Modelling NFT Projects

NFTs, Networks and Rhinos in Top Hats

Viroshan Naicker
10 min readOct 8, 2021


This year has been really, really interesting in the cryptospace. Apart from the massive growth in decentralised finance, the NFT metaverse has truly opened up and presented a broad spectrum of use cases. NFTs are being used to capture real-world value in many different arenas — from finance to artwork to gaming, and the number of projects in the space continues to expand exponentially. This begs the question, though, what are the hallmarks of a good NFT project? And, how does one model these projects in a sensible way?

Here are some experimental musings…

Trading Cards

The basic conceptual entry point for an NFT is the trading card space. We have a collection of items that are produced in some finite amount. So, trading cards. They have a hierarchy structure — e.g. the most rare and difficult to find cards are at the top of the hierarchy, and therefore have the most value to collectors. And, the cards are produced with hierachy in mind, so that collectors can remain interested until they have got all the rare cards for a particular season — just like it is in the diagram.

The goal of the card supplier is to capture the initial sale (so think Panini cards) and create sale volumes as buyers try to complete their collections through the law of large numbers, and through trading on secondary markets. The buyer’s aim is to create a rare event — a complete collection.

Later as collections are lost, and people lose interest, the value of completed collections (and rare cards) goes up. Similarly, if any one player’s value in the collection goes up the value of the whole collection goes up to — and, if enough time passes, history shows that someone might buy it. It’s just a question of optimal stopping for the holder or their grandchildren who find the cards in an attic somewhere. The buyer and seller are essentially trading the value of the optimal stopping problem again, where the buyer is willing to pay the seller a the current price because they have a higher than current price discounted current value for the collection. OK — maybe the buyer needs fire starters, but they’re paying for utility in that case too.

Embedded Economics

The digital-NFT opportunity is a little bit more interesting because the NFT is also a smart contract, and smart contracts can have embedded rules that allow us to do a variety of interesting things. For example, reward the supplier with value from secondary sales. This is wonderful if you are making art — since artists generally get no value out of resales, and it’s only once the optimal stopping problem has been passed around several times over that the value of the artwork stabilizes. This is good, but the opportunity has changed as the definition of art has changed, and the existence of NFTs has expanded what we mean by artwork. :-)

Generative Artwork

Generative artwork creates a collection by inclusion of traits, and there is some technical combinatorics that one can do in order to model rarity. We can use network graph theory, for example: Each trait is a node in a network, and if two traits can occur together then join the nodes by an edge.

Let’s consider an example. Suppose that we are interested in the Rhino’s in Top Hats collection. There are three Rhino bodies red, yellow and green, and three top hats also red yellow and green. We don’t allow colour clashing, so red rhinos don’t go with red top hats, and the same for green-green and yellow-yellow combinations.

We can draw the network diagram below on the right. There are a total of six different artworks that can be created, and this is just the sum of the number top hats allowed per rhino body. (Generally, the formula is to take the product over the number of each elements in each trait class to get the upper limit on the total possible unique items.)

The basic utility about using networks to understand generative NFTs is the easy visualisation. We can see that there are three groups with that are similar but different — the red, green, and yellow boundary lines. These groups have essentially equal status, and so have roughly equal value. We can start playing around with this way of ascribing value by letting the red hats have a blue trim. Now, we’ve created an elevated status for red hats on any rhino body versus green and yellow hats. And, further, this can be considered quantitatively by assigning weighting values to traits and summing over these values.

A hypergraph or a set system (as they are sometimes called) is a generalisation of a network graph to edges that connect more than two nodes (traits). In most projects, there are usually more than two traits, and the structural representations using networks can be quite intricate. Any particular generative NFT is also a hypergraph on the trait space. The key point is that we can understand the collection dynamics by looking at these structures. For example, if no two NFTs in a collection share common traits, then the hypergraph has no overlapping edges. More generally, if each item in the collection is unique, then the designer is aiming to construct a Sperner family over the set of traits.

Another tool that can be used is the notion of binary inclusion: If there are a total of N-traits, and each trait can either be swtiched on or off, then each artwork corresponds to a binary vector of length N. The set of binary vectors of length N map neatly to the hypercube graph — a cube if N=3 and a tesseract if N=4. Nodes at distance one from each other in the hypercube differ in exactly one position. For generative artwork this model can get more involved too, since one may need to consider tensored spaces of binary vectors (a vector in each trait category) to get the complete model.

Of course, the full machinery of graphs, and more generally hypergraphs becomes available to project designers when one thinks in this way about NFTs. But that’s for a more technical article. The value in these models from a business perspective is that one can consider the collection as a whole, and look at the value drivers and differences. From a coding and artwork perspective, we can use the models themselves to manage the rarity of a given drop according to set theoretic rules — this takes the grunt work out of calculating rarity scores; and adds an element of value distribution/optimisation over the trait space. Then, of course, there is machine learning, price-trait prediction, and a whole host of other things that can be done with a good model.

