Rarity Leaderboard

[Han_the_Dragon]

After seeing the data that was posted on the previous page,  I kind of like it. 

 

TheYuriG          1014621  
Han_the_Dragon    1009478

 

I find the bit of data above quite funny,  since I have 3x as many trophies as @TheYuriG as well as a few more UR trophies and more than double the VR, but at the same time I know fully well that he has way more sub-1% trophies than me, ending up essentially even our place in the leaderboard. Yes, now I could complain that it is a bit to steep towards the value of sub-1% trophies, and ask to value more the trophies up to 2%, but that wouldn't change much for me, and I know fully well how hard it is to go for those sub-1% plats (that's why I avoid them most of the time ?)

 

Still, I wonder where I would end up in the Portuguese leaderboard, since I was #3 on the previous version...

[JoesusHCrust]

13 minutes ago, Han_the_Dragon said:

After seeing the data that was posted on the previous page,  I kind of like it. 

 

TheYuriG          1014621  
Han_the_Dragon    1009478

 

I find the bit of data above quite funny,  since I have 3x as many trophies as @TheYuriG as well as a few more UR trophies and more than double the VR, but at the same time I know fully well that he has way more sub-1% trophies than me, ending up essentially even our place in the leaderboard. Yes, now I could complain that it is a bit to steep towards the value of sub-1% trophies, and ask to value more the trophies up to 2%, but that wouldn't change much for me, and I know fully well how hard it is to go for those sub-1% plats (that's why I avoid them most of the time )

 

Still, I wonder where I would end up in the Portuguese leaderboard, since I was #3 on the previous version...

Yes, that is a bit odd. You have 10,000 more trophies than him, and 60 more UR's! 

[Han_the_Dragon]

24 minutes ago, JoesusHCrust said:

Yes, that is a bit odd. You have 10,000 more trophies than him, and 60 more UR's! 

Yes, but I have 15 UR under 1%, he has over 80 UR under 1%. On top of that, he probably has more trophies under 2-3% than me too, since about half of my URs are likely above 3% (didn't checked).

 

And you can subtract about 5k of my trophies, while subtracting only 1k from his (our common trophies). If looking at raw numbers. It's more like I have over 6k trophies than him, not 10k. And I have a lot of Uncommon ones too, so, comparing total trophy count between both it's a bit pointless with the current point values.

 

Still, as I pointed out on my post, I'm fully aware of what we are trying to achieve here, and the comparation on both profiles ending with a similar score is proof that the equation works quite well to favor the sub-1% above everything else (I didn't went to see what's more prevalent in the UR section of both profiles, so, I assume that's me having a lot of trophies in the high UR range, while TheYuriG as more trophies in the lower UR range).

 

I will not complain about it, I was mainly pointing out that this equation does work for what I assume it's being the final target (at my eyes it seems like it may be overvaluing sub-1% to a little extent when compared to 1-2% range, but I may as well be totally wrong in what I'm saying..).

 

Edited March 26, 2021 by Han_the_Dragon

[grimydawg___]

36 minutes ago, JoesusHCrust said:

Yes, that is a bit odd. You have 10,000 more trophies than him, and 60 more UR's! 

Not odd really.  It's simply the type of trophies folks are getting.  That's all.

[scemopagliaccioh]

Interesting, the person closest to me, AJ_Radio has like more than 100 plats than me  but we're pretty close. I might even throw my hat in this UR hunting, if the Leaderboard is approved, it's  motivating.

[Atoya]

27 minutes ago, scemopagliaccioh said:

Interesting, the person closest to me, AJ_Radio has like more than 100 plats than me  but we're pretty close. I might even throw my hat in this UR hunting, if the Leaderboard is approved, it's  motivating.

My dude this is a rarity leaderboard the plat difference is irrelevant, it’s the rare trophies that do matter, ikemenzi has like 2018 plats more than me and I am still above him

Edited March 26, 2021 by Atoya

[scemopagliaccioh]

1 hour ago, Atoya said:

My dude this is a rarity leaderboard the plat difference is irrelevant, it’s the rare trophies that do matter, ikemenzi has like 2018 plats more than me and I am still above him

?

That is exactly my point, if you look at previous messages, you'll  see me commenting on MMDE's draft in the first place.

I'm perfectly aware of what "rare" means, I was contemplating, after we got the numbers on all trophies an individualon how it makes things completely  different, than the standard Leaderboard.

[MMDE]

6 hours ago, Atoya said:

My dude this is a rarity leaderboard the plat difference is irrelevant, it’s the rare trophies that do matter, ikemenzi has like 2018 plats more than me and I am still above him

 

4 hours ago, scemopagliaccioh said:

That is exactly my point, if you look at previous messages, you'll  see me commenting on MMDE's draft in the first place.

