Rarity Leaderboard

[Bezenko]

I'd love more leaderboards, especially a rarity, but please add a completionist one as well!

[Zenodin]

12 minutes ago, imouto38 said:

I like the idea of a rarity leaderboard, but the way it's described sound still way too much abusable IMHO.

 

There is games like Magicka 2 which are full of ultra rare trophies while not being really hard, and on the other hand there is really hard or long games to complete just because of one single trophy.

It would be more fair i think to give points for the rarest trophy obtained in a game, weighted by the completion of the game ...

 

That's where the difference between rarity and difficulty comes into play. A rare trophy is indeed not particularly a difficult trophy. Magicka 2 is indeed a good example. Measuring the rarity of a trophy is possible, while measuring the difficulty of a trophy is not entirely possible ... I could be forgetting something, so do correct me if I'm wrong.

 

A leaderboard that will reward you for hard trophies is something different from what would be a rarity leaderboard.

[PSXtreme_]

If we're going to add the rarity leaderboard, you might as well add the other two PSNTL leaderboards also (Adjusted and Completist).

 

[Sly Ripper]

How's this look? https://psnprofiles.com/leaderboard/rarity

[Stardroid]

2 minutes ago, Sly Ripper said:

How's this look? https://psnprofiles.com/leaderboard/rarity

 

Thank you for all the work you put in. 

[DaivRules]

Wow. The people above and below me have 4 times my number of common trophies, but I have 4 times their number of Ultra Rares. 20,010.81 Points, 99,936 place. Interesting.

[Lucas]

40 minutes ago, DaivRules said:

Wow. The people above and below me have 4 times my number of common trophies, but I have 4 times their number of Ultra Rares. 20,010.81 Points, 99,936 place. Interesting.

Yeah, the guy who's one place above me on the Dutch rarity leaderboard has 6000 more common trophies than me . Nice addition Sly! 

[NathanielJohn]

1 hour ago, Sly Ripper said:

How's this look? https://psnprofiles.com/leaderboard/rarity

 

Looks great! I think it'd look better without the decimal places, but that's just personal preference.

[thegirlruka]

1 hour ago, Sly Ripper said:

How's this look? https://psnprofiles.com/leaderboard/rarity

Would you be able to make it and the other sub-leaderboards searchable?

[Myu]

19 minutes ago, Lucas said:

Yeah, the guy who's one place above me on the Dutch rarity leaderboard has 6000 more common trophies than me . Nice addition Sly! 

 

The guy below me has a lot more UR and VR than me, it's weird.

[Satoshi Ookami]

Glorious o.O

Though, I'm a bit concerned that I'm lower on rarity country leaderboard than normal country leaderboard, better get more URs

[zajac9999]

1 hour ago, Sly Ripper said:

How's this look? https://psnprofiles.com/leaderboard/rarity

 

Seems awesome, could you explain what formula you've used to work out the values? Some people seem oddly high/low and I'm not sure why.

[AlphaTrash]

Nvm, the rarity leaderboard should URs only lmao. It's literally pointless when including everything else. Was so hyped for this too.  

[Bezenko]

Awesome, climbed from 234 up to 53 on the national LB  I really hope common (and uncommon) does not count anything to the score, please share the formula!

 

Also climed nearly 40K posistions on the global LB

Edited April 13, 2017 by Bezenko

[Sly Ripper]

On 4/11/2017 at 0:54 PM, NathanielJohn said:

Points = 1 + (MAX - 1) * ((50/Rarity)^N - 1) / (5000^N - 1)

 

MAX = 500

N = 0.2718281828459

[MMDE]

Went up 3 positions on the national leaderboard!  

Edited April 13, 2017 by MMDE

[dmland12]

Nice addition!  I made a quick calculator on google spreadsheet using the formula listed in case anyone else was interested in seeing how many points certain trophies were getting them on the rarity leaderboard.

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

 

 

[zajac9999]

Would increasing the max value 'stretch' out the numbers to create a bigger difference between values, i.e. 10% and 5%

I like that the scale goes from 0-500, but I find it crazy that a trophy of 0.1% rarity isn't even half of the 'max' possible value. I understand why it's like that, but really it effectively makes the scare from 0-250 as hardly anyone will have more than 1 trophy of under 0.1% rarity. Could increasing the max value to something like 1000 'solve' this issue somewhat. 

 

Of course people may not feel it is an issue lol, but to me it seems to be one.

[NathanielJohn]

3 minutes ago, zajac9999 said:

Would increasing the max value 'stretch' out the numbers to create a bigger difference between values, i.e. 10% and 5%

I like that the scale goes from 0-500, but I find it crazy that a trophy of 0.1% rarity isn't even half of the 'max' possible value. I understand why it's like that, but really it effectively makes the scare from 0-250 as hardly anyone will have more than 1 trophy of under 0.1% rarity. Could increasing the max value to something like 1000 'solve' this issue somewhat. 

 

Of course people may not feel it is an issue lol, but to me it seems to be one.

 

To see how the formula works, see the post where I introduced it here.

 

Short version: Increasing MAX just stretches things as linearly as possible (e.g., increasing MAX to 1000 would then make the scale from 1 - 1000 instead of 1 - 500, but the *relative* point values would remain almost unchanged).

