Yes, I mean something similar to a live score comparison (I've seen there were a lot of duplicate requests for that), but instead of comparing with others' scores at a certain point, just have the max score that you can still achieve, and you can compare that with the scores in the top 40 or with your local scores. I have a simple way to implement it that I believe will work also.
There are so many reasons why I think it'd be cool to have this. If it showed the max possible score that you could still achieve along with the top 40 on the side, then people spectating you could know you're still on pace for #1 despite that 100, or you could miss a note in the middle of a long song and know right then that your potential max score went from 15 million to 8 million, or you could watch your replay and see just how badly that 100 streak killed your score, etc etc...
There are so many reasons why I think it'd be cool to have this. If it showed the max possible score that you could still achieve along with the top 40 on the side, then people spectating you could know you're still on pace for #1 despite that 100, or you could miss a note in the middle of a long song and know right then that your potential max score went from 15 million to 8 million, or you could watch your replay and see just how badly that 100 streak killed your score, etc etc...
SPOILER
I think it would be relatively easy to implement if you think about it as subtracting out the points you miss out on whenever you miss a note or don't get 300.
Requirements:
total # of objects [hit circles+sliders+spinners] remaining, and the current max possible score M
After note hit:
This would just be subtracting out the points you missed from not getting a 300.
After missed note:
This would be subtracting out the points you missed from not getting a 300, and then subtracting out all the points you miss out on because your combo is [your previous combo + 1] lower than what it could have been.
After missing the end of a slider:
This would be subtracting the 30 points missed from the end of the slider plus the effect from having 1 less combo multiplier for all the remaining notes.
The spinner bonus could be added to the max:
Basically, when you start the song, just the total number of objects and the max possible score need to be known, and then the remaining number of objects and new max possible score can be updated every time they change. I've tested all of this on a small sample map and it's worked for that. This concept works because when you lose your combo, when there are the same number of objects remaining you miss out on the same amount of points regardless of what the objects are or in which order they are in.
Having a math degree I can understand the desire to see some kind of proof for a statement like this:
Let's say you are comparing two runs which are the same, but then the second player misses a note after N notes. Using [note pos] as the combo multiplier for each note for the second player if the second player gets perfect, the total remaining score for both players would be
Player 1: sum over all remaining notes[300*((N+1+note pos)*DM*MM/25 + 1)] + spinner points + slider ticks
Player 2: sum over all remaining notes[300*((note pos)*DM*MM/25 + 1)] + spinner points + slider ticks
difference: sum over all remaining notes[300*((N+1)*DM*MM/25 + 1)] /////This no longer depends on the individual note
=300*((N+1)*DM*MM/25 + 1)*sum over all remaining notes[1] = 300*((N+1)*DM*MM/25 + 1)*# of remaining notes.
And then induction for missing multiple notes, or something.
One problem is that there could be rounding errors (I'm not sure how the rounding works so I'm not sure how to minimize them). Maybe at the extreme the projected max could be 500 points off of what you actually scored when there are 1000 notes, but considering that there would only be errors when you don't get 300s and most people don't get 1000 100s on a 1000 note song, it probably wouldn't be that bad.
Finally, if anything's not clear, I could try and explain it better.
Requirements:
total # of objects [hit circles+sliders+spinners] remaining, and the current max possible score M
After note hit:
This would just be subtracting out the points you missed from not getting a 300.
M = M-(300-hit value)*(CM*DM*MM/25 + 1)where CM=combo multiplier (the wiki says it's combo before hit-1 but from what I've tested it seems to be combo after hit -1), DM=difficulty multiplier, MM=mod multiplier. For a spinner you would also have to subtract out the points that would have been earned from spinning enough to get a 300.
After missed note:
This would be subtracting out the points you missed from not getting a 300, and then subtracting out all the points you miss out on because your combo is [your previous combo + 1] lower than what it could have been.
M = M-(value of missed note)-300*((Cprev+1)*DM*MM/25)*(# of objects remaining)where the value of the missed note is 300+300*CM*DM*MM/25 for a normal hit circle/slider/spinner (for a spinner: +the number of points you would have gotten for spinning a 300) or 30 or 10 for the slider ticks, and Cprev is the combo you had when you missed.
After missing the end of a slider:
This would be subtracting the 30 points missed from the end of the slider plus the effect from having 1 less combo multiplier for all the remaining notes.
M = M-30-300*(DM*MM/25)*(# of objects remaining)The points lost from getting 100 on the slider would be subtracted in the note hit part.
The spinner bonus could be added to the max:
M=M+bonus earnedSo yeah, your "max score" could go up I guess. It would go up by how much you actually got minus the amount you would have gotten for spinning exactly 300.
Basically, when you start the song, just the total number of objects and the max possible score need to be known, and then the remaining number of objects and new max possible score can be updated every time they change. I've tested all of this on a small sample map and it's worked for that. This concept works because when you lose your combo, when there are the same number of objects remaining you miss out on the same amount of points regardless of what the objects are or in which order they are in.
Having a math degree I can understand the desire to see some kind of proof for a statement like this:
Let's say you are comparing two runs which are the same, but then the second player misses a note after N notes. Using [note pos] as the combo multiplier for each note for the second player if the second player gets perfect, the total remaining score for both players would be
Player 1: sum over all remaining notes[300*((N+1+note pos)*DM*MM/25 + 1)] + spinner points + slider ticks
Player 2: sum over all remaining notes[300*((note pos)*DM*MM/25 + 1)] + spinner points + slider ticks
difference: sum over all remaining notes[300*((N+1)*DM*MM/25 + 1)] /////This no longer depends on the individual note
=300*((N+1)*DM*MM/25 + 1)*sum over all remaining notes[1] = 300*((N+1)*DM*MM/25 + 1)*# of remaining notes.
And then induction for missing multiple notes, or something.
One problem is that there could be rounding errors (I'm not sure how the rounding works so I'm not sure how to minimize them). Maybe at the extreme the projected max could be 500 points off of what you actually scored when there are 1000 notes, but considering that there would only be errors when you don't get 300s and most people don't get 1000 100s on a 1000 note song, it probably wouldn't be that bad.
Finally, if anything's not clear, I could try and explain it better.
