after maybe a thousand nights camping in the Sierras I've had 2 big cats come to my camp, one by mistake, and one was stalking my wife and I, both ran away but the one I had to yell at 3 times and wave my arms to frighten off. Both of these incidents together gave me a life total of about 6-7 seconds of seeing wild cougars. I HAVE been threatend by deer though.
These are my own opinions based on wisdom earned through many wrong decisions. Your mileage may vary.