@GameplayerMcGee I assume by "gladiator" you mean the level 7 monster with the shield. There's definitely a pattern, you just need a ton of games to see it. There's always 4 of them, one per quadrant of the board. The grid is 13x10 so each quadrant ends up being roughly 6x5, excluding the dragon's column. After observing countless runs (you can just click the dragon early to die instantly and see the whole grid), I've never seen one spawn on the dragon's row either. So they basically avoid the central column and the dragon's row entirely.
One detail that's really subtle on the devs' part: each gladiator's shield marks which quadrant they belong to. The center of the shield has a 2x2 yellow square, and one of those four pixels is red. The position of the red pixel inside the 2x2 maps to the quadrant. So the top-right gladiator has the red pixel in the top-right corner of its 2x2, and so on.
About rats, they're not totally random either. Their sprite tells you where the rat king is relative to them. If a rat is facing right, the king is somewhere in a column to its right. If it's facing left, king is to its left. If it's standing upright facing forward, it means the rat is in the same column as the king. And once the rat king dies, all rats switch to that standing pose.
Bats, skeletons and green slimes I haven't been able to figure out either, they just seem to be filler. Their role seems to just be contributing their level to the danger numbers around them. If anyone else spots a pattern there, let me know.