Bagon, Dragonair (Tail Whap), Fraxure (Scratch), Shelgon, Axew (Signs of Evolution), Exp. Share, Dratini (Hypnotic Gaze), Dragonite, Fraxure (Grit), Druddigon, Super Rod, First Ticket, Dragonair (Healing Melody), Haxorus, Shelgon, Dratini (Wrap), Exp. Share, Salamence, Dragonair (Tail Whap), Latias, Bagon, Dragonite, Dratini (Hypnotic Gaze), Axew (Lunge), Fraxure (Scratch), Druddigon, Latias, Super Rod, Rayquaza, Axew (Signs of Evolution), Fraxure (Grit), Salamence, Dratini (Wrap), First Ticket, Super Rod, Bagon, Dragonair (Healing Melody), Axew (Lunge), Exp. Share, Dratini (Hypnotic Gaze), Rayquaza, Haxorus, Latios, Axew (Lunge), Druddigon, Dragonair (Tail Whap), Fraxure (Scratch), Shelgon, Salamence, Dratini (Wrap), Latias, Bagon, Axew (Signs of Evolution), Fraxure (Grit), Dragonite, Latias, First Ticket, Dratini (Hypnotic Gaze), Shelgon, Axew (Lunge), Rayquaza, Latios, Dragonair (Healing Melody), Fraxure (Grit), Haxorus, Salamence, Dratini (Wrap), Super Rod, Axew (Signs of Evolution), Bagon, Dragonair (Tail Whap), Exp. Share, Latios, Rayquaza, Dratini (Hypnotic Gaze), Axew (Lunge), Dragonair (Healing Melody), Latios, First Ticket, Fraxure (Scratch), Shelgon, Axew (Signs of Evolution), Dragonite, Dratini (Wrap), Druddigon, Haxorus, Fraxure (Grit), Exp. Share, Salamence, Dragonair (Tail Whap), Axew (Lunge), Dratini (Hypnotic Gaze), Latias, Dragonair (Healing Melody), Super Rod, Kyurem, First Ticket, Dragonite, Druddigon, Axew (Signs of Evolution), Dratini (Wrap), Fraxure (Scratch), Bagon, Shelgon, Dragonair (Healing Melody), Rayquaza, Salamence, Latios, Dratini (Hypnotic Gaze), Super Rod, Haxorus, Axew (Lunge), Fraxure (Scratch), Dragonair (Tail Whap), First Ticket, Exp. Share, Bagon, Dragonite, Axew (Signs of Evolution) †
(As a reminder, the dagger marks signify that it is not known where the sheet begins and ends.)
edit: nvm found the post
let me try my hand at it
tried it for a bit for 151 common and uncommon cards - was just wondering, should there be 121 different variations? Meaning that, each card has a chance of being the first in the sequence when opening the pack.
It kind of seems like it, but that made me curious as to why/how that is possible?
Not quite sure if I get the question. The set has 66 commons and 62 uncommons, at least according to Pokecardex. That would mean - provided we still have 11x11 sheets:
-55 C2 cards (printed twice on sheet)
-11 C1 cards (printed once on sheet)
-59 U2 cards
-3 U1 cards
So in theory, if you see for example a Caterpie anywhere in the pack, there should be at most two options for the next card. Unless the cards got flipped when inserted, or different print runs insert the cards in opposite directions. So yes, 121 options in theory.
It should be possible to reconstruct. Good luck!
Thanks!
I lost interest in it after 398 entries because there were fewer and fewer new combinations and a number of combinations that don’t seem to fit anywhere even accounting for flips.
I can share with you the data if you want to take a look and see if I did anything wrong haha.
With all the memes about Metapod and others being hard to find, it would be interesting to see but yeah I’m not even sure when or where those variations would eventually come up.
I don’t know if this is because their batching has been terrible or if it’s meant to be this difficult - saw many packs with the same cards in the same product lol.
Interesting! I would be interested in looking at the data if you could share. The last sheet I reconstructed chronologically was the Evolving Skies commons. It is of course possible that something has changed with the Scarlet & Violet era.
