Hello, I'm trying to understand the best approach to model the probability of a stock move. My initial approach, however naive, was to create an X day rolling average of the stock prices over the trading history, then create a cumulative distribution function to determine what the probability was of a stock price being at or above a certain level X days from now

Ok, its im the ballpark probably somewhere. But recently I thought that, the probability must be somehow related to the current volatility estimate of the stock. If the stock's IV is very high right now, but for a large majority of the past it was very low, then the probability should be higher than what my rolling average analysis returns.

This lead me to discover the "Expected move" formula, which does seem to incorporate volatility. However, the classic expected move formula returns a range of prices for which the stock will be within 1 standard deviation over the time frame in question.

How could I rework this equation to answer my original question, or is there an alternate equation which incorporates volatility to get an estimate for the probability of a stock move?

Thanks for considering my questions. I am relatively new to this field but very eager to learn.