Jürgen HubertWhile reading German folk tales, I am repeatedly struck by the notion that "random encounters" in typical #dnd -type #ttrpg settings are assumed to be _combat_ encounters. While direct attacks by supernatural creatures _do_ occur in folk tales, it is far more common for them to appear, frighten the bejeezus out of a witness, and then vanish again without lasting harm.
Yes, that huge cat with the glowing eyes is scary, but as long as you don't attack it, it won't bother you. A headless horseman might travel along the road, but that doesn't mean he will necessarily try to run you down. And if the Wild Hunt passes overhead, just throw yourself on the ground and you will be safe. And that "little grey man" might shout "Heh! Heh!" and then simply scuttle off into the undergrowth.
This goes even more for more "natural" creatures. Attacking a full party of armored adventurers is a decidedly odd action, if you think about it - creatures who have co-existed with humans will usually have learned to be careful around them, or go extinct. Even if they _do_ attack humans for food, it's more likely they will go after lone stragglers than an entire group of people. So if they attack an adventuring party, they must either be _really_ confident about their success, or too aggressive or stupid to care about their odds.
So if a predator comes across an adventuring party, it needs a reason to attack them outright. If it is defending its territory, it will likely make some threat displays first, since combat is always risky. If it is hunting for food, it will likely follow the party for some time and observe if there is any specimen that might get separated from the herd - but it might give up if the party shows no obvious weaknesses.
So what I am trying to say is: Some random monster charging the PCs in the wilderness is an option, but it should be less common the monster observing or passing by the PCs without actual violence.
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