Digression: Box Ratios for Boundaries Crossed, Plasma Storm, Plasma Freeze and Plasma Blast
This is more of an introduction than a digression. For the last three sets, I assumed 2.00 Pokémon-EX, 1.00 full art and 0.33 secret rare per box on average. Since each set has six “regular” Pokémon-EX, six full arts and either three (Dark Explorers) or four (Next Destinies, Dragons Exalted) secret rares, that means the full arts are twice as rare as the regular Pokémon-EX, and the secret rares are twice as rare as the full arts in two of the sets (for Dark Explorers the secret rares are 1.5 times as rare as the full arts).
For the next four sets, things get more complicated. First of all, the texturing of the secret rares changes; unlike those in the previous sets, they are textured all over. A miscut secret rare Garchomp from the Plasma Freeze set is an indication that the secret rares were printed on the same sheet as the full arts (see the silver edge on the bottom):
Why is this the case? Well, it may have to do with the large number of different sheets required to print the sets (see below):
“SP” indicates the Ace Spec cards which come in the reverse slot. Since the Team Plasma cards have blue borders, the uncommons, rares and holos have to be printed on separate sheets to avoid unappealing stripes of the wrong color on the cards edges due to slightly misalligned cutting. (This is not a problem for the Pokémon-EX and full arts as the cards are slighly appart from each other on the sheet; there are no Team Plasma commons.) The fact that the Team Plasma cards were printed on separate sheets is confirmed by the fact that the first uncommon in the pack for the three sets is alway a Team Plasma card while the other two are not, and by this video from PokeRev:
It is an error box where instead of non-Team Plasma uncommons, non-Team Plasma rares were inserted into the packs. There are other videos of such error boxes on YouTube as well.
With that being said, it is time to go back to the box ratios. I showed those for Next Destinies, Dark Explorers and Dragons Exalted further back in my post on Next Destinies. Here is my estimate for the next four sets:
The sample size (at least 1000 packs per set, significantly more for Plasma Freeze) is large enough to be relatively confident that the observed pulls are largely representative. Let’s go through the individual types of cards:
Thus to summarize, the number of Pokémon-EX, combined full arts/secret rares and Ace Specs per box generally depends on the number of Pokémon-EX, full arts and Ace Specs per set, though not on the number of secret rares, though there are small irregularities with the full arts/secret rares in Plasma Storm and the Ace Specs in Plasma Blast. I am still assuming that the “sequence length” for inserting cards is 216 packs or one case.
As to the ratio between secret rares and full arts, that is controlled by how many spaces on the sheet are used for secret rares. I will discuss that when I talk about the individual sets.
Edit 2023/10/28: added reference to upcoming post on Plasma Storm
Boundaries Crossed
Here is the rarity table for Boundaries Crossed:
There is not much to say about the holos, rares, uncommons, commons and Ace Specs (labelled SP for “special” in the table, they come in the reverse slot), nor for the “regular” Pokémon-EX. As mentioned in my previous post, I am assuming that the full arts and secret rares were printed on the same sheet. The question is, how many slots on the 10x10 sheet were used for secret rares? With the sample size mentioned in the last post - 28 box openings watched on YouTube - the uncertainty is too large to say anything for sure. The observed box ratio for secret rares was 0.36 for this set. I will be working under the following two assumptions for this set and the next three sets:
Given the insertion rate of the full art/secret rare sheet determined in the last post, namely 11 per case (1.83 per box), that would mean that the 4 secret rares are FA5 cards, i.e. printed on the sheet 5 times each (though it must be stressed that this is just an assumption). That leaves 80 spaces on the sheet for full arts, meaning 8 would appear 9 times on the sheet and 1 8 times.
The raw data for the holos, rares, Pokémon-EX, full arts/secret rares and Ace Specs is as follows (dashed lines indicating where the transition from H7 to H6, etc., would occur):
Nothing can be said about individual card rarities, nor is there any indication of “artificial” rarity differences. The fact Celebi EX full art was observed only once is probably not relevant.
This is the first set since Supreme Victors to require more than one sheet to print the reverses. 112 reverses ought to appear twice if two sheets were used to print them, 18 only once. Like in earlier sets where this was the case, I did a statistical analysis of the reverses to check which type of reverse (rare holos, rares, uncommons or commons) were most likely printed only once on the two sheets. As I have shown for earlier sets, the number of times reverses are printed on the sheet or sheets usually (though not always) depends on their rarity. In the table below, you can see that “model 1” (two sheets used, 18 of the 20 reverse rare holos printed only once, all the other cards twice) fits the observed data very well; I also tried a “model 2” assuming 3 sheets used for printing the reverses (as seems to have been the case with Expedition and Aquapolis) and all 20 reverse rare holos and 7 reverse rares printed twice, the other 103 cards printed three times, but the model doesn’t fit as well:
Thus, I went with model 1 in the rarity table. One interesting conclusion about this set: Though the number of full arts was increased compared to earlier sets, the pull rates for the individual cards remains about the same as in the last few sets.
