In a round robin system (which, I believe the question to be about), the question is about the difference in strength. If the players have an even distribution of strength, and the differences between the players are rather large, the probability of a scenario you describe occuring increases.
If the best player is 2800, the second best is 2500, the third 2200, 1900, 1600, 1300 etc, odds are, the 2800 player is going to win all the match ups - perhaps only drawing the one black against the 2500.
So in a realistic event, the players are more closely matched up, and the differences in player strength is a lot closer. That makes drawing chances a lot closer. In a real tournament situation, among grand masters, the draw is the most likely outcome.
This means that stronger players will try to push their white advantage against weaker players - and really try to push and win against the weakest player. Not all will succeed.
I bet it isn't hard to put the results of the grand chess tour or the likes into SPSS and work out the empirical evidence - and I bet a mathematician can work out the mathematical odds, but my guess would be that 50% + n/n decisive result, where n is the amount of players in the tournament (so if n=10 than 5 + 10/10 = 6 points or in a double 10 + = 10/10 = 11) is usually enough for a top result.
This is kind of a weird question, but I have these thoughts.
How many points would a player realistically need to be fairly sure of finishing in a certain place in a tournament?
Let's say there is a tournament of 8 players who all play each other twice.
If every player was of different strength and would win all his games against weaker opponents, but lose everything against stronger opponents, the winner would end up with 14 points, no.2 with 12, no.3 with 10 and no.8 with 0 points. So you need 10 points to be mathematically certain of 3rd pace. But in reality, there will be draws and players will lose against weaker opponents, so the player ending up in 3rd place will probably have fewer points than 10.
Alternatively, if all players were of exactly equal strength and would draw every game, except for one player you manages a single win (in addition to drawing everything else), he would be the outright tournament winner with 7.5 points. But of course in reality you're going to need more than that.
Are there any systems or tables that give an indication of how many points a player would normally need to have a fair chance of finishing in 3rd (or first, or any other) place?