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).