{
  "url": "https://www.moonstonehq.com/articles/booster-box-expected-value",
  "slug": "booster-box-expected-value",
  "title": "Booster Box Expected Value Has Error Bars",
  "summary": "Across 27 English sets with a real box and odds traceable to a published study, a box's contents are worth a median 0.380 of its ask, valued at asks on both sides. One bookkeeping assumption moves that by 47.5%.",
  "section": "Quant research",
  "published": "2026-09-22",
  "readMinutes": 11,
  "publisher": "moonstone",
  "findings": [
    {
      "value": "0.380",
      "measures": "median contents value as a share of the box ask",
      "basis": "27 sets, closed-form expectation over published odds of which 20 are inherited era baselines, 2026-09-22; contents valued at TCGplayer ASKS, which overstates what a seller realises"
    },
    {
      "value": "0.168",
      "measures": "the same median counting only cards worth $5 or more, at 85% realisation",
      "basis": "not a different market, a different assumption"
    },
    {
      "value": "12 of 27",
      "measures": "boxes whose pull rates carry no published confidence interval at all",
      "basis": "eleven Sword & Shield boxes whose anchoring study publishes point estimates only, plus Scarlet & Violet, whose own study is a different one that also publishes none"
    }
  ],
  "tables": [
    {
      "title": "Closed form against the site's Monte Carlo engine, 3,000 boxes each",
      "columns": [
        "Set",
        "Closed-form EV per box, at ask",
        "Monte Carlo EV per box, at ask",
        "Difference"
      ],
      "rows": [
        {
          "Set": "[Stellar Crown](/set/stellar%20crown)",
          "Closed-form EV per box, at ask": "$149.73",
          "Monte Carlo EV per box, at ask": "$151.70",
          "Difference": "+1.32%"
        },
        {
          "Set": "[Surging Sparks](/set/surging%20sparks)",
          "Closed-form EV per box, at ask": "$117.47",
          "Monte Carlo EV per box, at ask": "$118.25",
          "Difference": "+0.66%"
        },
        {
          "Set": "[Lost Origin](/set/lost%20origin)",
          "Closed-form EV per box, at ask": "$225.16",
          "Monte Carlo EV per box, at ask": "$228.69",
          "Difference": "+1.57%"
        },
        {
          "Set": "[Mega Evolution](/set/mega%20evolution)",
          "Closed-form EV per box, at ask": "$128.30",
          "Monte Carlo EV per box, at ask": "$128.95",
          "Difference": "+0.51%"
        },
        {
          "Set": "[Journey Together](/set/journey%20together)",
          "Closed-form EV per box, at ask": "$105.12",
          "Monte Carlo EV per box, at ask": "$104.58",
          "Difference": "-0.51%"
        }
      ]
    },
    {
      "title": "Contents value against box ask, 27 sets, 2026-09-22",
      "columns": [
        "Set",
        "Era",
        "Box ask",
        "Contents at ask",
        "Coverage",
        "Contents, $5+ at 85%",
        "Coverage",
        "Odds CI swing"
      ],
      "rows": [
        {
          "Set": "[Temporal Forces](/set/temporal%20forces)",
          "Era": "SV",
          "Box ask": "$315.64",
          "Contents at ask": "$192.19",
          "Coverage": "0.310",
          "Contents, $5+ at 85%": "$97.87",
          "Odds CI swing": "±2.9%"
        },
        {
          "Set": "[Perfect Order](/set/perfect%20order)",
          "Era": "ME",
          "Box ask": "$175.99",
          "Contents at ask": "$91.72",
          "Coverage": "0.164",
          "Contents, $5+ at 85%": "$28.86",
          "Odds CI swing": "±6.8%"
        },
        {
          "Set": "[Pitch Black](/set/me05%3A%20pitch%20black)",
          "Era": "ME",
          "Box ask": "$191.88",
          "Contents at ask": "$99.93",
          "Coverage": "0.171",
          "Contents, $5+ at 85%": "$32.87",
          "Odds CI swing": "±8.0%"
        },
        {
          "Set": "[Stellar Crown](/set/stellar%20crown)",
          "Era": "SV",
          "Box ask": "$308.48",
          "Contents at ask": "$149.73",
          "Coverage": "0.220",
          "Contents, $5+ at 85%": "$67.99",
          "Odds CI swing": "±3.6%"
        },
        {
          "Set": "[Paradox Rift](/set/paradox%20rift)",
          "Era": "SV",
          "Box ask": "$279.86",
