Ancient Origins
The box ratios for this set are identical to those for Roaring Skies, but there are a few interesting observations nevertheless. Here is the rarity table:
There is nothin in particular to say about the holos; the raw data looks as follows:
As to the rares, were it not for the observations made in various other sets, I would have likely concluded that the fact that Metagross (with Magnetic Wrap) and Regirock, the two featured as Theme Deck exclusive holos, appear slightly fewer times than the others in the raw data was just coincidence. As it is, I am modelling them as R8 cards - just slightly less common than the other rares. (This is calculated as (43 + 45) / 670 * 121 / 2 = 7.95.) This is the raw data:
There isn’t anything special about the raw data for the “regular” Pokémon-EX:
That for the full arts and secret rares is interesting, though. With 17 cards in total (15 full arts and 2 secret rares) assumed to be printed on a 10x10 sheet, that means 15 FA6 and 2 FA5 cards. Is it reasonable to assume the two FA5 cards are the secret rares? The raw data below doesn’t really support this, with the observed number of secret rares being 0.29 per box. Not certain by any means with this sample size, but I would actually guess that the two FA5 cards are actually full arts and not secret rares, making these two full arts the rarest cards in the set! They are probably also not any of the three Primal Pokémon-EX (marked green below).
(Side note: The situation is somewhat similar to Neo Revelation, though there I went with the guess that it was indeed the two secret rares - Shining Magikarp and Shining Gyarados - printed the fewest times on the holo sheet.)
I more or less reconstructed the reverses sheet, on which all reverse commons and all but two reverse uncommons appear twice. I say “more or less” because it appears this is another one of those sets where cards in certain positions on the sheet have a tendency to get flipped around. This is the same thing I noticed with the commons in the HeartGold & SoulSilver set. Again, the “flipping” positions are spaced 11 cards appart, so they would be right above each other on the sheet. I have underlined them in the sheet sequence below:
† Cottonee, Dangerous Energy, Golurk (Dig Out), Sableye, Jolteon, Gardevoir, Forest of Giant Plants, Inkay, Larvesta, Golett, Ampharos Spirit Link, Ralts, Flash Energy, Malamar, Metang, Goodra, Porygon-Z (Θ Stop), Vileplume, Meowth, Ariados, Registeel, Porygon-Z (Cyber Crush), Gloom, Virizion, Unown, Magikarp, Persian, Vespiquen (Θ Double), Hex Maniac, Entei (Θ Double), Vespiquen (Intelligence Gathering), Entei (Burning Roar), Eevee, Oddish, Bellossom, Metagross (Magnetic Warp), Relicanth, Beldum, Quagsire, Level Ball, Regirock, Flareon, Baltoy (Θ Stop), Goomy, Spinarak, Volcarona (Solar Birth), Sceptile Spirit Link, Baltoy (Slap), Porygon, Kirlia, Lysandre, Wooper, Vaporeon, Golurk (Θ Stop), Golett, Combee, Eco Arm, Tyranitar Spirit Link, Golurk (Dig Out), Gyarados (Berserker Splash), Whimsicott, Paint Roller, Gyarados (Θ Double), Rotom, Hex Maniac, Inkay, Larvesta, Energy Recycler, Dangerous Energy, Ariados, Cottonee, Sliggoo, Unown, Magikarp, Sableye, Level Ball, Kirlia, Gloom, Faded Town, Flash Energy, Vespiquen (Intelligence Gathering), Beldum, Porygon2, Quagsire, Malamar, Metang, Lucky Helmet, Whimsicott, Baltoy (Slap), Forest of Giant Plants, Ralts, Flareon, Eevee, Ace Trainer, Eco Arm, Meowth, Oddish, Paint Roller, Sliggoo, Persian, Sceptile Spirit Link, Porygon, Vaporeon, Bellossom, Ampharos Spirit Link, Energy Recycler, Regice, Spinarak, Goomy, Porygon2, Volcarona (Θ Stop), Tyranitar Spirit Link, Baltoy (Θ Stop), Rotom, Relicanth, Metagross (Θ Double), Faded Town, Wooper, Combee, Claydol, Ace Trainer †
The middle one (Goomy/Spinarak) particularly could just as well have been printed on the sheet the other way around. Still, the reconstruction should be basically correct.
Edit 2024/03/24: Changed sequence length from 180 to 360. This has no impact on pull rates.