Implementing ARS in RF season 3

Proposals by Gotchi Gov'nuhs
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Hello frens! We have heard for many moons about the concept of ARS, or Absolute Rarity Score. This has led to rampant speculation by the community as to how this will impact future rarity farming seasons (where my low BRS crowd at??). If you’re not familiar with the concept, I highly suggest you check out the description on the wiki: https://wiki.aavegotchi.com/en/rarity-farming.

Absolute Rarity Score (ARS) is derived from the particular rarity of the Aavegotchi’s traits in the overall Aavegotchi ecosystem. For example, if a lot of players have trained their Aavegotchis to have highest Energy Level, then the ARS for high Energy Level - TURNT would be lower than that of lowest Energy Level - WASTED. ARS is calculated in terms of percentiles out of 100 for each of the Aavegotchi traits. So if 5% of all Aavegotchis possess a WASTED trait for example, then the WASTED trait will contribute to a total score of 95 to the Aavegotchi’s energy trait ARS.

The wiki clarifies that " The formula for ARS is not determined yet. As a result, the values in the ARS column in the above table are imaginary." Coderdan has previously suggested that if the community wants ARS implemented, we should submit the details for a Coreprop. Taking the hypothetical provided by Pixelcraft in the wiki and making some modifications, I suggest the following.

I propose that ARS be added in as a feature for rarity farming season 3. I know we just started season 2, but there are many details to be fleshed out and we need to give pixelcraft sufficient lead time to implement this without delaying other priority project. I am proposing that ARS can contribute a total theoretical additional 300 points to an aavegotchi’s BRS (the numbers laid out in the wiki imply that ARS could theoretically equal 600, which is the same as total BRS. This seems too high to me). For each trait of an Aavegotchi, at the time of the rarity farming snapshot a calculation will be made to determine what percentage of all Aavegotchis possess that trait. For each trait, I’m proposing that we have 10 tiers, rather than the 8 proposed by Pixelcraft, with the addition of a “Godlike” tier for traits that are greater than 99 or less than 0. Some gotchis have traits that are uniquely above/below mythical status, and should be recognized as such. So there will be Godlike Low, Mythical Low, Rare Low, Uncommon Low, Common Low, Common High, Uncommon High, Rare High, Mythical High, Godlike High. Based on the percentage of gotchis with that trait, the aavegotchi can be awarded a potential total of 50 points for that trait (6 traits * 50 points = 300 total possible points). So if a gotchi has -1 Aggression (Godlike low), and 1% of all gotchis have Godlike Low aggression, then the Aavegotchi is in the 99th percentile and would be awarded 49 points for his aggression. Lets look at an example (using made up numbers).

Tommy Gotchi

  • NRG: common high - 76% of gotchis have this (24th percentile) => 12 points
  • AGG: uncommon high - 55% of gotchis have this (44th percentile) => 22 points
  • SPK: godlike high - 2% of gotchis have this (98th percentile) => 49 points
  • BRN: rare high - 25% of gotchis have this (75th percentile) => 37 points
  • EYEC: mythical low - 12% of gotchis have this (88th percentile) => 44 points
  • EYES: uncommon low - 60% of gotchis have this (40th percentile) => 20 points

For each of the above, I’ve multiplied the percentile the trait is in by 50. So this gotchi would receive a total ARS score of 184 (12+22+49+37+44+20), which would be added to his Base Rarity Score to get his final rarity score.

The biggest question I see for community discussion is whether ARS should be based on the gotchi’s naked rarity score (his/her BRS), or based on that score in addition to the wearables equipped (the “modified base rarity score”)? In other words, should leveling up with XP be the only way to increase a gotchi’s ARS, or should the wearables also count?

My suggestion is that we use the modified rarity score. This will further reward players who skillfully select wearables that enhance their gotchis traits, rather than work against them, but I’d love to hear the community’s thoughts on that.

Any other pressing details we need to firm up?