Edit 2023/10/28: error in rarity table corrected
Can do, let me clean it up. Sorry for the late reply.
Just dropping this error picture in here for posterity:
Are tera cards printed separately? If so, how do they equalize pull rates? Who knows (yet)
Plasma Storm
Here are the rarity tables for Plasma Storm:
These tables - two of them as the set also features error boxes where non-Team Plasma uncommons are replaced by non-Team Plasma rares - are pretty huge, which is due to the set featuring blue-bordered Team Plasma cards in addition to the regular yellow-bordered cards; these must have been printed on separate sheets - as is confirmed by the error boxes. I will go through the sheets one by one.
First, the holos. In my introductory post, I concluded that the set featured 8 holos per box. But how many are Team Plasma (Hb sheet) and how many are not (Ha sheet)? Well the set features 6 Team Plasma and 4 non-Team Plasma holos. Looking at the raw data from the YouTube videos, I would guess that there are 5 Team Plasma and 3 non-Team Plasma holos per box, which means all the hollos have similar pull rates. The raw data is shown below (dashed lines indicating the transition from Ha31 to Ha30, and Hb21 to Hb20):
Next, the rares. Ignoring 72 non-Team Plasma rares from one error box which came in the uncommon slot, the sample yielded 330 non-Team Plasma rares and 336 Team Plasma rares, so my assumption is the box ratio for both is the same (12 each per box on average). Here is the raw data:
The uncommons were printed on two sheets as well; each pack contains one Team Plasma and two “regular” uncommons. In some error boxes, the latter are replaced by “regular” (non-Team Plasma) rares. The commons are all “regular” Pokémon, and thus assumed to be printed on one sheet.
As to the “regular” Pokémon-EX, like all the ultra rares they are printed with slight spacing between the cards (I am assuming on a 10x10 sheet) as the illustrations run all the way to the card edge, so there is no need to use more than one sheet to print them. The raw data (see below) gives me the impression that there are “artificial” rarity differences in play here - Black Kyurem EX and White Kyurem EX appeared significantly fewer times than the others and I don’t think this is coincidence. So, just as in Neo Genesis and HeartGold & SoulSilver, it appears some higher-value cards were intentionally made rarer. My guess for the model is the two are printed 8 times on the sheet and the other 6 cards 14 times, which would correspond to half the pull rate of the most common Pokémon-EX (rounded up to fill out the sheet). This is a conservative estimate, just going by the raw data the two cards could be even rarer, but uncertainty is high. Here is the raw data:
Next it is time to look at the combined full art/secret rare sheet. In the introductory post for these later Black & White Series sets, I wrote that based on the set having 5 full arts, the expected ratio for this sheet would be 7 per case (1.17 per box), but instead raw data suggests it to be 1.33. This may be because instead of aiming for approximately 2 secret rares per case (one in every third box), the Pokémon Company decided to make them slightly more accessible, with 3 per case (one in every otheer box) - possibly because the secret rare Charizard was obviously going to be a highly coveted card. The raw data yielded 14 secret rares from 28 boxes. The 95% confidence interval assuming a binomial distribution is 0.5 ± 1.96sqrt(0.5(1-0.5)/28) = [0.31, 0.69]. That means one secret rare in three boxes is still within the confidence interval, but only just. I would thus assume that the secret rares were intended to be approximately one in every other box and were printed on the sheet accordingly. The best approximation would be to print each of the secret rares 12 time on the sheet. That would leave 64 positions for the full arts, meaning 4 of them would be printed 13 times on the sheet and the final one 12 times, just like the secret rares. The raw data looks as follows:
The Ace Specs have a rarity of 1.5 per box. Dowsing machine appeared in the sample the most times, but that bears no statistical significance.
