Rarity Leaderboard

[Kapika96]

Nice to see this is actually a thing now, and that I fare better on it than the regular leaderboard.

 

Any chance there could be a link for it added to the leaderboard section of the site though? Would be much easier than having to look through this thread for the link

[dmsleight]

4 minutes ago, Kapika96 said:

Nice to see this is actually a thing now, and that I fare better on it than the regular leaderboard.

 

Any chance there could be a link for it added to the leaderboard section of the site though? Would be much easier than having to look through this thread for the link

I don't think it is a settled board yet.  But, as another poster already mentioned, add "/rarity" to the end of the leaderboard url and it will come up.

 

I don't mind the idea of having a complex formulaic method that calculates values, but It would be good to have information to that affect easily available for people to understand (or try to).  Transparency is a good thing.  Some other calculations are not straight forward and the explanations are not so easy to find too (e.g. dlc).  That said, there was a lot of talk of talk of rewarding rarer trophies at a higher rate.  Keeping on that thought, one thing I would like to change is to lower the cap for uncommon trophies.  The cap space can be increased in higher rarities. Other posters have wanted to minimize the effect of simply playing a lot of games and lowering uncommon trophies should mitigate that issue better.  As it is, there are people on the leaderboard that are above me who have significantly less rare-ultra rare trophies but because they have twice as many uncommons as me.

 

Certainly, as long as uncommons have any value, people with a lot of trophies will rank high.  To that point, I am not a fan of only awarding points for high rarities, but I would like to see uncommons have a diminished impact on rankings.

[Gage]

2 hours ago, andylaw31 said:

I believe inverse percentage is the most accurate and only direct way to represent sum rarity (rather than average rarity) in a points system: 99.99% = 0.01 points; 0.01% = 99.99 points.

 

The issue with that is that it skews extremely hard toward just total trophies. Two 50% trophies are worth more than one 0.01% trophy (or functionally worth the same), so at that point it still just basically becomes massive quantity over actual rarity value. 

 

I don't think there can ever be one "proper" way to measure rarity due to just how all over rarity is and how skewed it can be on some games. Unpopular games that might actually be hard but most people who actually play attempt to finish won't be as rare as mainstream games that might have one mildly annoying thing that isn't nearly as hard. 

Edited April 18, 2017 by Gage

[ProfBambam55]

2 X 50/2 = 2 X 0.01/2?...this is interesting...remember the idea with ratio/average is to divide by number of trophies...

Edited April 18, 2017 by ProfBambam55
Question mark

[NathanielJohn]

6 minutes ago, ProfBambam55 said:

2 X 50/2 = 2 X 0.01/2?...this is interesting...remember the idea with ratio/average is to divide by number of trophies...

 

What? That's clearly not what the proposed formula was -- why would a 0.01% trophy early you *fewer* points than a 50% trophy?

 

The formula suggested by andylaw was 100 - Rarity. For this formula, 2 * 50 > 1 * 99.9, which is what Gage said (two 50% trophies are worth more than 1 0.01% trophy). Dividing both sides of that equation by 2 does not change whether or not that inequality is true.

[TheYuriG]

First in Brazil, as expected. Now if we could change to show this stat in the trophy card and psn profile, that would be awesome. Fuck world ranking for quantity

[ProfBambam55]

Ah, I see...sum rarity...skimmed forum...saw numbers...didn't make sense...not equal in average...knew I should stay out of this...haha...apologies...best to let people who care about this make the decisions...my interest is simply in the numbers...love math...

Edited April 18, 2017 by ProfBambam55
Apologies

[NathanielJohn]

Anyway, since there are some new people in the thread and a lot of stuff is now buried behind a page and a half of arguments, here's a summary of where the formula stands:

 

The current formula that you see in use on the rarity leaderboard is Points = 1 + (MAX - 1) * ((50/Rarity)^N - 1) / (5000^N - 1) with MAX = 500 and N = 0.2718281828459. This creates a point distribution from 1 point for Rarity = 50% and 500 points for Rarity = 0.01%.

 

The main objections people raised to this formula were that (1) it wasn't "extreme" enough (i.e., people with lots of uncommons were still drowning out people who focused on rares and ultra rares), and (2) since it maxes out at 0.01%, the vast majority of people never get the maximum number of points (since so few games even have 0.01% trophies to begin with).

To fix these problems, the formula Points = 50/Rarity has been proposed, and we cap the score at 500 points per trophy (i.e., anything with rarity <= 0.1% gives the same number of points). See this post for reasons why this formula is nice, but the short version is that (1) it is more "extreme" than the current formula, (2) it fixes the 0.01% problem mentioned earlier, and (3) the formula is simple and easy to understand.

 

Any further thoughts on the pros/cons of this formula?

[yndajas]

I agree 2 x 50% being more than 1 x 0.01% feels weird and devaluing of higher rarity trophies, though I'd still argue it's technically the most accurate measure of actual sum rarity - you beat 50% of people on a trophy, you get 50 points; beat 90% of people, get 90 points and so on - but I think 50/rarity does feel better. An explanation that it's weighted and therefore slightly distorted, and potentially an unweighted points column would be good (the latter would need scaling up to 0-500 if 500 is the max in the weighted column in order to provide a useful comparison).