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I’m a fan. Personally leaning more toward modified rarity score over naked score since as you mention it lets you skilfully change ARS with fitting wearable strategy. There’s already two stat categories in any case that can’t be modified by equipment and will still carry weight in the “naked luck” of a generated gotchi. Thanks for writing this up. Excellent choice on the example gotchi, too. Pajama hats off!

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Thank you for writing this up. I believe it aligns very well with Pixelcraft vision, plus matching what has been on Wiki for community to see and expect for a vey long time now.

I feel it’s a no-brainer that it includes wearables- as they are a key part/driver of our cyclical economy, utility for wearables going up- is constructive all across the ecosystem.

The only thing I do not like about your proposal is to multiply by 50- this is effectively half the effect from what is on wiki- why halve it? The testing I did awhile back did not shuffle the leaderboard much with full effect (if u multiple by 100 in your model)- so halving the effect could make ARS less inspiring or consequential for the overall lore than if executing the original Pixelcraft vision.

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I’m fine going with a total potential score of 600 (multiply each trait percentile by 100). I just wasn’t sure where this number came from and seemed high to me – under this approach ARS would be the same size as BRS

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Looks like modeling time!
We have so many awesome statisticians and modelers in the community… hopefully one jumps on board of thread to help us out to compare the effects of 50 vs 100 and other details perhaps.

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One reason to use 50 is that it is consistent with the points provided by a godlike wearable. Having a godlike wearable gives you a 50 BRS bonus, and having a godlike trait would presumably give you roughly 50 points (since you’d be in the 99th percentile)

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I think this is interesting cause most people don’t claim gotchi’s that have average traits, but rather go for those mythical traits, but since everyone has been doing that, those traits have become more common than the average trait gotchis as shown by this trait distribution below.

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After hearing the balancing of what traits will do in the realm also brings into consideration that an average gotchi that has traits around 50 might actually be better because they are more balanced. For example, a high NRG gotchi may have more speed in the realm but has limited Alchemica carrying capacity, while a gotchi with low NRG has the opposite, so a gotchi with NRG around 50 might be more preferable when it comes time to gather yield in the realm.

Not sure how this would translate to what you guys are talking about, but probably should be considered as the amount of high BRS gotchi’s have, in reality, become the most common gotchi’s. By the distribution shown above the most scares gotchi’s have actually become the ones who possess traits between 40-60, but this has no consideration when it comes to rarity farming. So I do think implementing ARS would potentially help balance the ecosystem.

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This is a common misconception when discussing ARS, both from the exact wiki implementation as well as @Bearded 's proposed variation. The common traits only appear less when you look at them at an individual number basis, which is not the way ARS would be implemented. For ex, ALL common NRG traits would get the exact same ARS score, i.e. every number between 25-74. This means that even tho mythical traits are much more likely to be selected, since they are only 4% of the possible trait numbers versus 50% for commons, mythical ranges would get a much higher ARS score.

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Would it be worth including collateral type in ARS? Feels like a pretty visible difference between gotchis and adds some interesting dynamics in gotchi value between haunts with exclusive collaterals.

I think modified rarity score (after sets even) is the correct way to evaluate traits:

  1. We already have two immutable traits.
  2. We don’t want to devalue wearables. Wearables become pretty homogenous if we don’t include them in ARS. Why do I care which godlike wearable I have? I’ll get at least 44 BRS from it regardless.

I’m not sure how I feel about godlike traits. Let’s say godlike is less than 0 and greater than 99. We might find that mythical traits end up being a bit rarer (except for eyes) since their range is so small. We’d need to do some thorough analysis (from both a statistical and game theory perspective) to ensure we aren’t unbalancing things here.
New traits below 0 and above 99 should be a separate proposal in my opinion. I’d almost rather see a different system entirely for “extreme” traits.

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agree

tend to agree here. Depends on what consensus shapes up to be- but if new GL traits ends up being a complication or unpopular feature of the proposal- I prefer dropping that while moving forward with the other elements of ARS.