The reverses, like the holos, rares and uncommons, were obviously printed on two sheets. A sub-sample of 21 boxes yielded 543 “regular” (yellow border) reverses and 181 Team Plasma (blue border) ones. Based on that I estimated that a case will contain 52 (= approx. 1/4) Team Plasma reverses and 155 (=approx. 3/4) “regular” reverses, adding up to 207 cards. The remaining 9 packs in the case will contain an Ace Spec in the reverse slot.
For the 88 non-Team Plasma reverses, the best model is that 33 reverse commons were printed on the sheet twice, the other cards once:
For the 31 Team Plasma reverses, things are a bit more complicated. It seems clear the rarest cards are reverse rare holos - if the reverses all appear 3 or 4 times on the sheet, 3 of the 6 reverse rare holos would appear only 3 times (model 1). However, the raw data would actually better fit a model where all reverse rare holos were printed only 3 times, the other cards 4 times in general, except for 3 reverse uncommons appearing 5 times on the sheet:
I went with model 1 even if it doesn’t fit quite as well, since I don’t consider it conclusive that there are reverses printed 3, 4 and 5 times on the sheet - which would ammount to another “artificial” rarity difference, something I don’t want to postulate unless I am certain about it.
Edit 2023/11/16: minor errors in rarity table & text fixed
Plasma Freeze
Just like for the previous set, the rarity table for Plasma Freeze is pretty huge due to the fact it includes both yellow-bordered and blue-bordered cards:
Again, I will go through the categories of cards one by one. First, the holos: Like in the previous set, there are yellow-bordered holos (labeled Ha in the table) and blue-bordered (Team Plasma) holos (Hb). As mentioned earlier in my digression on the box ratios, there seem to be 8.30 per box, or 50 per case. My (quite large) sample from YouTube videos yielded 253 yellow-bordered and 320 blue-bordered holos, so I am assuming 22 yellow-bordered and 28 blue-bordered holos per case. The raw data is shown below (dashed lines indicating where the transition from Ha21 to Ha20 and Hb16 to Hb15 would occur):
While I wouldn’t be surprised if Sceptile (first holo in the set) and Ghetsis (the only holo trainer card) were the cards with Ha21 and Hb16 rarity, respectively, I don’t consider the data sufficient to assume that with reasonable certainty.
For the rares, the raw data shows that there are likely the same number of yellow-bordered and blue-bordered rares per box on average, even if the set contains 10 yellow-bordered and 12 blue-bordered holos. Here is the raw data:
Nidoqueen is the best bet as to the Ra13 card due to the size of the sample, but still don’t think it’s really certain. As to the Rb11 card (blue borders), it is probably either Seismitoad or Raticate.
The uncommons, like in Plasma Storm, were printed on two sheets, with each pack containing one Team Plasma (blue border) and two yellow-bordered uncommons. All the commons are yellow-bordered.
The number of “regular” Pokémon-EX per case seems to be 12 per case, or twice as many as are in the set (6) - as in the other sets released around this time. The raw data looks as follows, and unlike in Plasma Storm there is no indication of artificial rarity differences being introduced:
For the full arts and secret rares, they appear to have been printed on the same sheet as can be seen by the image of a miscut secret rare Garchomp I posted a while back. The number per case appears to be equal to the number of full arts plus 2, i.e. 10 - like in Boundaries Crossed and Plasma Blast. Despite the set containing 6 secret rares, the average number of secret rares per box is down to approximately one in every third box, making the secret rares the rarest cards so far (see conclusion at the bottom). With the sample containing 22 secret rares and 96 full arts, I am assuming each of the secret rares appears 3 times on the 10x10 sheet. Here is the raw data:
The Ace Specs are 1 per box on average, and Rock Guard appeared slightly more often in the sample than Life Dew - though this isn’t statistically significant.
For the yellow-bordered reverses, my guess based on a sub-sample (much smaller than the sample for the holos, rares, etc.) is that all but one of the reverse commons and reverse uncommons is printed twice on the sheet (in the model below I assume 1 reverse uncommon to appear only once on the sheet):
The blue-bordered (Team Plasma) reverses show much the same pattern as those from Plasma Storm: Assuming no artificial rarity differences, you would have 28 reverses appearing 4 times on the sheet, and the remaining 3 (likely reverse rare holos) 3 times (model 1). However, the observed data better fits model 2, which has all 8 reverse rare holos appearing 3 times, most of the other cards 4 times and 5 reverse uncommons 5 times.