Edited April 18, 2017 by andylaw31
Correct formula

[dmsleight]

On 4/18/2017 at 3:15 PM, NathanielJohn said:

Anyway, since there are some new people in the thread and a lot of stuff is now buried behind a page and a half of arguments, here's a summary of where the formula stands:

 

The current formula that you see in use on the rarity leaderboard is Points = 1 + (MAX - 1) * ((50/Rarity)^N - 1) / (5000^N - 1) with MAX = 500 and N = 0.2718281828459. This creates a point distribution from 1 point for Rarity = 50% and 500 points for Rarity = 0.01%.

 

The main objections people raised to this formula were that (1) it wasn't "extreme" enough (i.e., people with lots of uncommons were still drowning out people who focused on rares and ultra rares), and (2) since it maxes out at 0.01%, the vast majority of people never get the maximum number of points (since so few games even have 0.01% trophies to begin with).

To fix these problems, the formula Points = 50/Rarity has been proposed, and we cap the score at 500 points per trophy (i.e., anything with rarity <= 0.1% gives the same number of points). See this post for reasons why this formula is nice, but the short version is that (1) it is more "extreme" than the current formula, (2) it fixes the 0.01% problem mentioned earlier, and (3) the formula is simple and easy to understand.

 

Any further thoughts on the pros/cons of this formula?

 

This is certainly simpler and more extreme.  I would say it goes to far to the extreme in my opinion.  Uncommons won't have much weight, but neither do most ultra rares.  Maybe I'm alone on that though.

[dmsleight]

Maybe it doesn't matter anymore, but I thought I would share something I came up with.  It's not too complicated.

 

%	Points	point value
49	1	0.25
48	1.25
21	7
20	9	2
19	11
11	25
10	33	8
9	41
6	65
5	99	32
4	131
1	227
0.9	259	32
0.1	515
0	549

 

Uncommon %s are worth .25 pts.  Originally, I had uncommons at .5 pts, but they seemed to still have too much value, so I halved them.  In that formula, each levels' points quadruples (except now uncommons increase is now half), so rares are worth 2 points, Very rares 8, Ultra rares 32.  The Uberstupidmega rares (trademarked) are 32 for every .1%, which more than quadruples their incremental value (a 10x increase, verse 4x).  If I kept with the origional 4x increase, they would be worth 12.8 points for every .1%.

 

What I like about this table, is that uncommons have little value, yet ultra rares still have some value.  The extremist can still be happy because uberstupidmega rares are rewarded heavily.  The method is not terribly complicated either.  If it is too extreme, the usm rares increase could be dropped too.  At 27.2 points, they are an 8x increase, or as above, 12.8 for 4x.

 

10% is more than triple 20%.  5% is triple 10%.   Any thoughts?

Edited April 25, 2017 by dmsleight
chart didn't load

[- Deleted -]

On 25 April 2017 at 5:02 PM, dmsleight said:

Maybe it doesn't matter anymore, but I thought I would share something I came up with.  It's not too complicated.

 

%	Points	point value
49	1	0.25
48	1.25
21	7
20	9	2
19	11
11	25
10	33	8
9	41
6	65
5	99	32
4	131
1	227
0.9	259	32
0.1	515
0	549

 

Uncommon %s are worth .25 pts.  Originally, I had uncommons at .5 pts, but they seemed to still have too much value, so I halved them.  In that formula, each levels' points quadruples (except now uncommons increase is now half), so rares are worth 2 points, Very rares 8, Ultra rares 32.  The Uberstupidmega rares (trademarked) are 32 for every .1%, which more than quadruples their incremental value (a 10x increase, verse 4x).  If I kept with the origional 4x increase, they would be worth 12.8 points for every .1%.

 

What I like about this table, is that uncommons have little value, yet ultra rares still have some value.  The extremist can still be happy because uberstupidmega rares are rewarded heavily.  The method is not terribly complicated either.  If it is too extreme, the usm rares increase could be dropped too.  At 27.2 points, they are an 8x increase, or as above, 12.8 for 4x.

 

10% is more than triple 20%.  5% is triple 10%.   Any thoughts?

 

I think that works pretty well. With it being a rarity leaderboard, common and uncommon trophies need to have as little value as possible and this table does just that. If this is still going to be a thing, this looks like the ideal chart IMO.

[dmsleight]

18 hours ago, ryankamal1998 said:

 

I think that works pretty well. With it being a rarity leaderboard, common and uncommon trophies need to have as little value as possible and this table does just that. If this is still going to be a thing, this looks like the ideal chart IMO.

 

I appreciate the support.  I don't think its going to get any traction though.

[- Deleted -]

5 hours ago, dmsleight said:

 

I appreciate the support.  I don't think its going to get any traction though.

 

Eh it might. Sly  has been getting a ton of suggestions the past couple of months it seems so just give it some time and we'll see.

[dmsleight]

7 hours ago, ryankamal1998 said:

 

Eh it might. Sly  has been getting a ton of suggestions the past couple of months it seems so just give it some time and we'll see.

