Rarity Weighting

[N1NJ4_V4MP1R3]

It's not necessarily commonplace knowledge but a lot of us are aware of the rarity leaderboard on the website: 

https://psnprofiles.com/leaderboard/rarity

 

I'm wondering however, how exactly rarity is calculated for this leaderboard? It's not as simple as I suspected, as raw numbers don't tell the story, see my position in the leaderboard relative to the person above me, who has less trophies in all categories of rarity:

 

[pot1414]

I don't know the formula but it is clear that it takes into consideration the specific rarity of a trophy. So for example a trophy with 1% would be more valuable than a trophy with 3% even though they are both ultra rare. It would be interesting if Sly or a staff member who knows the formula told us. Simply out of curiosity.

Edited September 14, 2021 by pot1414

[xZoneHunter]

https://forum.psnprofiles.com/topic/46506-rarity-leaderboard/?do=findComment&comment=1286879 is probably the formula used, but who knows.

 

I wouldn't pay much mind to this leaderboard. As it's not maintained as the main one and generally considered broken or unofficial.

[dmland12]

The short answer is that it's broken as it currently stands.

 

The long answer is that the formula used is this:

POINTS = 1+(500-1)*((50/RARITY)^0.2718281828459-1)/(5000^0.2718281828459-1)

 

I made a google spreadsheet of it back when it was first implemented if you want to play around with the numbers and see what different rarities are supposed to be worth:

https://docs.google.com/spreadsheets/d/1FQjiwTgI8e3W9ABRSUl92LjSRZXj8xQGHkT3v35n07U/edit?usp=sharing

 

But, that's not all, because it's clear from watching that leaderboard over a few years that it just isn't counting trophies from some games at all.  Additionally, it seems impossible to ever lose points, so if you do manage to get points added to the leaderboard, but the trophies lose value (or you even hide your entire profile), you'll at worst stay with the total points that you have.  (The current #1 has hidden their entire profile for example.)  Some combination of this is likely why you're seeing the difference you're seeing.