Just as in Plasma Storm, in the rarity table I went with model 1, even though model 2 now appears to me increasingly more likely. I have tried to avoid modelling artificial rarity differences (in this case REb3, REb4 and REb5 cards on the sheet) unless the evidence is very conclusive. This is a point to think over for future edits of the model, though.
So, what can be said about this set to conclude? The most important conclusion ist that the 6 secret rares appear to be very rare indeed. With a pull rate of 1:720 packs, they are rarer than the rarest secret rares in Next Destinies and Boundaries Crossed (1:435,6 packs according to the model).
Plasma Blast
This is the third and final set to include blue-bordered Team Plasma cards, and due to the complexity of the rarity tables arising from this I am glad to be done with them in this guide. Here is the raritty table - the types of sheets assumed are the same as for the previous two sets:
Again, I will go through the various rarities one by one. The analysis of the number of ultra rares per case some posts earlier points to 12 “regular” Pokémon-EX (twice the number of different cards in the set) and 8 full arts and secret rares (the number of full arts plus 2). Thus, for every third pack to contain a “hit”, there should be 52 holos in a case. Based on the raw data, there would by approximately 41.44 yellow border and 10.56 blue border (Team Plasma) holos per case; based on the number of holos in the set (9 yellow border and 2 blue border) the expected number would be approximately 42.54 and 9.46. So in the model I went with a medium estimat of 42 yellow border and 10 blue border holos. Here is the raw data (dashed lines indicating the same thing as always):
The quite low number of Salamence in the sample data is probably not significant.
As to the rares, both the raw data and the number of rares in the set point to a case containing 96 yellow border and 48 blue border rares. Here is the raw data:
Azelf and Accelgor are good bets for Ra13 and Rb25 cards, for Azelf I felt confident enough to include it in the rarity table, albeit with a question mark.
As to the uncommons, each pack contains 1 blue border and 2 yellow border uncommons. Since the set doesn’t have that many Team Plasma uncommons (or Team Plasma cards in general) that gives the Team Plasma uncommons significantly higher pull rates than the other uncommons.
For the commons, I reconstructed the sheet. It looks as follows - though as with all reconstructed sheets, it is not possible to say where the sequence begins and ends, thus the dagger marks:
† Squirtle, Teddiursa, Aron, Houndour, Ducklett, Surskit, Shelmet, Porygon, Munna, Throh, Kangaskhan, Solosis, Remoraid, Larvesta, Golett, Snorunt, Axew, Machop, Bagon, Squirtle, Teddiursa, Solosis, Drifloon, Houndour, Ducklett, Snorunt, Remoraid, Throh, Surskit, Karrablast, Golett, Druddigon, Munna, Axew, Shelmet, Kangaskhan, Snover, Machop, Bagon, Larvesta, Porygon, Teddiursa, Solosis, Houndour, Lapras, Tynamo, Remoraid, Sawk, Surskit, Aron, Drifloon, Kangaskhan, Throh, Munna, Shelmet, Snover, Ducklett, Porygon, Snorunt, Bagon, Squirtle, Teddiursa, Machop, Golett, Axew, Karrablast, Tynamo, Druddigon, Houndour, Solosis, Remoraid, Ducklett, Surskit, Larvesta, Munna, Aron, Snorunt, Snover, Lapras, Porygon, Sawk, Drifloon, Bagon, Axew, Druddigon, Tynamo, Shelmet, Golett, Machop, Throh, Kangaskhan, Teddiursa, Porygon, Squirtle, Aron, Houndour, Karrablast, Remoraid, Ducklett, Surskit, Lapras, Munna, Solosis, Snover, Drifloon, Tynamo, Sawk, Kangaskhan, Larvesta, Golett, Snorunt, Axew, Druddigon, Tynamo, Karrablast, Machop, Sawk, Snover, Lapras, Aron, Bagon †
The sheet contains a number of repeated sequences of 3 and one repeated sequence of 4, but I am relatively confident I got it right. The C4 cards are also those that appeared the fewest times overall in the packs I watched opened on YouTube.