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This is a good point regarding overvaluing mythics. The counterpoint though is that if we don’t separate out mythics and godlikes then THAT may be too big a range for mythics because they including everything from 98+ or 1-, and then folks will get punished for maximizing their gotchis. I think we just need more data. Anyone able to run an analysis of what percentages we are looking at ?

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I love the idea of including collateral in ARS, would make a very interesting dynamic.

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I’m very interested in getting ARS implemented but am curious about how the new gameplay or meta strategies will work in practice.

Can the concept of ARS be expressed in terms of what new kinds of choices a player might make once implemented?

ex: One will choose a 90/92/90/92/90/92 over a 91/91/91/91/91/91? or the opposite choice?

or: One will choose to use wearable to get take my 94/94/70/70/0/0 to 94/94/75/75/0/0 instead of 99/99/70/70/0/0? or the opposite choice?

And what information might be required to make those choices? How would one know the better outcome of the above situation while interacting with the portal or wearable?

One might need to see data about how rare each category range currently is.

And where that information might need to come from?

Would the absolute rarity be displayed in the UI of the portal? Of the gotchi page? Of the dressing room? or on a third party tool? I wouldn’t want this to be too frustrating or obscure.

In practice, are any of these choices different than current strategies around base and wearble scores?

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Some quick and dirty charts. I ran some quick numbers from the subgraph to see what the distribution is like if we use “naked” gotchi score vs. equipped, and if we combine Myth/godlike, or have them separate. The Y axes represent the percentage of gotchis with that trait range:

This first set of charts shows the distribution of traits including equipped wearables and set bonuses. The top chart accounts for godlikes (>99 or <0) separately, and the bottom chart lumps godlike and myth together:

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Apparently I can only put one media file in a post. to be continued…

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The second set of charts shows the same thing, but looks only at the “naked” traits of the gotchis, and doesn’t take into account the wearables:

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I think this is a really cool idea, I would second 001’s points around the information that needs to be displayed/available to the user to make decisions, it would be unfortunate if someone bought a new wearable which boosted their BRS but negatively impacted their ARS and as a result didn’t see much improvement on their overall score.

Is the overall goal here to make the mechanics more interesting/challenging to get up ontop of the leaderboard? Or to balance things out for users who don’t have high naturally high BRS gotchis? I only ask as an observation with some of the new people joining is that the whole BRS, wearables, XP, Kinship, land is already a pretty steep learning curve (especially when compared with many other NFT projects), if you add the ARS to the equation it could start to be overwhelming to a newcomer.

I would 1,000% support the idea in future (post H3, maybe when more laands open up) to add some variety but just making the comment here that we don’t want it to be too complicated for newcomers. That being said the wiki’s, guides and Discord support in Aavegotchi is second to none so if anyone is going to get it right and make it clear for new users it will be this project.

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Looking at the charts I included above, raising BRS should never harm your ARS score, since the ARS distributions match the trait curves — eg, rare is a higher score than uncommon for both BRS and ARS, legendary is a higher score than rare for both BRS and ARS, etc etc. So I don’t think anyone will ever feel rugged after buying a wearable.

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That makes sense.

Are you leaning towards having Mythical/Godlike together or separate?
Seems interesting if they are seperate that a lower BRS gotchi that had a single trait that was low/high could try to stack the stat and get a nice ARS boost.

Will also be interesting if BRS has effects in the reaalm other than particular stats giving you certain strengths/weaknesses and how any ARS changes would effect those mechanics, if any exist.

Just reiterating my point that we don’t want it to be confusing or overwhelming for new users to onboard but I’m sure that is in all of your minds as well. As long as the change comes with a clear guide (which has been produced for everything else so far) it should be ok. It’s also a great example of an active DAO helping shape the project.

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I have created a separate discussion thread for introducing godlike trait tiers. I think this discussion will be more productive if we stick to strictly ARS discussions within the current parameters of the game.

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It appears (discussed in Discord) that this thread is intending to propose ARS with the introduction of a godlike tier as a packaged deal. I cannot delete my other topic but we can continue discussion here.