With an Examination of the Odds for the Legendary Exclusive 1-of-1 70th Anniversary Collectible
ToppsMLB Series 1 Sale Recap
The ToppsMLB Series 1 sale on April 20 was the biggest sale Topps has conducted on the WAX Blockchain to date. The sale brought a record number of buyers and sold out very quickly.
- A total of 1,384,050 NFTs in 79,090 packs were sold
- 74,090 total available packs sold out within 1 hour
- 137,291 buyers showed up to participate in the sale
- Standard Packs: $5 to $67 = 1240% above primary market price
- Premium Packs: $100 to $682 = 582% above primary market price
- Mike Trout Mint #1, Legendary Exclusive collectible sold for $87,672 in the secondary market just 3 days after the primary sale
- 10K lucky people received an exclusive Opening Day Pack
- WAX now ranks #2 on Blocktivity for most active blockchains
There were also a few sale lowlights:
- Delays in payments being processed due to the record number of people attempting to buy packs
- The sale website (toppsmlb.com) had delays for the same reason
- The 25 limited quantity Legendary Exclusive 1-of-1 70th Anniversary Facsimile Signature Collectibles were claimed much faster (after 2,500 packs were opened) than many people expected. We examine this situation below.
Questions Regarding the Odds for the Legendary Exclusive 1-of-1 70th Anniversary Facsimile Signature Collectible (25 limit supply)
There have been questions about how quickly the 25 Legendary Exclusive 1-of-1 70th Anniversary Collectibles were claimed. All 25 of these collectibles were drawn when 2,500 premium packs had been opened. Some have suggested that the odds must have been incorrect for that outcome to have occurred since there were 24,090 premier packs. This view presupposes that the 25 Legendary Exclusive 1-of-1 70th Anniversary Collectibles should have been drawn once every 963 packs (24,090 / 25 = 963 rounded). But based on the ToppsMLB unbox.nft smart contract odds, and the limited quantity of 25 of these collectibles, that is not the case. In fact, per the odds that Topps assigned to the unbox.nft smart contract configuration, all 25 collectibles should have been claimed when 2,500 packs were opened. Which is exactly what happened. That is because the odds of drawing a Legendary Exclusive 1-of-1 70th Anniversary Collectible, per their smart contract configuration, was 1 out of every 100 premier packs opened (i.e. a frequency of 1 out of every 4,500 collectibles since each premier pack has 45 collectibles).
The Legendary Exclusive 1-of-1 70th Anniversary Collectible odds can also be expressed as the numerical value 0.02% (rounded; 0.02̅2̅% unrounded), which when combined with the 0.02% odds of the other Legendary Exclusive Collectible that was offered in MLB Series 1 (i.e. the 1986 Anniversary Collectible) equals the 0.04% (rounded; 0.04̅4̅% unrounded) odds that Topps published for the Legendary Exclusive Collectibles category on the toppsmlb.com website (see Topps MLB Shop image below).
If the Odds Were Correct, Why Were All 25 Collectibles Claimed When Just 2,500 Packs (out of 24,090) Had Been Opened?
So why are some people questioning the Legendary Exclusive 1-of-1 70th Anniversary Collectible odds? Didn’t the odds per the ToppsMLB unbox.nft smart contract work as they were supposed to? Yes, they did. But some people had a different expectation for the frequency in which these 25 collectibles would be drawn. They expected that the 25 Legendary Exclusive 1-of-1 70th Anniversary Collectibles would be distributed across the entire base of 24,090 packs, not just the first 2,500 packs opened. This outcome is plainly inconsistent with the 0.02̅2̅% (rounded) smart contract odds, and the quantity limit of 25 collectibles, but we think we understand why some people had this expectation.
While the publicly viewable (on the WAX blockchain) unbox.nft smart contract odds for the Legendary Exclusive 1-of-1 70th Anniversary Collectible worked properly, there were 2 factors that made things confusing. First, the limit of 25 of these collectibles meant that the ToppsMLB unbox.nft smart contract odds of 0.02̅2̅% (rounded) only applied so long as quantities remained. But given the 1 out of every 100 pack odds of receiving a Legendary Exclusive 1-of-1 70th Anniversary Collectible, all 25 collectibles were drawn after 2,500 packs were opened. At that point, the published odds no longer mattered because those odds only applied while supply remained. This leads us to the second factor that confused things for some people. Topps published the combined odds of the Legendary Exclusive 1-of-1 70th Anniversary Collectible — 0.02̅2̅% (rounded) — with the odds of the Legendary Exclusive Anniversary Collectible — also 0.02̅2̅% (rounded). Combining these 2 odds into one summary level category, Legendary Exclusive Collectibles — 0.04̅4̅% (rounded) — meant people could not easily determine the odds of just getting a Legendary Exclusive 1-of-1 70th Anniversary Collectible. And while this information is publicly viewable to everyone on the WAX blockchain, clearly many people did not inspect the Topps MLB unbox.nft smart contract configuration to see it.