For the “regular” Pokémon-EX, the raw data is as follows:
For the full arts and secret rares, my guess based on the observed pulls is that the the four secret rares are printed six times each on the sheet, yielding (4 * 6 / 100) * 8 / 6 = 0.32 secret rares per box, or approximately 1 in every third box. The raw data looks as follows:
For the Ace Specs, G Booster appeared the most often in the sample, though this is not statistically significant. The Ace Specs seem to be 1.5 per box on average, making the pull rates slightly lower than in the previous three sets (based on the set having 4 Ace Specs, you would actually expect 2 per box on average.
For the reverses, I am assuming the same distribution I did for Plasma Storm, namely 155 with yellow borders and 52 with blue borders, which fits the raw data well. For the yellow border reverses, my best guess is that all the reverse commons and all but two reverse uncommons appear twice on the sheet, the last two reverse uncommons, the reverse rares and reverse rare holos once:
There are only 14 blue border reverses in the set, so each should appear 8 or 9 times on the sheet. The best fit with the observed data would be if the reverse uncommons and reverse rare holos appear 9 times and the reverse rares 8 times:
Legendary Treasures
Though officially a “regular” set and sold in booster boxes, this set has in common with “special” or “holiday” sets that the odds of pulling a “hit” - in this case a Pokémon-EX, Full Art (from the Radiant Collection sub-set) or secret rare, or even just a holo - are much higher in total than for other sets.
Let’s look at the pack composition first. Each pack contains 4 commons, 2 uncommons, a reverse slot, a rare slot, and 2 cards from the Radiant Collection subset, of which the first is either an uncommon or an ultra rare (Pokémon-EX or full art) and the second is always a common.
The reverse slot contains either a reverse or a holo, with each option being equally likely, i.e. a box should on average contain 18 holos. (Side note: At some point I might make a post on how boxes went from very reliably containing a specific number of holos, Pokémon-ex etc. in the WotC and early TPCI eras to showing more variance for recent sets.)
The rare slot contains either a rare, a Pokémon-EX or a secret rare (gold Reshiram an Zekrom); there are no full arts in the regular set. The pull rates, based on the sample of YouTube videos, seem to be 6 Pokémon-EX per box, 1 secret rare in every third box, and thus 29.67 rares per box.
Here is the rarity table for the set:
The first thing that strikes my eyes is that the reverses are quite rare - not surprising as they are only 1 in every 2 packs. I will also note that to my knowledge this set, unlike a lot of special sets, does not contain any reverse basic energy cards, though I didn’t go so far as to re-watch any YouTube footage of pack openings to verify this. If I am mistaken, I would greatly appreciate correction.
There isn’t much to say about the holos, rares, Pokémon-EX and secret rares. The raw data for these cards is as follows (dashed lines indicating where the transition from H5 to H4, etc., would occur; secret rares not shown as they likely both have the same exact rarity):
As to the Radiant Collection, the fact that the common is always the second card of the two in the pack indicates that two separate sheets were used for printing them. I am assuming the commons sheet is a 11x11 sheet since there is no reason it shouldn’t be - no cards have illustrations going all the way to the edge. The raw data for this sheet I labelled SPb is unremarkable:
The Radiant Collection uncommons and ultra rares are more interesting. The sub-set has 9 uncommons, 1 “regular” Pokémon-EX (Meloetta EX) and 5 full arts, of which 4 are Pokémon-EX and 1 (Reshiram) is not. A photo showing part of the sheet can be seen at Uncut Sheets. Importantly, so can the complete uncut sheet for the uncommons and ultra rares from the second Radiant Collection, that in the Generations set. The latter is a 10x10 sheet. Looking at the Legendary Treasures sheet, particularly the Shaymin EX in the bottom row, it is clear there is some spacing between the cards, so I would assume the uncommons/ultra rares sheet from the first Radiant Collection is also a 10x10 sheet.
The visible part of the sheet contains 48 (69.57%) uncommons and 21 (30.43%) ultra rares. The raw data showed 71.85% uncommons and 28.15% ultra rares. The sample size is not nearly large enough to conclude what the exact ratio is, so I will be assuming each of the 6 ultra rare is printed 5 times on the sheets (in total 30) and the 9 uncommons are printed either 7 or 8 times on the sheet (in total 70). I like this model better that a 28 to 72 ratio as it gives all the ultra rares the same pull rate. Here is the raw data:
This concludes the Black & White series. In my next post, I will give an introduction to the XY series, and look into the question whether the “sequence length” - the maximum number of packs after which the pattern of cards inserted starts to repeat - of 6 boxes (1 case) I have been postulating still fits the raw data, or whether a different sequence length ought to be used.