          "Contents at ask": "$133.13",
          "Coverage": "0.221",
          "Contents, $5+ at 85%": "$61.86",
          "Odds CI swing": "±3.6%"
        },
        {
          "Set": "[Scarlet & Violet](/set/scarlet%20%26%20violet)",
          "Era": "SV",
          "Box ask": "$294.80",
          "Contents at ask": "$138.66",
          "Coverage": "0.226",
          "Contents, $5+ at 85%": "$66.48",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Journey Together](/set/journey%20together)",
          "Era": "SV",
          "Box ask": "$237.12",
          "Contents at ask": "$105.12",
          "Coverage": "0.139",
          "Contents, $5+ at 85%": "$32.90",
          "Odds CI swing": "±4.0%"
        },
        {
          "Set": "[Twilight Masquerade](/set/twilight%20masquerade)",
          "Era": "SV",
          "Box ask": "$354.05",
          "Contents at ask": "$155.39",
          "Coverage": "0.203",
          "Contents, $5+ at 85%": "$71.72",
          "Odds CI swing": "±4.2%"
        },
        {
          "Set": "[Chaos Rising](/set/chaos%20rising)",
          "Era": "ME",
          "Box ask": "$191.83",
          "Contents at ask": "$81.41",
          "Coverage": "0.133",
          "Contents, $5+ at 85%": "$25.51",
          "Odds CI swing": "±8.2%"
        },
        {
          "Set": "[Mega Evolution](/set/mega%20evolution)",
          "Era": "ME",
          "Box ask": "$311.78",
          "Contents at ask": "$128.30",
          "Coverage": "0.168",
          "Contents, $5+ at 85%": "$52.49",
          "Odds CI swing": "±8.2%"
        },
        {
          "Set": "[Phantasmal Flames](/set/phantasmal%20flames)",
          "Era": "ME",
          "Box ask": "$397.69",
          "Contents at ask": "$157.07",
          "Coverage": "0.172",
          "Contents, $5+ at 85%": "$68.29",
          "Odds CI swing": "±10.5%"
        },
        {
          "Set": "[Surging Sparks](/set/surging%20sparks)",
          "Era": "SV",
          "Box ask": "$303.14",
          "Contents at ask": "$117.47",
          "Coverage": "0.173",
          "Contents, $5+ at 85%": "$52.45",
          "Odds CI swing": "±5.2%"
        },
        {
          "Set": "[Paldea Evolved](/set/paldea%20evolved)",
          "Era": "SV",
          "Box ask": "$477.53",
          "Contents at ask": "$184.82",
          "Coverage": "0.218",
          "Contents, $5+ at 85%": "$104.06",
          "Odds CI swing": "±4.3%"
        },
        {
          "Set": "[Astral Radiance](/set/astral%20radiance)",
          "Era": "SWSH",
          "Box ask": "$411.79",
          "Contents at ask": "$156.54",
          "Coverage": "0.174",
          "Contents, $5+ at 85%": "$71.63",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Battle Styles](/set/battle%20styles)",
          "Era": "SWSH",
          "Box ask": "$283.61",
          "Contents at ask": "$103.49",
          "Coverage": "0.106",
          "Contents, $5+ at 85%": "$30.03",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Destined Rivals](/set/destined%20rivals)",
          "Era": "SV",
          "Box ask": "$421.02",
          "Contents at ask": "$150.05",
          "Coverage": "0.163",
          "Contents, $5+ at 85%": "$68.70",
          "Odds CI swing": "±6.0%"
        },
        {
          "Set": "[Brilliant Stars](/set/brilliant%20stars)",
          "Era": "SWSH",
          "Box ask": "$582.41",
          "Contents at ask": "$205.35",
          "Coverage": "0.208",
          "Contents, $5+ at 85%": "$121.02",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Obsidian Flames](/set/obsidian%20flames)",
          "Era": "SV",
          "Box ask": "$372.17",
          "Contents at ask": "$126.78",
          "Coverage": "0.139",
          "Contents, $5+ at 85%": "$51.71",
          "Odds CI swing": "±3.0%"
        },
        {
          "Set": "[Silver Tempest](/set/silver%20tempest)",
          "Era": "SWSH",
          "Box ask": "$522.04",
          "Contents at ask": "$173.72",
          "Coverage": "0.184",
          "Contents, $5+ at 85%": "$96.25",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Lost Origin](/set/lost%20origin)",
          "Era": "SWSH",
          "Box ask": "$733.72",
          "Contents at ask": "$225.16",
          "Coverage": "0.168",
