The reason why the approach rate increases by 1.5x and the reason why you have 2/3 the timing window to hit circles accurately is because everything time-related is multiplied by 1.5. Not because of what you said.benguin wrote:
As for complications with other mods. I'm sure flashlight and hidden might have to be tweaked a bit but I don't see much concern there. For doubletime, the reason why the approach rate increases for doubletime is to accommodate for the change of the speed of the map since higher bpm maps are typically a bit easier on a slightly faster AR (like I wouldn't dare play an [easy] map with AR9). The logic is that if a map is at x AR, then it would be optimal for most players to have the AR at ax+b to accommodate for the increase in bpm from doubletime (I don't know the a and b values, or even if it's a linear function or w/e so sorry >.<) This only works though if the original AR is optimal for each particular player which it isn't. Basically what I'm trying to say, is that if you can change the AR of the map with no mods, you should be able to do the same for the DT mod. Also, the mod is called is called "double time", not "double time plus additinoal AR." The extra AR that's added, is there to accommodate for the faster chart, but with user-defineable AR, people can figure that out for themselves.
Reading confusing patterns with low approach rate is a part of the difficulty in osu!.