I am also thinking about covering the Sun & Moon series and subsequent sets, though there are still some questions I need to delve into before I can do so.
Edit 2024/02/11: I slightly edited the model as to the ratio between Radiant Collection uncommons and Radiant Collection ultra rares (SPa sheet).
Digression: Introduction to the XY Series - Which Sequence Length Should I Use?
(Note: This post has been completely rewritten, as I have come to new conclusions on how to best model the XY and Sun & Moon series sets. Basically, I decided that instead of going for a sequence length of 216 for the first four XY series sets and then one of 180 starting with Primal Clash, it is better to use a sequence length of 360 for all XY and Sun & Moon series sets.)
For all the sets up to Legendary Treasures, I have been using a sequence length of 216 packs (1 case) to model the rarities. The sequence length is the number of packs after which the types of cards inserted start to repeat.
Now, I would strongly assume that for a lot of the sets the sequence length is actually shorter, though my model implicitly assumes it is always a divisor of 216. That means that the rarest types of cards - i.e. the sheet from which cards are inserted into the packs the fewest times - are inserted at a rate of 1:216. This I am guessing is the case for the Alph Lithograph cards from Unleashed, Undaunted and Triumphant. (Note that these are not the rarest individual cards, as there is only one Alph Lithograph per set.)
As I wrote in my introductory post to this guide, I have the suspicion that for later sets, the sequence length is not 216 but something divisible by 10 - likely 360.
Now why do I like the idea of a sequence length divisible by 10? Here are the reasons:
That is my reasoning for using a sequence length of 360 in my models starting from here.
So much to the sequence length, now let’s look at the individual types of cards in the XY series:
The observed data for the XY series sets, as well as the number of boxes in the sample, is shown below. “Other” denotes the two red-bordered holos from Phantom Forces, as well as the Pokémon BREAK. The secret rares are included with the Pokémon-EX/full art sheets according to which sheet they were likely printed on:
I will go into how I modelled the XY BREAK series sets in a separate post further down (Digression: XY Break Series Box Ratios), but here are the ratios I will be using for the first 7 sets:
Two comments on these ratios - I will go into more detail when I cover the individual sets:
This was a rather lenghthy post on what is little more than gut feeling. But the purpose of this guide is to develop models for the rarities in the different sets and to keep them as simple as possible, so it was something I needed to think about. Now that it’s done, I can get back to looking at the individual sets.
Edit 2024/03/24: Complete rewrote post, as I am now using a sequence length of 360 beginning with XY Base Set.
XY
For XY Base Set, there are a lot of interesting things to go talk about. The set has no secret rares, so the sheets used for printing the set can be assumed to be commons, uncommons, rares, rare holos, Pokémon-EX, full arts as well as two reverse sheets (the set has 124 reverses, including both art variants of Vivillon, which wouldn’t fit on one sheet).
Looking at the box ratios, a sample of 29 boxes opened on Youtube yielded 8.34 holos, 2.93 Pokémon-EX and and 1.03 full arts. That’s 12.31 “heavy” packs per box.
Now, is that statisticly relevant? I am not going to do the math, as the box ratios aren’t really random and I thus wouldn’t know where to begin, but I can compare with earlier sets. To put it bluntly, it is unusual, as generally the average from the sample is between 11.90 and 12.10 provided it’s not a set with a tiny sample due to only very few videos of box openings available on Youtube.
If I exclude the sets where the sample is less than 14 boxes (504 packs), as well as Neo Destiny (“error” boxes affecting the average) and Legendary Treasures (far more than 12 “hits” per box), the outliers so far are:
All other sets starting with Rising Rivals have a sample size of at least 14 boxes and the total number of “hits” is between 11.90 and 12.10.
That Plasma Storm has more hits per box on average than other sets could potentially be due to the fact that non-holo rares were accidentally included in the uncommon slots in some boxes and the printing company may have thus ended up with a bunch of extra “hits” which led to them increasing the box ratios slightly for a part of the print run. But that is of course only speculation.
As to Skyridge and Jungle, I have no real explanation except that I am pretty confident that the “missing” holos from Skyridge aren’t simply ones I missed when watching the videos on Youtube as they take the place of a common in the packs. It must also be noted that the sample size isn’t huge (15 boxes each).
