It's time I make a very lengthy post again.
Stats for CtB:
Spacing difficulty (Dist)
This stat is an alpha of the jump difficulties. Each note has a difficulty assigned to it based on it's placement.
Since CtB is a constantly moving game, it's not just based on the distances between each fruit, but also the leading fruit. So, each fruit has their set difficulty to get to the next fruit, with an addition of the difficulty from the previous fruit's difficulty.
Control action speed (Speed)
Speed is the amount of rigorous hand movement and coordination required to catch the fruits in addition to the BPM.
Accuracy of movement required (Acc)
This is determined by the circle size, as well as the sliders involved. Not a big stat but can be more powerful with wild sliders and sliders going beyond walking speed as well as fruits getting very small.
Approach rate difficulty (App)
Higher AR rates are more difficult in terms of difficulty and are based on the time the fruits are on screen. AR11 is 1.5x more difficult than AR10.
Mods
and how they affect the game and difficulty.
Difficulty Increase
Hidden
This mod provides less visibility. In this case, it makes it harder to be accurate with the fruits, and requires a little more timing ability. Difficult jumps become increasingly harder. This isn't too much of a difficulty increase but it's enough to be very notable in jumpy maps. Low approach rates also make this mod a tiny bit more difficult because of how much more memorization is required. It becomes only slightly less difficult with higher and approach rates.
Slight boost to:
+Acc
Good boost to:
+Dist (Depends on AR a little too)
DoubleTime
This mod provides increased beatmap speed. This also means increased approach rate, increased need of control, and increased need for jump movement. This is the more difficult modifier of the two 1.06x score increases. This can also increase little slow streams into something more difficult.
Slight boost to:
+Acc
Good boost to:
+Dist
+App
Big boost to:
+Speed
HardRock
Also popular among players for the instant ticket to AR9.8 and AR10. It makes the fruits smaller and increases the approach rate where it can be increased. It makes it more difficult to get a good accuracy as well. It also scrambles the fruits a little, so the distance difficulty should be calculated as if the map were scrambled up with HardRock.
Good boost to:
+Dist
+App (Depends on the AR, it maxes at AR10)
Big boost to:
+Acc
Flashlight
Still the most powerful of the 1.12x score mods, is Flashlight. It provides limited visibility, including difficulty in seeing large jumps and getting good accuracy. It makes approach shorter because of the limited visibility above, as well.
Good boost to:
+Acc
Big boost to:
+App
+Dist
Difficulty Decrease
NoFail
his mod does nothing except prevent you from failing. No stat change whatsoever.
Easy
This modifier tones down the stats of the map, but not the notes. this includes reduced difficulty on needing to aim at jumps, the accuracy involved, and the approach rate. When joined with hidden, this increases the difficulty of aiming a little when AR is very low.
Slight decrease to:
-Dist (Except when AR gets low when used with hidden)
Good decrease to:
-Acc
Big decrease to:
-App
HalfTime
also a powerful difficulty reduction mod in it's own speculation. It reducdes speed as well as the approach rate and hit aim requirement a little, being the exact opposite of DoubleTime.
Slight decrease to:
-Acc
Good decrease to:
-Dist
-App
Big decrease to:
-Speed
I hope this helps you. In a lot of cases, you can't just use a % change for maps when using mods. It just doesn't work, with how diverse maps are.
I also think that my definition on jump distance here might rectify the "Long jumps being uber powerful" thing. In some cases they are though (Like Wild eyes and Go Berzerk, they have those jumps all over)