With some discussions with BATs and players, especially in osu!mania mode, I have come to a solution on making PP (especially osu!mania) more reliable when rating a player.
Method
1.A standard should be made as a “fair play”. This is the standard that when a song values “such PP” the player should get. In this explanation, I would set osu!mania score 900,000 as the standard. And a function playing the role as a multiplier should also be made. I would just make a linear score multiplier in this example.
2.When a song is published, a BAT assign a random initial “difficulty” number called PP-level. (This is not relevant to anything final, just an initial value to make the algorithm work.) e.g. When an insane is published, a BAT assigned 5,000 PP-level. (He or she would assign 6,000 or his birthday number or whatsoever.)
3.When a player plays this song and get a score, both the song PP-level and player PP would be adjusted. If a PP-weak player get a really good score on a PP-strong song, the PP-level of the song would be decreased, and the player would get a higher PP. vice versa.
e.g. If the player have PP 4,000 , playing this song and get 810,000 , he or she would get raw PP rating 4,500 (810,000/900,000*5000). Then the song PP-level would be adjusted to a lower level depending on the record the song already holds and some other parameters. Simply speaking in this example, the player would only get 4,450 song PP, and the song PP-level would be adjusted to something like 4,940. (If the player have only get 450,000 on the song, player would only get ~2,550 song PP and the song itself would have a slightly higher PP-rating.)
4.Finally after a great amount of score, the algorithm would ensure that a player getting “fair score” (900,000 in this example) would always get the PP-level PP, higher score higher PP,lower score lower PP. And (if this song is #1 best performance) a higher rank in this song should always means higher final PP.
5.The player’s final PP is biased on the few top scores, e.g. 18% on each of the 5 highest BP and 1% on following 10.
Q&A
1.What’s the good point of this method?
In short, this method use only relative score as metric and ensure that a strong player holds higher position on the total list.
This method would better eliminate the unknown factor (super strong player, player group strength increase because of time elapsing, etc) and would finally point out a “difficulty” metric based on “player votes” of their scores. This is better than just note density or HP/OD or something else. Furthermore, this algorithm would show real power of hard songs. In current PPV1 system, a really hard song would not give a lot of PP but a farming player with a lot of fair score would win on the list. (This is happening in osu!mania pp board; I don’t know how osu! Community would think about this)
2.What about PPV2?
PPV2 uses something like top player’s accuracy as “standard”. This way is better than V1 and simple enough, but are not accurate enough because it won’t give accurate song-relative difficulty, especially on osu!mania. When taking 2 songs with average 99.8% top average (like Scarlet Rose 0108 converted and some random easy song), it’s really hard to say that they are at the same difficulty level. What’s more, when considering osu! As a combo game, many high accuracy player would sadly found their score out of top players’ list because of a break in combo, even with DT+HR, making top players’ average accuracy even more inaccurate. Setting a static score as the standard would make ratings more standardized and without error when considering songs of different condition (new maps, old maps, etc.)
3.What’s the initial value?
Actually this doesn’t care – using star difficulty * 1500 as starting PP-rating and everyone’s PP as their initial PP is OK, and everything would go fine after a few days. (Just like the no-PP period of osu!mania first ranking days)
4.If some high-rating players intentionally plays a song extremely poor…
That would make that song high in PP abnormally. Don’t worry it would be fine after some PP-care players get a high score when they found this as a sweet cake…
As an immature thought, there are many things to be discussed. What’s your opinion?
Method
1.A standard should be made as a “fair play”. This is the standard that when a song values “such PP” the player should get. In this explanation, I would set osu!mania score 900,000 as the standard. And a function playing the role as a multiplier should also be made. I would just make a linear score multiplier in this example.
2.When a song is published, a BAT assign a random initial “difficulty” number called PP-level. (This is not relevant to anything final, just an initial value to make the algorithm work.) e.g. When an insane is published, a BAT assigned 5,000 PP-level. (He or she would assign 6,000 or his birthday number or whatsoever.)
3.When a player plays this song and get a score, both the song PP-level and player PP would be adjusted. If a PP-weak player get a really good score on a PP-strong song, the PP-level of the song would be decreased, and the player would get a higher PP. vice versa.
e.g. If the player have PP 4,000 , playing this song and get 810,000 , he or she would get raw PP rating 4,500 (810,000/900,000*5000). Then the song PP-level would be adjusted to a lower level depending on the record the song already holds and some other parameters. Simply speaking in this example, the player would only get 4,450 song PP, and the song PP-level would be adjusted to something like 4,940. (If the player have only get 450,000 on the song, player would only get ~2,550 song PP and the song itself would have a slightly higher PP-rating.)
4.Finally after a great amount of score, the algorithm would ensure that a player getting “fair score” (900,000 in this example) would always get the PP-level PP, higher score higher PP,lower score lower PP. And (if this song is #1 best performance) a higher rank in this song should always means higher final PP.
5.The player’s final PP is biased on the few top scores, e.g. 18% on each of the 5 highest BP and 1% on following 10.
Q&A
1.What’s the good point of this method?
In short, this method use only relative score as metric and ensure that a strong player holds higher position on the total list.
This method would better eliminate the unknown factor (super strong player, player group strength increase because of time elapsing, etc) and would finally point out a “difficulty” metric based on “player votes” of their scores. This is better than just note density or HP/OD or something else. Furthermore, this algorithm would show real power of hard songs. In current PPV1 system, a really hard song would not give a lot of PP but a farming player with a lot of fair score would win on the list. (This is happening in osu!mania pp board; I don’t know how osu! Community would think about this)
2.What about PPV2?
PPV2 uses something like top player’s accuracy as “standard”. This way is better than V1 and simple enough, but are not accurate enough because it won’t give accurate song-relative difficulty, especially on osu!mania. When taking 2 songs with average 99.8% top average (like Scarlet Rose 0108 converted and some random easy song), it’s really hard to say that they are at the same difficulty level. What’s more, when considering osu! As a combo game, many high accuracy player would sadly found their score out of top players’ list because of a break in combo, even with DT+HR, making top players’ average accuracy even more inaccurate. Setting a static score as the standard would make ratings more standardized and without error when considering songs of different condition (new maps, old maps, etc.)
3.What’s the initial value?
Actually this doesn’t care – using star difficulty * 1500 as starting PP-rating and everyone’s PP as their initial PP is OK, and everything would go fine after a few days. (Just like the no-PP period of osu!mania first ranking days)
4.If some high-rating players intentionally plays a song extremely poor…
That would make that song high in PP abnormally. Don’t worry it would be fine after some PP-care players get a high score when they found this as a sweet cake…
As an immature thought, there are many things to be discussed. What’s your opinion?