Mathematically defined by the person who creates the indicator to measure choppiness ina subjective way. If you don't think that the person has to measure choppiness then you might see issues in your trading.
Choppy markets are phenomenal to fade bollinger bands. Figuring ahead of time if it's going to be choppy or not is the difficulty.
market profile shows you where to trade reversion to the mean and where to trade momentum outside the value area. one of the most reliable tools ever when you get the hang of it. also think it's the only "indicator" that the cbot-cme licenses for use.
There will be some times when you switch and the market switches following. The market's periodicity works like this. Certain times, a 20 SMA will get you entirely winning trades. Other days, it will give you completely losers. Specific times, the data you get will tell you the market is choppy and you will switch to a mean reversion system and then the market will change to trending. Generally, a trend indicator is only good for telling you if the market has been trending, instead of if it's going to keep on trending. Regardless, the market can change at any place, so knowing that it has been trending is basically unhelpful. Can someone post an example of when a trend indicator was useful?
This is true of all technical analysis if you view the market as a random walk process. It seems random walk, with all of its' well known short comings is still the best model of market behavior. The switching of regimes between trend and chop (however they get defined) is randomly distributed through time. Anyone can give you an example of a trend indicator that was profitable on a given trade, but they probably can't, or will not, give you one that is quantifiably proven to be positive expectancy. Here's one: Ehlers Zero-lag moving average with an alpha of 0.2. Just follow the slope for long and short entries. Is it a positive expectancy MA? I can't tell you that at this time, not enough trades, but I doubt it will be. I doubt any indicator will be, because of random walk.
chart of the random walk - however when you tame it with standard deviation it becomes a little more predictable as far as timing.