Business Considerations

Finally, one can’t model, build and deploy without being embedded into a context of project and business. And, this is always the more difficult part. To think this aspect through, I ended up drawing the following diagram. This looks at the different trade-offs in a project (explained below).

  1. Scarcity vs Volume. How many NFTs do we mint in a collection? At high volumes there is a reduction the speculative aspect. On the other hand, if your NFT represents a ticket to a concert, then you need volume (at least to the size of the concert hall) and this is a totally different use case, but still an NFT collection. Memberships are semi-exclusive tickets, and these have been embedded into the sale of various NFT projects too. But they tend to be scarcer, and have an on-going, non-expiring future utility that can be traded.
  2. Speculative vs Expiring Value. Usually the prerequisite for speculation is longevity. It’s pretty difficult to speculate on something that is about to expire, since the value of it is going down. And, the buyer is buying into a pricing profile that eventually hits zero. Tickets on a secondary market could be speculative, it’s true — but only because the market tends to be small and restricted, and gets smaller the closer on gets to the ticketed event.
  3. Rarity vs Similarity. Amongst other items in a collection, a rarer item tends to have more value whereas given a set of identical items each of them has the same value. The basic effect is substitution. Within a single collection, so a collection of cards, for example, rarity plays a big role in value differentiation and this measures the gap between the floor and the ceiling in the secondary markets for items in that collection. We can think of differentiated collections as being ranked, and the price reflecting the markets allocation of rank to the collection — in the same way that token curated registry assigns a ranking. If the collection (or sub-collection) is of undifferentiated items, then there can’t really be a gap between the floor and ceiling. Unless there is price arbitrage between different secondary markets. Without rarity a collection is the same as any set of fungible tokens that don’t expire.
  4. Current vs Future Utility. When you’re airdropped an ape, for example, and you sell it on a secondary market, then you can extract utility from it quite quickly. If you put your ape on your twitter profile, then you are using it too. On the other hand, if you mint a free NFT that you can’t trade, and can use as a pass to a member’s only area that will be launched in a the future, then you are playing the wait-to-use game. Projects often offer combinations of current vs future utility as a value add to entice buyers. From the project perspective — it’s a question of when and how they capture the value of that utility. If you offer too much current utility, and the initial sale is not enough to cover the cost of that utility, then you lose. If you offer future utility and the cost of acquisition is too high, then you also lose. Part of the beauty of NFT design is in the economics and the market design, and this makes things dynamic but also more complicated.

Usually any given project is combination of the characteristics above — and, given a project the idea would be to figure out those axes that characterise the NFT collection, and attempt to make sense of the value drivers. As a test we can give each category a rating from 1–10, and then use that rating to really delve into the actual type of NFT that is being created: SuperRare, for example, is a 1–1 artwork NFT project which would score 10/10 for rarity, scarcity, and speculative value, and low on everything else. Degenerative Apes would have (possibly) a 7/10 for rarity, a 7/10 for speculative value and some current value, some scarcity and some volume. It’s pretty subjective, but my aim is to quantify this better in another post.

Moving on, from a design perspective, the next question is complexity.

Complexity Overheads

The price of all this choice is complexity: In designing NFT projects, this has to be managed somehow. There are some basic layers that structure every NFT project.

Setup. The setup phase where one considers the market context, the niche audience, rarity, scarcity, utility, and meaning. What goes into a given launch, and what are the parameters? Who cares about these NFTs anyway? And, what is the context of the market at the time of the drop?

Customer Layer. The next question is what about the different dynamics and choice points that a market will face when making buying decisions? This determines the economics of the collection which is the next phase, but generally remains hidden from view. Unless you like surveys and private NFT A/B testing beforehand — which I doubt anyone has done to date, but it could be an interesting experiement!

Economy and Signals. This could also be called the observable layer, but it’s all about the tokens linked to the NFT and the floor and ceiling price of the NFT. If you can measure it now or project it into the future, then this layer is where it ought to go in your reasoning process.

Economic Controls. Most current NFT projects don’t have too many built in controls that can be set after the first sale. The usual standard is some kind of percentage royalty but this is often fixed. There are also Harberger tax experiments that have been tried too. It will be interesting to see how this space evolves. Ideas like burn fees — in which some percentage of sales is allocated to buy the floor NFTs and drive the collection value upwards, seem like interesting control strategies. I expect that these will get more intricate as the tokenomics aspect of NFT markets evolves. Currently, there are some interesting rumours around Shiboshis and the dynamics of Shiba Inu which involve the burning of fungible tokens as the NFTs are traded. Let’s see.

So, in conclusion, the road to modelling and valuation is wide open and ideas abound. Feel free to drop me a comment, or find me on LinkedIn if you have questions, or simply press clap until you are bored — don’t worry, it’s that same feeling you get when watching 5 minute candles, but I’ll capture the upside as the writer, and write more things which is good for you, if you’ve read this far.



Viroshan Naicker

Token Engineer | Mathematician