 

Yeah, there has been a lot going on even after the update.  And I see other request threads that he has responded to.  He's go ambition

[Papidadi]

On ‎2017‎-‎03‎-‎23 at 9:48 AM, Zenodin said:

 

If the trophy is obtainable, whether it be by a glitch or not, ... why wouldn't it count ... ?

Hello Zenodin, I am guessing you meant to say *unobtainable? This was a hypothetical leaderboard proposed by someone other than myself. I was curious where they would stand on the glitched trophy issue.

[Zenodin]

On 6-5-2017 at 11:49 PM, Papidadi said:

Hello Zenodin, I am guessing you meant to say *unobtainable? This was a hypothetical leaderboard proposed by someone other than myself. I was curious where they would stand on the glitched trophy issue.

 

No, I did mean obtainable ... by a 'good' glitch. A glitch that could make a difficult trophy much easier to get. Why wouldn't a trophy obtained through a good glitch count ... It will immediately reflect in the rarity of that trophy ... Stays the same for everyone. 

[cris3f]

I do think this is a good idea. Personally I have a lot more respect for players who achieve very difficult trophies, than the massive number of 1 or 2 hour platinum games. But problem is that rarity isn't directly relayed to difficulty, as i have some rare and ultra rare trophies that are very easy to get anyway.

 

My personal opinion anyway.

Edited May 11, 2017 by cris3f

[Bezenko]

I love the idea of a rarity leaderboard and for the first time ever it has been fun chasing positions on a leaderboard. However I think it's far from perfect at the moment. On the national leaderboard I have the 7th most ulta rare trophies yet I'm only ranked 48th. I'm not saying it should be ranked by ultra rare, then very rare etc. But right now I'm tens of thousand points behind players I have far more UR trophies than, but they have 1000s more commons and uncommons. I think that on a rarity leaderboard only UR, VR and rare trophies should count at all.

[dmsleight]

11 hours ago, Bezenko said:

I love the idea of a rarity leaderboard and for the first time ever it has been fun chasing positions on a leaderboard. However I think it's far from perfect at the moment. On the national leaderboard I have the 7th most ulta rare trophies yet I'm only ranked 48th. I'm not saying it should be ranked by ultra rare, then very rare etc. But right now I'm tens of thousand points behind players I have far more UR trophies than, but they have 1000s more commons and uncommons. I think that on a rarity leaderboard only UR, VR and rare trophies should count at all.

 

I'm with you on ucs.  I don't think they need to have 0 value, but their value should be minimal.  I also agree the the current values are ok if we reduce uc values (hopefully by a good amount).  My suggested system ^^^ heavily minimizes their impact.  If it is used, I think I was a little too ambitions with the increase of .99-0% trophies.  I would reduce their increment.

 

To further you point.  When I compare with others on my page, I often have significantly less uc/cs than everyone on the page.  There will usually be one or two guys that have even less, but I usually have hundreds/thousands less than nearly everyone, but I am ranked with them.  All the same,  I like having a rarity board!  I will never be anywhere mentionable on the other lb, but this one is much more level for everyone.

[waltdisneypixar]

Above me there is a guy with 17 plats and below me with 107 plats in world rank

 

How about that for Rarity Leaderboard

 

P.s. i don't care about ranks or whatever

Edited June 10, 2017 by waltdisneypixa

[dmsleight]

So I just updated my profile, and I noticed that my points were added but the leaderboards haven't updated.  As such, it made it easy to see about how many points I earned.  I got 2 Ultra rare trophies at 2.75 and 2.78%.  According to this chart, I should have gained about 700 pts.  However, in reality,  I gained less than 132 pts.  This is the chart for the leaderboard... but somethings not adding up...

 

Am I missing something here? 

 

On 4/9/2017 at 9:25 PM, Sly Ripper said:

 

 

0, the points start at 50%.

 

On a 1-500 scale:

50.00 = 1.00

40.00 = 3.47

30.00 = 12.02

20.00 = 41.66

10.00 = 144.41

5.00 = 268.88

4.00 = 304.47

3.00 = 344.78

2.00 = 390.42

1.00 = 442.10

0.01 = 500.00

 

This way a 5% trophy isn't the same as getting two 10% trophies, it's much more worth getting the rarest trophies possible.

 

[Tosmasta00]

372620 not bad that is going by the points from the first post.

[Matrim_Drasgen]

I got lost. There was a point value and that was perfect, easy to follow. Made sense. Then graphs and % got thrown in and inverse Pi with X squared divided by '0' and it all become black lettering on a white page to me.

[dmland12]

On 6/17/2017 at 0:59 PM, dmsleight said:

So I just updated my profile, and I noticed that my points were added but the leaderboards haven't updated.  As such, it made it easy to see about how many points I earned.  I got 2 Ultra rare trophies at 2.75 and 2.78%.  According to this chart, I should have gained about 700 pts.  However, in reality,  I gained less than 132 pts.  This is the chart for the leaderboard... but somethings not adding up...

 

Am I missing something here? 

 

 

 

That's not what sly ended up using.  Here's a link again to a calculator/spreadsheet I made using the formula that's currently being used.

 

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