I very much liked how the 4e MM was organized. The start of a section would offer up some lore as an intro for the DM. The stat blocks were very easy to run for a DM. Minions! Each would have some suggested combat tactics, and at the end would be some lore based on the DC of a die roll by the players.
Knowing that a monster’s offensive style was based around
brute, controller, skirmisher, lurker would absolutely help a DM know how that particular creature might also behave in a role-play situation.
In fact, if you wanted to emphasize lore/role-play style alongside the stat block…why not add a line out to the side with 3-5 keywords that emphasize the personality style of the monster? Something like:
Over-bearing, abusive, disrespectful
Cautious, sneaky, opportunistic
Voracious, predatory, lurking
Social, cunning, predatory
Daring, intelligent, tactical
Cowardly, brazen in numbers, selfish
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