The table below illustrates the odds for all collectible categories for the Topps MLB Series 1 sale.
TABLE — ToppsMLB Series 1 Collectible Categories and Odds
Odds in Unbox.nft Smart Contract Configuration Vs Odds Published on Toppsmlb.com
There are few things we would like to highlight here. Note the two columns that contain odds information. The column labeled Pack Odds Per The ToppsMLB smart contract lists the odds for each of the 7 collectible categories in the MLB Series 1 sale as reflected in the ToppsMLB unbox.nft smart contract configuration. The column labeled Pack Odds Per The ToppsMLB Website lists the MLB Series 1 odds that were published on toppsmlb.com. We should mention that the Topps unbox.nft smart contract configuration uses a weight based system for expressing odds. The odds published on the toppsmlb.com website are expressed in percentages. But the important point here is that the weights and the percentages are mathematically equivalent. In other words, the odds that Topps published on its website are the same odds programmed into their unbox.nft smart contract configuration, with one caveat.
The one caveat is that in a few instances Topps grouped multiple collectible types together and published the cumulative odds as one collectible category on toppsmlb.com. They did this for Common Collectibles and for Legendary Exclusive Collectibles. For example, the published odds for Common Collectibles of 59.4% is the sum of the odds of Common Collectibles, Epic Base Common Collectible and Legendary Exclusive Base Common Collectible.
The odds for Legendary Exclusive Collectibles of 0.40% (rounded; 0.044% unrounded) is the sum of the odds for the quantity-limited Legendary Exclusive 1-of-1 70th Anniversary Collectibles and the non-quantity-limited Legendary Exclusive 1986 Anniversary Collectible. In hindsight, publishing the cumulative odds for a quantity-limited collectible and a non-quantity limited collectible was probably not a good idea. We want to state again, however, that the odds per the ToppsMLB unbox.nft smart contract configuration are mathematically the same as the odds published on the toppsmlb.com website. The only quibble we would make is that it might have been helpful if Topps had broken out the specific odds for the limited quantity Legendary Exclusive 1-of-1 70th Anniversary Collectibles and noted that these odds only applied for the first 2,500 premier packs opened, after which there would be no more supply. We also believe it would have been helpful if Topps had expressed the odds not just in percentage terms but also in other intuitively simple ways such as the statistically expected per pack frequency of a collectible. For example, the odds for the Legendary Exclusive 1-of-1 70th Anniversary Collectible could have been separately broken out and expressed as:
Alternative Ways the Legendary Exclusive 1-of-1 70th Anniversary Collectible Odds Could Have Been Expressed
- 0.022% (i.e. 0.01 occurrences every 45 collectibles), or;
- 1 out of every 4,500 collectibles (i.e. 45 collectibles per pack / 0.01 occurrences per pack = 4,500), or;
- 1 out of every 100 packs (i.e. 4,500 collectibles per occurrence / 45 collectibles per pack = 100 packs), or;
- “While supplies last! Given the stipulated odds and the limited supply, all 25 Legendary Exclusive 1-of-1 70th Anniversary Collectibles will be drawn within the first 2,500 pack openings.”
More Intuitive Odds Disclosure Going Forward
What can be done in the future to prevent this type of misperception in the odds from happening? Going forward, when WAX is directly involved in a sale and when WAX controls the website where the sale is occurring, we will generate a copy of the unbox.nft smart contract configuration odds for each collectible category type being sold. We will then publish those figures on the NFT sale website. The whole idea of smart contracts on a public blockchain is that they can be inspected by anyone. But until that becomes a more common practice, WAX will publish the unbox.nft smart contract odds configuration and compute the statistically expected per pack frequency an NFT collectible type should be drawn.
What Factor Did Pre-Minting Play, If Any?
The ToppsMLB Series 1 collectibles were pre-minted. This allowed mint numbers to be randomized across all packs, a popular request that Topps implemented for the MLB sale. However, the pre-minted collectibles were not assigned to packs prior to opening them. The odds in the unbox.nft smart contract determined that outcome. If collectibles were assigned to packs prior to opening them, the transparency afforded by the blockchain would make the collectibles visible before the packs were opened, completely removing the mystery of the pack opening experience. Pre-minting collectibles worked as designed and played no part in the Legendary Exclusive 1-of-1s all being drawn in the first 2,500 packs that were opened. That occurred, as explained above because that is how the odds were set.
The Value of a Publicly Viewable Blockchain When Questions Arise
Lastly, we would be remiss if we didn’t mention the great benefit a blockchain provides in quickly revealing whether there is any discrepancy in the reported vs actual odds of a sale. If Topps had conducted the MLB Series 1 sale with traditional digital items, or with physical cards, or on Flow, there would have been no way for the community to reliably ascertain what actually happened. The WAX public blockchain made that simple. This is why collectors are far better off participating in a sale conducted on a public blockchain like WAX.