I'm perfectly aware of what "rare" means, I was contemplating, after we got the numbers on all trophies an individualon how it makes things completely  different, than the standard Leaderboard.

 

yeah, you both agree. ?

 

You see ferryjan is right next to him too. grimydawg beat em both, by like 50% more points, and he's at 137 plats!  Danny, at the very top, is not even in the world top 10k.


In case anyone wonders about the point distribution:

 

points(50)=0
points(49.99)=1
points(49)=1
points(48)=1
points(47)=1
points(46)=1
points(45)=1
points(44)=1
points(43)=1
points(42)=2
points(41)=2
points(40)=2
points(39)=3
points(38)=3
points(37)=3
points(36)=4
points(35)=4
points(34)=5
points(33)=5
points(32)=6
points(31)=7
points(30)=7
points(29)=8
points(28)=10
points(27)=11
points(26)=12
points(25)=14
points(24)=16
points(23)=18
points(22)=20
points(21)=23
points(20)=26
points(19)=29
points(18)=34
points(17)=38
points(16)=44
points(15)=51
points(14)=58
points(13)=67
points(12)=78
points(11)=91
points(10)=107
points(9)=127
points(8)=152
points(7)=185
points(6)=233
points(5)=306
points(4.9)=316
points(4.8)=326
points(4.7)=336
points(4.6)=348
points(4.5)=360
points(4.4)=372
points(4.3)=386
points(4.2)=400
points(4.1)=415
points(4)=431
points(3.9)=448
points(3.8)=467
points(3.7)=486
points(3.6)=507
points(3.5)=529
points(3.4)=553
points(3.3)=578
points(3.2)=605
points(3.1)=634
points(3)=666
points(2.9)=699
points(2.8)=735
points(2.7)=774
points(2.6)=816
points(2.5)=861
points(2.4)=910
points(2.3)=962
points(2.2)=1019
points(2.1)=1080
points(2)=1146
points(1.9)=1218
points(1.8)=1295
points(1.7)=1380
points(1.6)=1471
points(1.5)=1571
points(1.4)=1679
points(1.3)=1796
points(1.2)=1924
points(1.1)=2064
points(1)=2216
points(0.9)=2383
points(0.8)=2566
points(0.7)=2766
points(0.6)=2987
points(0.5)=3230
points(0.4)=3499
points(0.3)=3798
points(0.2)=4134
points(0.1)=4518
points(0.09)=4559
points(0.08)=4602
points(0.07)=4646
points(0.06)=4690
points(0.05)=4736
points(0.04)=4783
points(0.03)=4831
points(0.02)=4882
points(0.01)=4935
points(0)=5000

 

[NamoPh]

Interesting. Did you use a logarithmic distribution to determine the point values? Sorry if I'm asking too many questions, I like to understand the logic.

[pot1414]

@MMDELooks good.Get Sly on the phone!

 

Also please do me if you would be so kind?

Edited March 26, 2021 by pot1414

[MMDE]

9 minutes ago, NamoPh said:

Interesting. Did you use a logarithmic distribution to determine the point values? Sorry if I'm asking too many questions, I like to understand the logic.

 

The function is actually somewhat simple, yet not so simple to guess.  There's no "ln" stuff. I suspect you wonder about this due to the cut-offs, which is not how I accomplished that. It's a pure math function, no extra logic, so there's some other trickery. There are ways to ensure that you hit both the max at 0 and 1 at 50. I suspect everyone actually knows how to derive at this if they still remember their math from school. haha  

Edited March 26, 2021 by MMDE

[Floriiss]

This is looking very promising @MMDE. I'm seeing a lot of familiar names on top of the leaderboards from whom I believe that they deserve to be top spot. What I like about this leaderboard is that it rewards players based on the rarity of their trophies and that it puts a lot of emphasis on ultra rare trophies. Even within the ultra rare category there's a big difference in numbers and it's nice to see that the closer you get to that 0% rarity, the more points you will earn.

 

For comparison sake, one of the more "popular" rarity leaderboards over on PSNTL rewards players with so called "prestige points". From my understanding you get these prestige points when a trophy is below a certain treshold in rarity (or has X amount of achievers). Personally I never really liked this system, as those prestige points gave a ridiculous amount of points and never made any distinction in the rarity of the trophies within it's category. Correct me if I'm wrong, but don't all of these prestige trophies reward the player with the same amount of points? So for example, if I obtain a 0.04% Crypt of the NecroDancer platinum trophy, this would earn me just as much points as obtaining a random bronze 1% DLC trophy for DCUO, which is quite ridiculous if you think about it. I feel like the rarity leaderboard on PSNTL is rather easily exploitable. Just stack DCUO twice and play the old school pinball games. Massive prestige points and you'll be in top 10 easily. That's why I like the current concept of the rarity leaderboard a lot better, as I feel like it's less exploitable and more rewarding as it serves justice for those who go for extremely rare trophies. Heck, look at @Danny_Johansen who hasn't played the old school pinball games and still remains first place on this leaderboard, because the point system makes a lot of distinction in rarity and rewards players with more points the rarer the trophies are. Now that's an example of a good rarity leaderboard! I like it.

