Rarity Leaderboard

[thegirlruka]

4 hours ago, Sly Ripper said:

How about exponent based so 50% = 1 and 0.01% = 1,000 (or any other max) but it isn't linear:

 

So sub-50% would be 1 point, 0 points, or a fraction of a point?

[Zenodin]

2 minutes ago, Jibril said:

So sub-50% would be 1 point, 0 points, or a fraction of a point?

Trophy rarity between 100%-50% would result in points between 0-1.

Anything between 50%-0.01% would result in points between 1-1000. 

[thegirlruka]

6 minutes ago, Zenodin said:

Trophy rarity between 100%-50% would result in points between 0-1.

Anything between 50%-0.01% would result in points between 1-1000. 

That's what I'd originally thought but tracking such small numbers would be difficult.

[Zenodin]

2 minutes ago, Jibril said:

That's what I'd originally thought but tracking such small numbers would be difficult.

It depends on how you want to start the calculation or how you want to show the result. 

 

One could decide, contrary to what I just said before, to give 0 points to everything from 50.01% and above and make the math for all other trophies that vary between 50.00%-0.01%. 

 

Or one could calculate it all and round up/down to 2/1/0 number(s) after the comma. 

 

@Sly Ripper didn't actually say anything about the trophies between 50%-100%, but there's always a way to avoid the small numbers. 

[Sly Ripper]

 

36 minutes ago, Jibril said:

So sub-50% would be 1 point, 0 points, or a fraction of a point?

 

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.

[Zenodin]

2 minutes ago, 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 10% trophy isn't the same as getting two 5% trophies, it's much more worth getting the rarest trophies possible.

 

Superb! This is excellent ... Precioussss trophiesss ...

 

This looks best indeed. No categories ... The rarer, the better. 

[zajac9999]

5 hours ago, 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.

 

Love this idea! Hope we can see it sometime soon.

[xZoneHunter]

31 minutes ago, zajac9999 said:

 

Love this idea! Hope we can see it sometime soon.

 

You would probably blow everybody out of the water if this would get implemented

[Se7en]

10 hours ago, Sly Ripper said:

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

 

Actually, on presented scale of 1-500 two trophies with 10% rarity are worth 2 × 144.41 = 288.82 points, which is more, than one 5% rarity trophy with 268.88 points. I like the whole idea, though. Just the scale itself needs adjustment, maybe 1 to 1000/5000/10000 or something else.

[AlphaTrash]

17 hours ago, 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.

 

You have no idea how much I'd love to see this happen... 

Please make this a thing. ?

 

Also, could we please a new class for trophies below 1%? so 5% to 1% are Ultra Rares and below 1% is something even greater? 

SSSuper Rare as someone suggested perhaps. I'd personally prefer Uber rare or something like that. Ultra and Uber Rare. 

"

Edited April 10, 2017 by Jeff

[Sly Ripper]

7 hours ago, Se7en said:

 

Actually, on presented scale of 1-500 two trophies with 10% rarity are worth 2 × 144.41 = 288.82 points, which is more, than one 5% rarity trophy with 268.88 points. I like the whole idea, though. Just the scale itself needs adjustment, maybe 1 to 1000/5000/10000 or something else.

 

You're right

 

On a 1-10k scale 2 x 10% = 3,174.46, 5% = 3,987.68.

[AlphaTrash]

@Sly Ripper Thinking about it, could just change the requirements for the current system. 
Make trophies below 1% Ultra rare, trophies from 1%-5% very rare, 5%-20% rare, 20%-50% uncommon and 50% - 100% common. 

[Zenodin]

@Sly Ripper, ... another something you could take into consideration:

 

Would you want to value trophies purely on their rarity, whether it be a B/S/G/P trophy, ... or would you still take the trophy type into account ... ? Maybe multiply the rarity points as you mentioned before with the trophy xp value? 15/30/90/180 ... or 1/2/6/12 ... ?

 

Like this a 1% plat would still be worth much more than a 1% bronze trophy ... 