          "Contents, $5+ at 85%": "$123.09",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Vivid Voltage](/set/vivid%20voltage)",
          "Era": "SWSH",
          "Box ask": "$313.00",
          "Contents at ask": "$85.44",
          "Coverage": "0.058",
          "Contents, $5+ at 85%": "$18.00",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Chilling Reign](/set/chilling%20reign)",
          "Era": "SWSH",
          "Box ask": "$479.51",
          "Contents at ask": "$121.27",
          "Coverage": "0.098",
          "Contents, $5+ at 85%": "$47.13",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Rebel Clash](/set/rebel%20clash)",
          "Era": "SWSH",
          "Box ask": "$483.63",
          "Contents at ask": "$111.22",
          "Coverage": "0.048",
          "Contents, $5+ at 85%": "$23.39",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Darkness Ablaze](/set/darkness%20ablaze)",
          "Era": "SWSH",
          "Box ask": "$367.47",
          "Contents at ask": "$83.11",
          "Coverage": "0.049",
          "Contents, $5+ at 85%": "$18.13",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Sword & Shield](/set/sword%20%26%20shield)",
          "Era": "SWSH",
          "Box ask": "$688.99",
          "Contents at ask": "$117.90",
          "Coverage": "0.061",
          "Contents, $5+ at 85%": "$41.91",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Fusion Strike](/set/fusion%20strike)",
          "Era": "SWSH",
          "Box ask": "$968.97",
          "Contents at ask": "$161.38",
          "Coverage": "0.086",
          "Contents, $5+ at 85%": "$83.13",
          "Odds CI swing": "none published"
        },
        {
          "Set": "[Evolving Skies](/set/evolving%20skies)",
          "Era": "SWSH",
          "Box ask": "$2,408.12",
          "Contents at ask": "$290.83",
          "Coverage": "0.083",
          "Contents, $5+ at 85%": "$199.75",
          "Odds CI swing": "±6.7%"
        }
      ]
    },
    {
      "title": "Each input moved on its own, as a share of the ask-basis expected value",
      "columns": [
        "Input",
        "What we change",
        "Median effect",
        "Range across 27 sets"
      ],
      "rows": [
        {
          "Input": "Published odds",
          "What we change": "every rate moved by its own published 95% half-width, combined in quadrature",
          "Median effect": "3.0% over all 27, 5.2% over the 15 with an interval",
          "Range across 27 sets": "0% to 10.5%; the twelve zeros are absent intervals, not narrow ones"
        },
        {
          "Input": "Realisation",
          "What we change": "a stated 0.85 factor for fees, shipping and seller discount",
          "Median effect": "15.0% (this row is 1 minus 0.85, an assumption restated, not a measurement)",
          "Range across 27 sets": "flat by construction"
        },
        {
          "Input": "Sellability",
          "What we change": "drop every card worth under $5 as unsellable individually",
          "Median effect": "47.5%",
          "Range across 27 sets": "19.2% to 75.3%"
        },
        {
          "Input": "Pool draw",
          "What we change": "value each tier at its median card rather than its mean card",
          "Median effect": "28.9%",
          "Range across 27 sets": "10.0% to 62.5%"
        }
      ]
    },
    {
      "title": "Where a box's expected value actually sits, by card price",
      "columns": [
        "Card price band",
        "Median share of box EV",
        "Median dollars per box, at ask"
      ],
      "rows": [
        {
          "Card price band": "Under $1",
          "Median share of box EV": "39.7%",
          "Median dollars per box, at ask": "$53.30"
        },
        {
          "Card price band": "$1 to $4.99",
          "Median share of box EV": "10.2%",
          "Median dollars per box, at ask": "$12.78"
        },
        {
          "Card price band": "$5 to $24.99",
          "Median share of box EV": "17.5%",
          "Median dollars per box, at ask": "$23.61"
        },
        {
          "Card price band": "$25 to $99.99",
          "Median share of box EV": "13.4%",
          "Median dollars per box, at ask": "$19.43"
        },
        {
          "Card price band": "$100 and above",
          "Median share of box EV": "15.2%",
