Pokemon Pull Rates by Set: What Is Published

Pokemon pull rates are published for fewer sets than almost anyone assumes, and most of the figures in circulation are borrowed. Of the 110 English sets in our catalog that our sealed catalog actually sells booster packs for, 31 have pull rates traceable to a published large-sample study. Those 31 sets rest on eleven distinct studies. And of the 35 sets our pack model can simulate at all, only 11 carry odds measured on that set. The other 24 inherit an era baseline measured on a different set entirely.

The two columns differ because seven of the 35 sets mix sources: a set-specific study replaces some tiers and the era baseline still supplies the rest. Counting a set only where one study supplies every rate it uses, 21 of the 35 sets in the model rest on two studies alone. Ten Scarlet & Violet sets rest entirely on the Stellar Crown study and eleven Sword & Shield sets rest entirely on the Lost Origin study. That is not a criticism of either study, both of which are large and carefully reported. It is a statement about how thin the published record is: a claim about the odds in Silver Tempest is, in fact, a claim about what happened in 8,000 packs of Lost Origin.

The last column is the one to read. Eleven sets carry at least one rate measured on themselves, which is the figure we cite, but only four of those eleven are measured all the way through. Temporal Forces is the thinnest case: its own study supplies a single tier, the special illustration rare, and the other five rates are the Stellar Crown baseline. Calling such a set "measured" without saying how much of it was measured would overstate the record, which is why the count sits beside the label.

Inheritance is a defensible modelling choice and we make it deliberately, because pack anatomy within an era is stable and the alternative is refusing to say anything about 24 sets. It is not, however, a measurement, and it is the reason The Big Hit Went From One Per Box to One Every Third Box is a study of the handful of sets where the rate was measured rather than of every set.

Seventy-six of the 110 English booster-selling sets we track have no published pull-rate study of any kind, covering 8,940 cards. Four more sit in our model's explicit refusal list, and three of those four are inside this openable universe. Refused is not one condition but two: for Celebrations and Shining Fates something was published and is not good enough to use, while Champion's Path and Pokemon GO are refused on structure, because neither contains a non-holo Rare and the era pack model therefore does not describe their packs. The correct output for all of them is a missing panel, not an estimate.

The top of that list is the finding. The five largest English sets with no published odds are all Sun & Moon sets, each of them sold in booster boxes our catalog prices today, and none of them has a large-sample study we can cite. The XY and Sun & Moon eras together account for 22 of the 76, and our pack model does not even carry a pack anatomy for them, which is why no set from either era appears among the 35 we can simulate.

Four sets are refused for a reason stronger than absence. Celebrations has only a 541-pack community sample carrying its own accuracy disclaimer. Shining Fates has no large-sample study of its Shiny Vault subset, which is the whole point of the set. Champion's Path and Pokemon GO contain no non-holo Rare cards at all, so the era pack structure in our model does not describe their packs and simulating them with an era baseline would misrepresent them.

The second row is the honest denominator. Counting against all 236 English sets would score promo sets, deck exclusives and subsets as coverage failures when those sets were never sold in packs and could not have a pull rate. Restricting to the 110 sets our sealed catalog actually sells boosters for gives 28.2% coverage, and that is the figure worth citing. Getting that denominator right took two attempts: an earlier pass stripped only the colon form of the sealed catalog's era prefix and not the dash form, which silently dropped 22 XY and Sun & Moon sets that our catalog plainly sells booster boxes for, and scored coverage at 31 of 88, or 35.2%. The sets were always there; the string handling was not.

The Mega era is the best documented of the three eras our model covers and the Sword & Shield era is the worst, because the study that anchors it reports point estimates only. Seven of the 101 rolled SWSH tier rates carry an interval and every one of those seven comes from the separate Evolving Skies study. These denominators count rolled tiers with cards in the pool, so they are smaller than the per-set column above, which counts every rate resolved including aggregates the simulator never rolls; the methodology gives both numbers.

