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