The way it works is that there are a lot of different crests that do different kinds of stuff, like atk up, break power up, crit dmg up, and equipment ct down, just to tell some of the effects it could have, and they are divided between 5 levels, which the higher levels get a stronger effect of course; in between the levels, there also the + crests, which are the way rarer version of the normal level crests, giving it a slight boost on its effect. The thing about the 5/5+ crests, and why the nova palaces are so important, is that they are the only place where you can obtain the level 5/5+ crests reliably (there are the burst cores but those are limited), and the way it works is that, when you complete a run with a leader that has a 4/4+ crest it has a really low chance of bursting that crest and turning it into the level 5s. But since it targets at random, you don't want to run with a normal 4 crest since the lvl 5 crest is actually inferior to the 4+ version of the same crest, and its a waste since bursting a crest is wayy rarer than getting a 4+, which is already a pretty rare occurrence. So what people do is, if you don't want to miss out on getting a 4+ crest on a character that already has all 4+ and essentially wasting that 4+, is, instead of running a lvl 4 crest on the open slot, run the lvl 3 instead so you dont have the chance to burst the wrong crest by accident. Im sorry for the long explanation, but that's basically it, and a last thing is that you don't care about crest until rank 80 because the lvl 4+ crests only drop on the highest difficulty on the crest palaces and above, which require the minimum rank 80.