 

On the other hand, N determines how skewed the distribution is. N can be anything between 0 and 1. Values close to 1 result in very steep distributions that reward ultra-rare trophies very heavily, whereas values close to 0 result in flatter distributions that reward middle-of-the-road rarity trophies more heavily.

[Zenodin]

6 minutes ago, zajac9999 said:

...

 

I understand why it's like that, but really it effectively makes the scare from 0-250 as hardly anyone will have more than 1 trophy of under 0.1% rarity.

 

...

 

lol ... I'm 'hardly anyone' ...  

[Undead Wolf]

I love it! I want to focus on getting more difficult platinums, so having a leaderboard that shows the progress I'm making is a welcome addition. Hopefully it will encourage me to go for more.

[zajac9999]

7 minutes ago, NathanielJohn said:

 

To see how the formula works, see the post where I introduced it here.

 

Short version: Increasing MAX just stretches things as linearly as possible (e.g., increasing MAX to 1000 would then make the scale from 1 - 1000 instead of 1 - 500, but the *relative* point values would remain almost unchanged).

 

On the other hand, N determines how skewed the distribution is. N can be anything between 0 and 1. Values close to 1 result in very steep distributions that reward ultra-rare trophies very heavily, whereas values close to 0 result in flatter distributions that reward middle-of-the-road rarity trophies more heavily.

 

My main issue is that for low values of N the middle of the road skew isn't enough I.e. At N=0.2 three 10% trophies are worth as much as a 1%, which I don't feel to be the case. So you'd assume I'd prefer a higher coefficient of N. But when you go higher and reduce that issue the thing becomes far too skewed in the other direction and trophies between 0.1% - 0.01% account for most of the possible points values. 

 

So in short, I'm not sure what the ideal solution is regarding that function lol

10 minutes ago, Zenodin said:

 

lol ... I'm 'hardly anyone' ...  

 

Indeed you are.

[dmland12]

16 minutes ago, NathanielJohn said:

 

To see how the formula works, see the post where I introduced it here.

 

Short version: Increasing MAX just stretches things as linearly as possible (e.g., increasing MAX to 1000 would then make the scale from 1 - 1000 instead of 1 - 500, but the *relative* point values would remain almost unchanged).

 

On the other hand, N determines how skewed the distribution is. N can be anything between 0 and 1. Values close to 1 result in very steep distributions that reward ultra-rare trophies very heavily, whereas values close to 0 result in flatter distributions that reward middle-of-the-road rarity trophies more heavily.

 

We could always go with a steep formula, with a higher MAX, but cap it near the rarest end at 500.  The formula is apparently already capped at 0 at the most common end (otherwise it would produce negative values for very common trophies and it's obviously not doing that since the lowest score anyone has is 1.00).

[NathanielJohn]

19 minutes ago, zajac9999 said:

But when you go higher and reduce that issue the thing becomes far too skewed in the other direction and trophies between 0.1% - 0.01% account for most of the possible points values.

 

Hrm, I guess I just don't see why a 0.01% trophy shouldn't be worth double a 0.1% trophy. You yourself said that a 1% trophy should be worth more than 3 10% trophies. Why should the pattern not continue? A 0.01% trophy should be worth a lot more than a 0.1% trophy, which should be worth a lot more than a 1% trophy, which should be worth a lot more than a 10% trophy (in my opinion).

 

Edit: Maybe instead of coming up with a bunch of formulas and seeing what their table-of-values look like, it would be more productive instead for people to post what they think the table of values should look like, and then we construct a formula that interpolates between those values? For example, I think that the table of values should look something like what I posted at the bottom of this post, which I why I came up with this formula in the first place. What do others think it should look like?

Edited April 13, 2017 by NathanielJohn

[zajac9999]

8 minutes ago, NathanielJohn said:

Hrm, I guess I just don't see why a 0.01% trophy shouldn't be worth double a 0.1% trophy. You yourself said that a 1% trophy should be worth more than 3 10% trophies. Why should the pattern not continue? A 0.01% trophy should be worth a lot more than a 0.1% trophy, which should be worth a lot more than a 1% trophy, which should be worth a lot more than a 10% trophy (in my opinion).

 

I would agree that they should be, but that's the problem for me, which is why I asked about the max initially. If a 0.01 trophy should be worth a lot more than a 0.1% trophy (it is currently, 500 against 242) then I'd expect other comparisons of value to wield similar results, but at the moment they don't. For example I'd expect 0.5% to be worth approximately double a 1% but at the moment it's 137 for 0.5% and 104 for 1% likewise I'd expect a 1% to be worth much more than a 2% but again it's not.

 

Due to this it ends up being too heavily weighted in the favour of getting trophies 0.1% or less, after about 3% rarity it barely matters if it's 3% or 10% etc as the points difference is miniscule. Since hardly anyone has many trophies that are in the 0.01% - 0.5% region the guys who have loads of trophies which are middle of the road, are ending up in front on the leaderboards because no one is getting many of the really high points values. 

 

https://gyazo.com/dea35d3d0467c7b0e55575a57b04a3d3 - as a random example of what I feel shouldn't be happening in the leaderboards but is. 

 

Hopefully I'm made my point clear, it's kinda hard to explain lol.