 

And another thing is ... just like the current trophy xp points are converted into a PSN lvl and a percentage, ... those massive amount of rarity points could be scaled into a rarity lvl and percentage as well ... Maybe using the same amounts of points per level as the PSN lvl does ... ? I am PSN lvl 23, but with a good amount of rare trophies I could perhaps be at a Rarity lvl 30 ... oslt ...

[NathanielJohn]

 

23 hours ago, Sly Ripper said:

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.

 

I guess I'll be the one to say that I don't like this proposed formula. There's a huge difference between a 50% trophy and a 10% trophy (a 10% trophy is worth 144 times as much as a 50% trophy!!), but hardly any difference between a 10% trophy and a 0.01% trophy (getting four 10% trophies is worth more than a 0.01% trophy). In other words, this formula heavily rewards middle-of-the-road rarity trophies, not *actually* rare trophies.

 

I propose the following formula instead, where MAX is the desired maximum point amount given to rarity 0.01%:

 

Points = 1 + (MAX - 1) * (sqrt(50/Rarity) - 1) / (50*sqrt(2)-1)

 

On a 1-500 scale (i.e., MAX = 500), this results in the following point distribution:

 

50% = 1

40% = 1.844906

30% = 3.082984

20% = 5.159883

10% = 9.847969

5% = 16.47792

4% = 19.14975

3% = 23.0649

2% = 29.63263

1% = 44.45766

0.1% = 153.9031

0.01% = 500

 

In my opinion, this formula much better captures rarity at both ends of the spectrum -- a 10% trophy is worth roughly 10 times as much as a 50% trophy, and a 0.01% trophy is worth 10 times as much as a 1% trophy, which is worth 4 times as much as a 10% trophy). In other words, it is much more spread out across the whole range of percentages, rather than already giving tons of points to trophies with 10% rarity or higher.

 

This formula also has the advantage of being very close to scale-invariant. If we change the MAX from 500 to something like 10,000, then the ratio of point value do not change nearly as dramatically as they did in Sly's example.

 

Edited April 10, 2017 by NathanielJohn

[Danny_Johansen]

@NathanielJohn

I think your formula is much better for the rarity leaderboards as it rewards you for going after trophies that are rarer than 5% timewise. However it also has a problem that is noticable on PSNTL. Some games will end up giving too many points that if you don't go for them, you can't compete. Take a game like Time Crisis: Razing Storm, it has 30 trophies below 1%. The 0.01-1% scaling needs a bit of tweaking.

 

An idea I had is to rewards point for every completed game based on the rarest trophy. It will make some of the harder non-plats just as rewarding.

[NathanielJohn]

2 hours ago, Danny_Johansen said:

However it also has a problem that is noticable on PSNTL. Some games will end up giving too many points that if you don't go for them, you can't compete. Take a game like Time Crisis: Razing Storm, it has 30 trophies below 1%. The 0.01-1% scaling needs a bit of tweaking.

 

I don't think it looks too bad (but of course am open to tweaking the formula). On PSNTL, that game is worth something ridiculous like 140,000 points, which I agree is way too much. Using the formula I posted, it gets a total of roughly 2500 points. That's a lot, but not really in the realm of "you must play this to compete" I don't think. Those same 2500 points could be gotten from 150 5% trophies, for example, which isn't really that many.

Edited April 11, 2017 by NathanielJohn

[dmsleight]

-

Edited April 11, 2017 by dmsleight
nvrmnd

[NathanielJohn]

As a follow-up to my previous two posts, here's a more general formula that we can easily tweak to weigh really rare trophies as heavily or lightly as we like:

 

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

 

where MAX is the maximum point value given to 0.01%-rarity trophies (MAX = 500 in the previous posts) and N is a parameter that determines how steep the point curve is. More specifically, N should be between 0 and 1. N = 0.5 gives the formula from my previous post (and in my opinion gives the best point curve). Smaller values of N weigh middle-of-the-road rarity trophies more heavily, while higher values of N weigh really rare trophies more heavily.