This is a census of what our pack model cites, not a census of everything ever published. A study we have not found is indistinguishable here from a study that does not exist, and the honest reading of "none published" is "none we can cite". We would rather be told about a missing study than guess at one, and the model file names a source URL and a sample size for every rate it carries so that any claim here can be checked directly.

Sample sizes are as the publishers state them. "8,000+ packs" is not a number we verified, and two of the eleven studies reach us with no stated sample at all, the Temporal Forces and Scarlet & Violet base reports. Three of the eleven reach us through secondary reporting rather than the original publication. A published interval is also not a guarantee of accuracy: it describes sampling error in that study's sample and says nothing about whether the sample was representative of the whole print run, which is the harder question and one nobody has answered publicly.

The openable universe of 110 sets is derived from our sealed catalog, which means a set sold in packs that our sealed catalog does not carry would be missing from the denominator. Card counts are catalog counts, a property of what we hold rather than a finding of this study.

A list of published large-sample pull-rate studies for sets we score as having none would move the 31-of-110 figure directly, and we would rather publish the correction than keep the number. A study measuring an inherited set against its era baseline and finding the rates materially different would break the inheritance assumption that 24 of our 35 sets depend on, and would invalidate the odds input to every expected-value number on this site for those sets. And if confidence intervals were published retroactively for the Sword & Shield era that proved wider than the Scarlet & Violet intervals, the claim that odds are a small source of uncertainty in box valuation would need to be restated era by era.

Universe: the 236 distinct set_name values in the cards table with lang = 'en', holding 24,635 cards. The openable subset is every one of those sets for which sealed_products holds at least one priced SKU whose name contains Booster Box, Booster Pack or Booster Bundle, after stripping the sealed catalog's era prefix (the leading token before a dash or colon) and normalising both names to lowercase alphanumerics; that subset is 110 sets holding 15,525 cards. The prefix strip must handle BOTH forms the sealed catalog uses, the colon form (SWSH07:, ME05:) and the dash form (XY -, SM -); handling only the colon form drops 22 XY and Sun & Moon sets and understates the denominator as 88. Odds coverage is resolved through resolveTierOdds() in src/server/pack-sim.ts, unchanged, against src/content/pack-model.json: a set is covered when it appears in SIMULATABLE_SETS and resolveTierOdds returns at least one tier with status 'active' and a parseable per-pack probability. A set counts as measured on itself when it carries a setOverrides entry, an eraBaselineAlternatives entry, or when the era baseline's own 'set' field names it; otherwise it is inherited. The explicit refusal list is EXCLUDED_SETS in the same file, with its reasons quoted verbatim. A study is counted as distinct by its source URL, which yields eleven across the 35 sets: the three era baselines, the six set-specific overrides, and the two per-set baseline alternatives (Destined Rivals and Scarlet & Violet base) that resolveTierOdds applies through eraBaselineAlternatives. The "sets it supplies a rate to" column counts sets with at least one active rate from that study and therefore overlaps between studies; the "resting on it alone" column counts sets where one study supplies every rate, and those 35 figures do partition. Study attribution, publisher, sample size and the presence of a published confidence interval are read from the model's source and sampleSize fields and from whether the per-pack string carries a +/- term; an absent interval is reported as 'none published' and never as zero. TIER COUNTS: the "Tier rates resolved" column counts every tier resolveTierOdds returns as active for that set, which includes aggregate tiers the simulator never rolls (ultraRareAny on all 13 SWSH sets, and trainerGallery, rainbowRare and goldSecretRare on Crown Zenith, whose slot plan replaces them). The confidence-interval table below counts ROLLED tiers with cards in the set's pool instead, which is the population the odds-swing figure in Booster Box Expected Value is computed over. That is why this study's column sums to 99 Scarlet & Violet tier rates and 134 Sword & Shield ones while the interval table's denominators are 87 and 101. They are different counts of different things and both are stated deliberately. No rate is estimated, inferred from a neighbouring set, or carried across eras. Scripts: apps/web/scripts/sealed-e-pullrates.mts and sealed-e2-pullrates.mts. All figures and queries are in apps/web/.scratch-sealed/figures.json.