When should your boss run away from a fight? There are several different things you can do by having a boss flee.

First, since it’s not really an unbelievable action for most creatures if they find themselves in a tight spot, it can be used to make the party feel powerful. That works best if you intend to have them catch up easily.

Second, it can initiate a chase. To use a chase boss correctly, you should have the end point of the chase well defined, and the boss should have ways to set traps and trip up the party. That way when they turn to fight the party is already a little drained from the chase, making a more challenging battle.

Third, you may want to use the boss again. This will absolutely feel cheap if the party is already halfway through beating the boss, so you should be careful how you set this up. The main point is that the boss has a plan A and a plan B, and plan B is to escape. The boss puts plan B into motion either as soon as it’s become clear plan A has failed, or as soon as plan A no longer requires them to be present. If it takes more than a couple of turns for that to happen, the party is winning, and you didn’t set up the idea that the boss has an escape route in advance, then it’s probably better to just let the boss fall.