Damn Bears and Bearity

Hello there, we are the Damn Bears team. And in our first article we wanna tell you about our attributes distribution system we worked hard for.

Bearity. Bearity is kinda like rarity but it is not. We’ll try to clear it all step by step. Each bear is guaranteed to have 5 attributes (properties): Fur, Body, Face, Head, Item. With a total amount of 500+ hand-drawn attributes, there are 2.5+ billion possible combinations. Only 10k of them will be represented in the collection.

Each attribute belongs to one of three buckets. Depending on which bucket the attribute is in, it’s awarded from 1 to 3 points. But there’s a nuance with the Item attribute: 1 point here means a bear’s got no Item, just a regular hand and nothing in it.

So the minimal and maximum sum of total points for a bear is:

The total points sum is the Bearity.

The next thing we want to talk about is the distribution of attributes.

Many collections are built the way when the overwhelming majority are the simplest and usually less valuable NFTs and then the value grows along with the increase in the rarity of any attribute, not always in direct proportion though.

We were faced with the task of finding a middle ground: on the one hand, we want rare bears with rare attributes to stay really rare, and on the other hand, we don’t want most of the collection to be full of bears with the very base attributes.

To find the key we analyzed not only new successful collections but also turned to the origins. On the official site you can see the attributes distribution stats for Cryptopunks:

Most punks have 2, 3 or 4 attributes. With a maximum of 7 attributes, those numbers are pretty average. And if we take a look at the Cryptopunks price we can see that the floor price for punk with 0 attributes is much higher than the floor price for punks with 2, 3 or 4 attributes. Yes, of course, the rarity of attributes affects price too, but we believe you’ve got the direction of our idea.

But all the bears have got a constant attribute quantity. So the point was to get the Bearity distribution graph close enough to the Gaussian curve and to get some (albeit small) number of bears with a maximum Bearity rate — 15. Having written a probability calculator, we began to balance the probability for each class of each attribute.

Setting each class probability to 33.33% was obvious but not the best idea, it became clear almost immediately. Why? In this case we would get about 67% of bears with items, which is way too far from our plans and expectations. The Item attribute was conceived as something rare that would make the bear stand out and add more character and expressiveness to it, perhaps even tell a story. And to tell you the truth, with all due respect to old man Gauss, we still wanted the left side of the graph to be a little “heavier” than the right one.

Bearity distribution graph

Ok, what we’ve got now. We have a graph of Bearity distribution for the entire collection. We do not focus on numbers, but show the percentage, because the final figures may differ slightly from those that the calculator gives us.

The vast majority of bears will have average Bearity scores. That means those bears will have at least a couple of uncommon attributes. The chance of a bear with a very high Bearity is still relatively low, but it is almost equal for Bearity 6 and 12, for example. Also, it’s important to note that Bearity 5 (the lowest) is the third rarest one. We are sure that it will have its own charm. Remember, every pawn can become a queen.

In the Opensea interface all the bears will have an indication of the level of each attribute they have and total Bearity to make sorting more convenient. Plus, it looks cool and can still come in handy. Each Bearity value will have its own background color. There are also Sets — the Bears who have complete sets of characters’ traits. Sets can include from 2 to 4 matching attributes. Sets will have special backgrounds regardless of Bearity.

New details and interesting news coming soon, stay tuned. Don’t forget to follow us on Twitter.



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