Stamina is what all the talk about object density is about. Breaks, sliders, spinners are areas with low density... areas with less time between notes are high density. However, if you're looking for information on how long and fast bursts are, that would be the realm of streaminess. It's best to keep things in the stats used as independent as possible... having stats that always move together means that you've screwed up and should have combined them into a single stat.
HakuNoKaemi wrote:
Instead of the Difficulty Setting, why not use something like
Drain ( 0 - 10 ) - HP Drain Rate
Precision ( 0 - 10 ) Mix of OD and CS (since higher CS means higher aiming precision and higher OD means higher clicking Precision)
Stream ( 0 - 10 ) - How Fast and Long are the Streams? How many are present?
Jumps ( 0 - 10 ) - How Long are the Jumps? How many Jumps?
Speed ( 0 -10 ) - Depending on Average Notes Distance and Approach Rate
could be a way to upgrade the Difficulty rating system too.
Things like Drain, OD, and CS shouldn't be part of a secondary chart. They're too important... they're not stats that tell you what the map is like, they're parameters that tell you the rules you'll be playing under. Besides, combining OD and CS is silly... the precision that affects OD isn't spacial, it's temporal. CS affects jumps and movement rate stats, because there the size of the target affects how difficult it is to hit. With OD, the change to timing windows means potential more 100s, and with a high DR, that can kill if you're not careful. But that's not important to combine... these are parameters that tell the player the rules of the game, they should be up front with the object and length information, always in sight, regardless of whether the player has up global/local scores or a star map. And that request has been made elsewhere.
Stream and Jump are pretty much universally consented. They're definitely important and what people want. The thing is that they refer to the burst rates of their domains (time for Stream and space for Jump)... they don't give a picture outside of that. Which is why there should be a measure of the base time and space rates as well. Base time is object density, stamina, effective BPM (which is to say, not the BPM of the song, but the BPM experienced in the map). Base space is a measure of the movement of a map, it's velocity, beat spacing, and slider speeds. Stream and Jump are the extremes that those go to.
Chaos has also been brought up a lot, but nobody seems to have presented a picture of what it would be. Well, if chaos is a measure of the entropy of a map, we need to consider what entropy is. Entropy is essentially a measure of the number of states of a system. Consider a glass, it's solid and has a certain shape. The way it's atoms can be arranged in that glass is large, but it's miniscule compared to the number of states if you throw the glass on the ground and break it... where the number of pieces and their shapes and there positions relative to each other adds a nigh infinite number of new positions. And so the glass has gained a lot of entropy by being broken.
What does that mean for osu!... well, consider a stream of 12 overlapping circles in straight line. When such a thing comes up in a map, it registers essentially as one object... it's like a slider, but you need to hit notes instead of holding them. From a stamina point of view, that adds something, but from a mental chaos point of view, it's the same, the stream can be processed as one thing. Now consider replacing one of the circles with a repeating slider. It has a different length than the rest, is a different type of object, and can had a variety of lengths (depending on the number of repeats), and could occur in any of the twelve spots... suddenly the processing has become more than one thing, it's gained some entropy. Take those twelve circles and have them bouncing around in a pattern, and you can get more entropy yet. Add a complex rhythm and you add more possibilities and entropy... add some emphatic spacing for that rhythm (ie jumps, changes in beat spacing) and you add even more.
So what I'm thinking for a way to measure entropy, is that you need to look at adjacent intervals between objects (under various size windows... I'd consider using combo groups as a width for windows (ie 1 group, 2 groups, 3 groups), because they should delineate patterns in the map to some degree). If they represent different notes or have different beat spacing, then entropy is definitely higher than a map of 1/2 beats that trudges around the map at the same beat spacing. Pattern entropy is a harder thing to measure. A simple way that might be worth looking into, is to consider changes in angle between intervals. A straight line is just 0, 0, 0... (note that we're talking change in angle (delta) so the exact direction doesn't really matter, only that each circle heads in the same direction). A slightly curved line might not be more complicated... say, 5, 5, 5 (degrees). Regular polygons (and polygrams) would also register as simple recognizable patters (ie squares would be sequences of 90s). Jumping back and forth from a series of radial points adds a bit more complexity: a 180 to get back to the center, alternated with the angle to the next poiint... as would a zig-zag. Random jumping around would be random. There are a number of ways to potentially analyze such things... one would be to look for cycles and other patterns, but a simpler way might just be to look at the numbers within a window and see if there are one or two dominant values. In the end, a lot of experimentation with real map data will be needed in any case to work out what the weights of any of the factors should be (and how they might combine... ie a sudden change in direction combined with a note of a different duration than anything around it combined with a change in beat spacing). Although, you could also try to apply machine learning to working out the factors... although, then you'd still need reliable expert opinion on what the values should be to teach it.
Anyways, there's a brain dump on "Chaos" as a stat for you.