Arceus
This set, the last of the Platinum series, contains Pokémon LV.X, Shining Pokémon (in the reverse slot) and a subset of 9 different Arceus cards (also in the reverse slot, definitely printed on a different sheet from the reverses as they have a different holofoil pattern). A sample of 14 box opening videos watched on Youtube yields the following observed ratios:
- Pokémon LV.X - 3.00 per box
- Arceus - 8.86 per box
- Shining Pokémon - 0.71 per box (though it is possible I missed one or two, as they look like normal reverses)
Based on this, I would assume the actual ratios to be:
- Pokémon LV.X - 3 per box
- Arceus - 9 per box, i.e. (usually) a complete set (assuming they are printed on a 121 card sheet, they will not all have exactly the same rarity as 121 is not divisible by 9)
- Shining Pokémon - each printed once on the reverse sheet, thus 3 / 121 * (36 - 9) = 0.67 per box
As to the reverse sheet, looking at observed data (a sub-sample of 6 boxes) 25 of the 29 uncommons were printed twice on the sheet, the other reverses and the Shining Pokémon once:
The observed data and the model don’t fit perfectly, but my guess is this is due to the relatively small sample.
The rarity table for this set looks as follows (“SP” - for “special” - designates the Arceus cards):
The raw data for the holos, rares, Pokémon LV.X and the Arceus subset looks as follows (dashed lined indicating where the transition from H11 to H10, etc., would occur):
I would say that Probopass and Sceptile (Green Breath) are likely candidates for the H11 and R7 rarities, though this isn’t certain.