OK, let's say you are going to win Stone-Skipping. Choose your car, start your event and make a jump. After your driver makes a couple of skips (or not), pause the game by pressing Esc. You need to do it before „Press Enter to end” text show up.

You will see something like this. Your result is already saved, but the game hasn't given any score to bots yet. Press Enter to continue. You will be placed again on starting point to make a 2nd try. Jump and again pause when your driver will be drown, but before being prompted to press Enter. If the button says „Retry event”, unpause and pause again, until you can continue.

The same story goes on: you already earned some points, while bots are still waiting for them. Continue by pressing Enter. You can't skip the last try, though, but I'm guessing it won't be as much hard to get a 1st place when you had 3 tries, while bots had only one.

You can do this trick on any stunt, but it will work best on those where a final result is a sum of all the tries (like in Soccer, Ski Jump or Basketball). In others it will work too, however it's mostly case of not letting bots getting more than one try, so this may slightly increase your chances in winning.