Are there official pull rates for Japanese packs?

What the Pokémon and ONE PIECE pages say

Product pages for recent Pokémon and ONE PIECE sets carry the same line, ※カードはランダムに封入されています (cards are packed at random). Next to it sit the cards per pack and the price, which the pack and box specs by set lay out in tables. ONE PIECE pages add a count of card types per rarity. EB-05, for example, lists 21 rares, 9 super rares and 1 secret rare among its 75 card types. That tells you how many different cards exist at each rarity, not how often one turns up.

The only odds-like facts in writing are per-pack guarantees:

The MEGA Dream ex page (M2a) lists 10 cards per pack and the random-packing line and nothing more about contents. The OP-17 and EB-05 pages have no guarantee wording.

A guarantee is a floor for one pack. A promise of an AR per pack doesn't tell you whether that AR is a plain one or the SAR most buyers are hoping for; what AR and SAR mean covers the difference.

Yu-Gi-Oh! states the box, not the odds

Konami's Japanese product pages say more about the box than the Pokémon and ONE PIECE pages above do. IMMORTAL PHOENIX is 5 cards a pack and 30 packs a box, with 80 card types: 4 ultimate rares, 8 ultra rares, 10 super rares, 18 rares and 40 normals. REVOLUTION BOOSTER (rv02) is 5 cards a pack and 15 packs a box, with 69 types. Both pages say one box won't give you every card, and both say how many cards also exist as secret rares (30 in IMMORTAL PHOENIX, 48 in rv02).

That is a count of versions, not a rate. Neither page uses 封入率 (insertion rate) or 確定 (guaranteed). IMMORTAL PHOENIX boxes from the first production run also come with a bonus pack holding one card from 15 types, 14 reprinted ultra rares and a token. The Yu-Gi-Oh! rarity guide explains the rarity names these pages use.

What no page gives you

• The chance of any named rarity per pack or per box, in any of the three games.
• A box-level guarantee for Pokémon or ONE PIECE. Pack counts on shop listings come from the shop, and the Pokémon booster box guide and the ONE PIECE one show how much "box" can vary. The Gundam booster list is in the same position.
• Any assurance about a sealed box you didn't buy at retail. Pokémon's notice on Pokémon Card 151 says listings of 「サーチ済みパック・ボックス」 exist: boxes with the packs holding SR, SAR and other shiny cards taken out. Resealed boxes are the buyer-side risk. Oripa are the case where a seller advertises its own rate, such as 「SR高確率封入」, and the same notice warns the advertised card may be packed at a low rate or not at all.

Does Japanese law require publishing odds?

Not on the Consumer Affairs Agency's page that covers chance-based sales. Its Q&A on online transactions and "card combination" (カード合わせ) defines gacha as a system that gives users items by chance, and treats items from paid gacha as the object of the sale itself rather than a premium. It bans card-combination prizes outright, and it says displays making online game items look far better than they are can break the premiums and misrepresentation act. The page has no provision requiring anyone to disclose insertion rates, and it doesn't deal with booster packs sold as products in their own right.

Reading a box-opening tally

Since tallies are the only source of rates, read what each one says about itself. Three examples, all unofficial:

• A TCGTalk article on ONE PIECE OP-17 says its figures are community estimates from "1,000+ packs" across three full cases plus extra boxes. It puts the secret rare at about one per two to three boxes and says Bandai does not publish hit rates. It doesn't say whether the packs were Japanese or English, and its "~22 per case" figure comes from a single case recount.
• A Cardcosmos article on Japanese ONE PIECE hit rates gives 4 to 5 SR and 0 to 1 SEC per 24-pack display, calls these "community experience values," and gives no sample size or source.
• A Samurai Sword Tokyo post relays TCGplayer's count for the English Pokémon set Pitch Black: more than 4,000 packs opened by TCGplayer's Authentication Center, with Special Illustration Rare at 1.25% ± 0.33% per pack and Mega Hyper Rare at 0.09% ± 0.09%. The post itself says these English rates can't be applied to the Japanese Abyss Eye set. The figures here are as the shop reported them.

Before using a tally, check the edition (Japanese or English), how many packs were opened and by whom, whether a margin of error is given, and whether the rate is per pack or per box.

Why the sample size changes the answer

PokéBeach reported TCGplayer's Prismatic Evolutions figures, from 1,200 pack openings, as one Special Illustration Rare per 45 packs. The rest of this section is our own arithmetic on that figure, not anything TCGplayer or PokéBeach published. At 1 in 45, 1,200 packs hold about 27 of those cards. With that few hits, a 95% range on the rate runs from roughly 1 in 72 to 1 in 33 packs, so two counts of the same set can disagree without either being wrong. The Mega Hyper Rare margin above, as large as the rate itself, is the extreme case.

Per box it gets looser. If a 30-pack box held an SIR at 1 in 45 per pack, and every pack were independent, about half of all boxes (0.51) would hold none. No publisher says packs are independent, so the sum shows how wide the spread could be, not what a box contains.