Hypothetically speaking, since most users seem to agree with current LB, how long would it take to implement this feature? Isn't the rarity leaderboard practically already there? Is it just as simple as implementing the formula and *poof* all set and done? Or do we have to wait a few months/years for it? Also it would be nice if the cheaters and players with hidden trophies would not show up on that leaderboard (they still do now at the current rarity leaderboard).

Edited March 26, 2021 by Floriiss

[MMDE]

27 minutes ago, Floriiss said:

Hypothetically speaking, since most users seem to agree with current LB, how long would it take to implement this feature? Isn't the rarity leaderboard practically already there? Is it just as simple as implementing the formula and *poof* all set and done? Or do we have to wait a few months/years for it? Also it would be nice if the cheaters and players with hidden trophies would not show up on that leaderboard (they still do now at the current rarity leaderboard).

 

@Sly Ripper Is the only one who can answer this, and I've given him the basic SQL query sum function on discord.

Edited March 26, 2021 by MMDE

[NamoPh]

 

49 minutes ago, MMDE said:

The function is actually somewhat simple, yet not so simple to guess.  There's no "ln" stuff. I suspect you wonder about this due to the cut-offs, which is not how I accomplished that. It's a pure math function, no extra logic, so there's some other trickery. There are ways to ensure that you hit both the max at 0 and 1 at 50. I suspect everyone actually knows how to derive at this if they still remember their math from school. haha  

 

The graph just looked vaguely logarithmic when I plotted it. With what you said I then recognized it also looks like one in the y = a / x ^ n variety. Tried solving for it in a quadratic function too just in case, though that went nowhere.

[BlindMango]

1 hour ago, MMDE said:

 

@Sly Ripper Is the only one who can answer this, and I've given him the basic SQL query sum function on discord.

 

So you're thinking all @Sly Ripper would have to do is plug that into the already existing https://psnprofiles.com/leaderboard/rarity board he's got set up and clear out those flagged accounts? 

[Joe Dubz]

I really like this idea! I'd be curious to see where I fall in this, as I've mostly been hunting URs and knocked out a few sub-1%s in recent times. @MMDE I think the formula you are working with works well, as it rewards better the lower the rarity and seems to make the most sense. Your hard work is appreciated!

[MMDE]

4 minutes ago, BlindMango said:

 

So you're thinking all @Sly Ripper would have to do is plug that into the already existing https://psnprofiles.com/leaderboard/rarity board he's got set up and clear out those flagged accounts? 

 

Nah, he would likely have to do some more, adjust it for his system, maybe change some caching or something, but I gave him how to do the actual calculation.

58 minutes ago, NamoPh said:

 

 

The graph just looked vaguely logarithmic when I plotted it. With what you said I then recognized it also looks like one in the y = a / x ^ n variety. Tried solving for it in a quadratic function too just in case, though that went nowhere.

 

It's def not quadratic, nor does it have any divide.  Not entirely true I guess, some constant values are pre-calculated, and those had divide.

Edited March 26, 2021 by MMDE

[Sword]

The more I look at the point distribution the more I like it. Awards the effort put into the super nail biting ultra rares but also allows points to be earned for games that have at least some difficulty/effort in them (20-30% range). 

 

Would players with hidden trophies be allowed on this one as in the current LB?

Edited March 26, 2021 by Sword

[hore]

On 3/25/2021 at 5:08 AM, MMDE said:

A larger sample:

[...]

 

I added a lot of "top rarity" accounts from other sites and some of the top of the world accounts on this site, and staff.

how could you exclude dav1d_123, the King of Canada??

[MMDE]

3 minutes ago, hore said:

how could you exclude dav1d_123, the King of Canada??

 

Eh, wait a little bit (an hour or two), and there'll be some few more relevant people.  If you want david, I already got his points: 2026429

Edited March 26, 2021 by MMDE

[DeepEyes7]

22 hours ago, DrBloodmoney said:

 

Surely 30% is too low a rarity to discount entirely, isn't it?

 

That would essentially discard a lot of pretty popular games - ones that certainly don't fall into the 'EZPZ' type category that a lot of people dismiss and that are often the subject of ridicule elsewhere on the site.

 

Horizon Zero Dawn, The Last of Us Part II, Assassin's Creed Origins, Nier Automata,God of War, Control, Mark of the Ninja, Far Cry 3 & Persona 5 Royal (to name but a few) all have platinums with rarities above 30%, and would all be considered worthless.

