A box whose stated average is not what you can realise
A hypothetical $100 box publishes odds that sum to 1. The seller's average is $97. What is left after a 70% sell-back, and why are those different numbers?
These figures are assumed, not a recorded product. Recorded boxes, when any exist, live under boxes and packs.
Inputs
| Input | Value | Unit |
|---|---|---|
| Purchase price | 100 | USD |
| Draws per purchase | 1 | draws |
| Sell-back rate | 70 | % |
Odds table
| Outcome | Probability | Stated value | Independent price |
|---|---|---|---|
| Top item | 0.01 | $2500 | $2000 |
| Middle item | 0.09 | $200 | $150 |
| Common item | 0.90 | $60 | $40 |
Working
- These figures are assumed, not a recorded product. The odds sum to 1: 1% + 9% + 90%.
- The seller's average uses the catalogue prices: 0.01 × $2,500 + 0.09 × $200 + 0.90 × $60 = $25 + $18 + $54 = $97.
- Prices observed elsewhere are lower: 0.01 × $2,000 + 0.09 × $150 + 0.90 × $40 = $20 + $13.50 + $36 = $69.50. That is the market expected value, before anyone tries to turn the item into money.
- A 70% sell-back applies to those observed prices, not to the catalogue: $1,400, $105 and $28. The realisable average is 0.01 × $1,400 + 0.09 × $105 + 0.90 × $28 = $14 + $9.45 + $25.20 = $48.65.
- Against a $100 price that is a 51.35% implied margin. Thirty percent of the observable value disappeared in the sell-back step alone — 1 − ($48.65 ÷ $69.50) = 30%.
Result
| Output | Value |
|---|---|
| Status | ok |
| Seller's expected value | $97.00 |
| Market expected value | $69.50 |
| Realisable expected value | $48.65 |
| Implied margin | 51.35% |
| Cash-out friction | 30% |
Takeaway
The seller's average, the observed average, and the realisable average are three different numbers. The gap between the first and the third is the one a purchase actually faces, and it is never printed on the product.
The formula behind it
M = Σ pᵢ (disclosed probability mass; the model refuses unless M = 1)
EV_declared = d × Σ (pᵢ × vᵢ)
EV_market = d × Σ (pᵢ × mᵢ)
realisableᵢ = max(0, mᵢ × b − s ÷ d)
EV_liquid = d × Σ (pᵢ × realisableᵢ)
Implied margin = (P − EV_liquid) ÷ P
Cash-out friction = 1 − (EV_liquid ÷ EV_market)
P(down) = Σ pᵢ over outcomes where realisableᵢ < P ÷ d
E[shortfall] = Σ pᵢ × ((P ÷ d) − realisableᵢ) ÷ P(down), over those same outcomes
Assumptions
- The published odds are the odds. The model checks that they sum to 1 and refuses otherwise, but it cannot check that a published table describes the draw that actually runs.
- Draws within one purchase are independent and identically distributed, which is what makes a per-draw figure meaningful. Where a seller guarantees one item of a given tier per purchase, that is not true and the per-draw figures do not apply.
- An independently observed value is a price someone else recorded for the same item, not an appraisal. Its venue, its basis and the day it was observed are published beside it.
- The sell-back rate and the cost of delivery are the ones the seller states. Where either is unstated it is left out and the figure it would have affected is not reported.
Limitations
- No expected value is produced from an incomplete odds table. Missing probability mass does not make a figure slightly uncertain; if the missing mass holds the largest outcome it decides the answer, so no figure is published at all.
- No expected value is produced from declared values alone where independent prices are missing. A catalogue price set by the seller is not a market, and averaging it would restate the seller’s claim as a finding.
- The downside figures describe one draw against the per-draw price. The chance that a whole multi-draw purchase loses money is a different question and is not answered here.
- An observed resale price is a record of past transactions at one venue. It is not a price anyone is obliged to pay, and a thin market can move a long way between observations.
- Nothing here models the time, effort, or minimum thresholds involved in selling an item, beyond the stated sell-back rate and cost of delivery.
- This is an average over the whole distribution. A single purchase is one draw from it, and for a box with a heavy top prize most purchases finish well below the average.
This is a theoretical calculation, not a prediction. It describes an average over a very large number of repetitions and says nothing about what will happen in any particular session.
Run these numbers yourself · All worked examples · Methodology