Back to XY Base Set. The number of hits, 12.31, is high enough that I am going to go with the hypothesis that for some reason, whether accidentally or intentionally, there are more than 12 “hits” per box on average. Thus I will be assuming three “regular” Pokémon-EX, one full art and 8.4 holos per box in my model. Why 8.4 holos and not 8.3? Just gut feeling, 8.4 is a “rounder” number.
The rarity table looks as follows:
It is interesting that the holo, rare and common sheets all seem to include “artificial” rarity differences (i.e. ones not simply due to sheet size), and the Pokémon-EX sheet may as well, though this is uncertain and I chose not to model it.
For the holos, the card at issue is Vivillon, which in the English set comes in two artwork variants: Meadow and High Plains. Looking at the raw data below, I would assume that the pull rate of both combined is about the same as that of the other holos, thus I am assigning H4 rarity to each variant:
(The dashed lines indicate where the transition from H8 to H7, etc., would occur.)
The raw data for the rares gives me the impression that Xerneas and Yveltal are rarer than the other ones. These are the two cards which are featured as holos in the theme decks. Were it only a matter of the raw data for this single set, I might ignore it, but with the same thing happening in future sets as well, I don’t think it is just coincidence. I am modelling the two as R3 cards, as this best fits the raw data. The raw data below also leads me to guess that the five R4 cards are Simisage, Simisear, Simipour and both variants of Wigglytuff, particularly since their pre-evolutions are all C2 cards:
I did not look at the uncommons, but I reconstructed the commons sheet. It looks as follows (dagger marks indicating it is not possible to tell where it begins and ends):
† Pumpkaboo, Bidoof, Skiddo, Pansear, Honedge, Spoink, Pawniard, Jigglypuff (Rollout), Fennekin, Rhyhorn, Panpour, Ekans, Fletchling, Shellder, Taillow, Timburr, Pikachu, Darkness Energy, Weedle, Zorua, Venipede, Skitty, Fairy Energy, Diglett, Chespin, Fighting Energy, Swirlix, Phantump, Lillipup, Inkay, Ledyba, Spritzee, Psychic Energy, Staryu, Doduo, Pumpkaboo, Jigglypuff (Rollout), Slugma, Honedge, Froakie, Bunnelby, Sandile, Voltorb, Skiddo, Scatterbug, Weedle, Rhyhorn, Bidoof, Spoink, Pawniard, Timburr, Fennekin, Grass Energy, Pikachu, Pansage, Fairy Energy, Venipede, Jigglypuff (Body Slam), Ledyba, Sandile, Diglett, Taillow, Ekans, Lillipup, Doduo, Slugma, Fire Energy, Froakie, Skitty, Shellder, Fletchling, Swirlix, Staryu, Pansear, Chespin, Inkay, Phantump, Bunnelby, Pumpkaboo, Panpour, Scatterbug, Water Energy, Rhyhorn, Honedge, Bidoof, Pikachu, Spritzee, Venipede, Skiddo, Zorua, Ekans, Timburr, Lightning Energy, Weedle, Fairy Energy, Skitty, Spoink, Pawniard, Fletchling, Fennekin, Voltorb, Chespin, Taillow, Spritzee, Ledyba, Lillipup, Froakie, Sandile, Diglett, Jigglypuff (Body Slam), Shellder, Phantump, Metal Energy, Inkay, Slugma, Pansage, Staryu, Swirlix, Scatterbug, Doduo, Bunnelby †
It is interesting that there are 32 C3 and 7 C2 Pokémon, and 8 of the 9 Basic Energy Cards have C1 rarity, but Fairy Energy is a C3 card. That makes sense though, as it would have been in a lot of demand from players.
The raw data for the Pokémon-EX looks as follows:
There are a lot of Blastoise EX and Venusaur EX, which is interesting as those are the two Pokémon with a Mega Evolution. I looked at the other XY era sets to see if that might be a trend, but it doesn’t seem to be. So I am assuming it’s just coincidence, and there are no artificial rarity differences here.
The raw data for the full arts is as follows - nothing unusual about it:
For the reverses, observed data for a sub-sample fits a hypothesis where the six reverses appearing only once on the two reverse sheets combined are all reverses rare holos:
Edit 2024/03/24: Changed sequence length from 216 to 360. This has a minor impact on the holo and non-holo rare pull rates.