          "Median dollars per box, at ask": "$15.20"
        }
      ]
    },
    {
      "title": "Confidence intervals in the published studies behind our odds",
      "columns": [
        "Era",
        "Sets",
        "Rolled tier rates with a published 95% interval"
      ],
      "rows": [
        {
          "Era": "Scarlet & Violet",
          "Sets": "16",
          "Rolled tier rates with a published 95% interval": "75 of 87"
        },
        {
          "Era": "Mega Evolution",
          "Sets": "6",
          "Rolled tier rates with a published 95% interval": "30 of 30"
        },
        {
          "Era": "Sword & Shield",
          "Sets": "13",
          "Rolled tier rates with a published 95% interval": "7 of 101"
        }
      ]
    }
  ],
  "charts": [],
  "sections": [
    "The stack under the number",
    "Every set, both ways",
    "Which assumption actually moves the answer",
    "Twelve boxes have no error bar at all",
    "What this study cannot show",
    "What would overturn this"
  ],
  "method": [
    "Universe: the 35 sets in SIMULATABLE_SETS in src/server/pack-sim.ts that have resolvable published tier odds in src/content/pack-model.json and non-empty catalog pools, intersected with the sets for which sealed_products holds a Booster Box SKU with a pack count of 36 whose name is exactly \"<set> Booster Box\". That intersection is 27 sets. The exact-name rule matters and is not a formality: Journey Together and Mega Evolution each hold TWO non-lot 36-pack Booster Box SKUs, a standard and an Enhanced, and the rule picks the standard box in both. A rule phrased as \"exactly one such SKU\" would return 25 sets, not 27. Expected value is computed in closed form over buildSlotPlans() and resolveTierOdds() from src/server/pack-sim.ts, unchanged: for each slot, each rolled tier contributes its published per-pack probability times the mean market price of its catalog pool, and the residual probability falls to that slot's default tier through the same defaultSplit the simulator uses. Structural slots (commons, uncommons) contribute their count times the pool mean. Per box is per pack times 36. Card prices are marketPriceByCardId(), the same resolver every card page uses; an unpriced card contributes $0, matching the site's Monte Carlo engine, and the unpriced share is under 1% on every set here. DEDUPLICATION: 1,212 TCGplayer product ids in our catalog are claimed by two card rows each, so any sum over cards that ignores the join key overstates itself. We checked every one of the 35 pools: no pool carries a duplicate card id, and no pool shares a tcg_id internally, because every one of those 1,212 collisions pairs a mainline row with a trainer-kit or foreign-language twin in a different set. Zero rows collapsed here, and the check is in apps/web/scripts/sealed-b5-dedupe.mts. Box prices are read directly from sealed_products on 2026-09-22 rather than through the cached boxprice:v4 resolver, which was found serving one stale figure. Tier counts in the confidence-interval table are ROLLED tiers: those that appear as an outcome in a slot plan AND have at least one card in that set's catalog pool. That excludes 11 Scarlet & Violet ACE SPEC and Hyper Rare rates for sets containing no such cards, and 9 Sword & Shield Radiant rates for sets predating Radiant Pokemon. Study 5 counts resolved rates instead, which is a larger number, and says so. The odds swing moves each tier's published rate by its own 95% half-width, valued as 36 times that half-width times the absolute price gap between that tier's pool mean and its slot's default tier pool mean, combined across tiers in quadrature; tiers whose published rate carries no interval contribute nothing and are reported as \"none published\" rather than zero. The $5 threshold and the 0.85 realisation factor are stated assumptions, not measurements. Medians take the upper-middle value on even samples. Scripts: apps/web/scripts/sealed-b-boxev.mts, sealed-b2-stack.mts, sealed-b3-summary.mts and sealed-b4-reconcile.mts, with every figure and query in apps/web/.scratch-sealed/figures.json."
  ],
  "terms": "Figures are moonstone's own recorded measurements, dated as published. Quote them with the population stated beside them. The article at `url` is the human form of this file."
}