I don't know whether it's coincedental but I've found through playing, that the better relations you have, and with the greater number of countries the less anti-badboy wars hit you. Two examples; playing as Bohemia, not much of an income, and a gradual expansion thanks to defensive annexing, and the occasional offensive war. Around 1700 I inherited Hungary, and the world spat at me. 9-10 countries at a time tried to tear me to shreds. I had a badboy of around 15, lower than either France or Spain, but I never had enough money or diplomats to foster relations with anyone other than my allies.
Played as France, and decided it was time to paint the world blue. Took Milan and some of Caribean early, and then through peacefull annexation, and reclaiming French land from Spain by 1700 I had all northern Italy, central Germany as well as the French CB provinces. Throughout the game I regularly shipped money around my allies, and all Europeans that were not my targets or natural enemies. The result, only 1 badboy DOW on me during the entire game. Was elected on and off to HRE, and my allies also gained, Papal States had the rest of Italy, Scotland took most of England, and Holstein took a lot of North Germany. I had a badboy in the 20's for most of the game, but the world turned on Poland, badboy rating was lower than me, and attacked until Poland was down to 3 provinces. When a large alliance turned on me, half the allies dropped out, possibly because I had a better relationship with them than their alliance leader.
Now this certainly is not scientific evidence, but a similar thing has happened before, sending money round Europe appears to decrease the badboy effect, though not the badboy number.