 

Here are some tables of values for a few different values of N (all of them use MAX = 500):

 

N = 0.1:

50	1.00
40	9.38
30	20.46
20	36.64
10	65.85
5	97.16
4	107.71
3	121.66
2	142.02
1	178.80
0.1	320.99
0.01	500.00

 

N = 0.2:

50	1.00
40	6.07
30	12.95
20	23.34
10	43.18
5	65.96
4	74.00
3	84.90
2	101.37
1	132.81
0.1	274.86
0.01	500.00

 

N = 0.3:

50	1.00
40	3.91
30	7.96
20	14.30
10	27.08
5	42.83
4	48.63
3	56.72
2	69.36
1	94.87
0.1	230.13
0.01	500.00

 

N = 0.4:

50	1.00
40	2.60
30	4.88
20	8.57
10	16.46
5	26.86
4	30.87
3	36.60
2	45.88
1	65.69
0.1	189.36
0.01	500.00

 

And N = 0.5 is the same as the table from my previous post.

 

Anyway -- thoughts? Which value of N looks the best, or do these all not look great (i.e., we should look at a different type of function altogether)?

[Sly Ripper]

4 minutes ago, NathanielJohn said:

..

 

Two 10% trophies is always more points than a 5%. I want to avoid being able to stock up on easier trophies instead of going for the harder ones.

[NathanielJohn]

10 minutes ago, Sly Ripper said:

 

Two 10% trophies is always more points than a 5%. I want to avoid being able to stock up on easier trophies instead of going for the harder ones.

 

This is mathematically impossible -- no function exists that does this for *all* percentage values. You've fixated on the comparison between 10% and 5% for some reason, but in your function, two 5% trophies is worth more than a 0.01% trophy. What's the point of actually rare trophies then?

 

Edit: Correction -- it's not mathematically impossible, they're just so extreme as to be pretty ugly and not scale-invariant. I'll try to find the "least extreme" one.

Edited April 11, 2017 by NathanielJohn

[Sly Ripper]

Just now, NathanielJohn said:

 

This is mathematically impossible -- no function exists that does this for *all* percentage values. You've fixated on the comparison between 10% and 5% for some reason, but in your function, two 5% trophies is worth more than a 0.01% trophy. What's the point of actually rare trophies then?

 

500 was a bad scale to post, I was trying a bunch and that was what I had at the time of posting.

 

At 10k, two 5% is 7,975.36

[NathanielJohn]

Just now, Sly Ripper said:

 

500 was a bad scale to post, I was trying a bunch and that was what I had at the time of posting.

 

At 10k, two 5% is 7,975.36

 

Right, so two 5% is still *way* more than one 2.5%, right? Two 5% trophies shouldn't even be *close* to 0.01%.

[Sly Ripper]

2 minutes ago, NathanielJohn said:

 

Right, so two 5% is still *way* more than one 2.5%, right? Two 5% trophies shouldn't even be *close* to 0.01%.

 

True, between 0.2 and 0.3 looks good in your calculation.

[NathanielJohn]

Just now, Sly Ripper said:

 

True, between 0.2 and 0.3 looks good in your calculation.

 

Alternatively, if you really want a function with the property that Points(2*Rarity) <= 2*Points(Rarity) for all Rarity values, the simplest function that works is just Points = 50/Rarity (which I believe someone suggested earlier).

 

50	1.00
40	1.25
30	1.67
20	2.50
10	5.00
5	10.00
4	12.50
3	16.67
2	25.00
1	50.00
0.1	500.00
0.01	5000.00

 

However, that function looks a bit extreme for my tastes (it would lead to the problem that Danny mentioned of some games being absolutely required to compete). And this is the least extreme function with this property -- every other function with Points(2*Rarity) <= 2*Points(Rarity) will weigh 0.01%-trophies even more heavily.

 

Anyway, here's the N = 0.25 table for my previous formula (since you mentioned liking between 0.2 and 0.3):

 

50	1.00
40	4.86
30	10.17
20	18.34
10	34.36
5	53.42
4	60.29
3	69.73
2	84.25
1	112.75
0.1	252.13
0.01	500.00

[imouto38]

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 :

 

For exemple : 

My rarest trophy in a game have a 4% rarity, and 4% worth 4000 points. I have 80% completion on that game, so i will earn 80% of 4000 points.

 

This way, it still negates the points gain of skipped visual novel, (0% or 100% of 0 points is still 0) while preventing over rewarding games for no reason.