Random event results are inversely related to need.
If you have no money, you are forced to take a loan
If you have a lot of money, you never get to spend it via event
If you have no navy, you get free ships
If you have too much infantry, you get infantry
If you have too much cavalry, you get cavalry
If you are in the first two centuries of play, you get cannon
If you are finally able to use cannon, you get no cannon
If you get a RM, it is with the nation you were about to DOW
If you get a relations boost, it is with the nation you were about to DOW
If you get a relations hit, it is with the vassal you are about to annex
If you have high centralization, you lose centralization
If you have high quality, you lose quality
If you have low inflation, you get an inflation reduction
If you have high inflation, you get an inflation increase
If you have good stab, you get a stab hit
Only Exception:
If you have bad stab, you still get a stab hit