If trader X is buying and averaging down in fixed size and in equal distances for example buy 1 lot every 100 pips , then it is impossible to always have the average entry price near the bottom , it will be exactly in the middle between the first entry and the last one , one would need 50% retracement just to get back to BE .
Ofcourse there could be another version of averaging down , for example first buy every 100 pips then buy every 50 and so on, while increasing size more aggressively all the way down just to try to make the average entry near the bottom , but that wont work every time , at some point you will run out of fuel before seeing the bottom , which will keep your average entry hanging up there way off the bottom . Not to mention the steep drawdowns you will suffer just to get back to BE .
Which brings me to the old saying : martingale works if you have unlimited money .
All of this is just to avoid taking a loss of few pips in the first place while being ok with taking the same amount as profits .