It also depends on how much you know about a stock. As you said,...

It also depends on how much you know about a stock. As you said, there are literally 1000's of stocks you can invest in, but how much do you know about them? It's impossible to have the same intimate knowledge of what's going on in all those stocks, eg. The prevailing sentiment, the future direction, etc.
I personally make my decision to average down on a stock based on fundamentals and based on what has actually transpired in the past to get the company to the present state. Like, a company drills up a duster, that's a huge red flag, so I won't average down.
If it's because a company has the goods, but had sh!tty luck, macros turned against them temporarily, I will average down because I still believe in my original investment. The low price invokes my earlier desire to buy the stock at a lower price, and that overwhelms the fear.
hope I made sense there, lol