 

I'm not arguing that those games are super difficult or anything, but they are 'real' games by anyone's standards, and some are quite the time-sink, and are by no means a cake-walk in all aspects. Even on a rarity board, it feels a bit much to consider them to be worth nothing.

 

Those could be "popular" games but in terms of rarity... yeah they are worthless, and that's the whole point of this.

 

Everything looks good MMDE!

Edited March 26, 2021 by DeepEyes7

[MMDE]

4 hours ago, MMDE said:

 

points(3)=666

 

 

?

[NathanielJohn]

On 3/25/2021 at 11:47 AM, MMDE said:

Pretty sure I've explained how the function works before. It's not particularly useful to see the exact values, as it's generated by an equation based on the criteria I've set and my own understanding of how growth in functions can be manipulated. I'm asking about the criteria, and then we can judge the result.

 

I mean, as evidenced by the last few posts, you've said basically nothing about how the formula works. You've said that it doesn't include logarithms, doesn't use division (which I don't believe for a second -- negative exponents are still division), and isn't quadratic.

 

Based on my testing, you seem to be using an inverted quadratic, as someone already guessed, just shifted and scaled to get values that you like. I don't know why you keep trying to make it more mysterious or opaque than that. You say that "it's not particularly useful to see the exact values", but then you give a table of 50+ values instead of just giving the formula?

 

Anyway, here is a function of the form y = a/(x+n)^b - c with b = 2.05 (so not quite quadratic, but pretty close) that almost perfectly matches your data, and goes through the points (0,5000) and (50,0) like yours: https://www.desmos.com/calculator/c3hbikyl4i

 

People can adjust the sliders there if they like to see what it looks like for other values of b and n (you can't freely adjust a or c, since those are constrained by the fact that we want the graph to go through (0,5000) and (50,0)).

 

Edited March 26, 2021 by NathanielJohn

[DrBloodmoney]

39 minutes ago, DeepEyes7 said:

 

Those could be "popular" games but in terms of rarity... yeah they are worthless, and that's the whole point of this.

 

Everything looks good MMDE!

fair enough I suppose 

 

I guess I just think this is going too far - in trying to create a leaderboard that is a diametric counter to the main one it goes - to my mind - way too far in the opposite direction.

 

Wasn’t this whole concept, at least somewhat, born out of the idea that the main Leaderboard encourages anyone who wishes to be competitive on it to eschew those kind of games, in favour of stacks and stacks of 30-minute platinums - and that that is a bad thing?

 

By completely discarding the trophies of half the most popular ‘good’ / ‘real’ / ‘AAA’ (whatever term you want - you know what I mean?) games, won’t any new ‘Rarity Leaderboard’ just encourage anyone who wishes to be competitive on it to do the same thing, but instead of stacks and stacks of 30 minute platinums, it will be for broken / obscure / untra-niche / ultra-grindy and downright bad games with UR trophies instead? 

 

That’s not to say I am smart enough to devise a Leaderboard that actually does benefit people for just playing a healthy dose of everything though - I’m definitely not ?

 

I guess it doesn’t matter much anyways though. 
I mean, folks like me, who have a mix of game difficulties and just plays what looks fun will no doubt just come out in roughly similar, middle-of-the-road spots anyways. ?

Edited March 26, 2021 by DrBloodmoney

[MMDE]

1 minute ago, NathanielJohn said:

 

I mean, as evidenced by the last few posts, you've said basically nothing about how the formula works. You've said that it doesn't include logarithms, doesn't use division (which I don't believe for a second -- negative exponents are still division), and isn't quadratic.

 

Based on my testing, you seem to be using an inverted quadratic, as someone already guessed, just shifted and scaled to get values that you like. I don't know why you keep trying to make it more mysterious or opaque than that. You say that "it's not particularly useful to see the exact values", but then you give a table of 50+ values instead of just giving the formula?

 

Anyway, here is a function of the form y = a/(x+n)^b - c with b = 2.05 (so not quite quadratic, but pretty close) that almost perfectly matches your data, and goes through the points (0,5000) and (50,0) like yours: https://www.desmos.com/calculator/c3hbikyl4i

 

People can adjust the sliders there if they like to see what it looks like for other values of b and n (you can't freely adjust a or c, since those are constrained by the fact that we want the graph to go through (0,5000) and (50,0)).

 

 

I think you misunderstand what I mean by me having talked about the formula. I've talked about it's properties, the relevant stuff for anyone who isn't a mathematician.

 

Quadratic specifically means x^2, with 2 as the exponent, and usually refers to famous ax^2 + bx + c, where the base is an unknown. I can assure you there's no unknown with 2 as exponent, in any calculation of this function.

 

There's no division.