I disagree with the "axiom" because, let's say, someone took 2nd place three times, 3rd place twice, and 4th place twice. It's almost 100% certain that they will be higher than everyone else in the total sum of all stages. And they won't be able to claim the top spot??? :confused:

But how? Let's say you showed such a result - three 2nd places, one 3rd place, and so on. And Vasya Pupkin played twice and took first place, not second. He'll tell you: what kind of leader are you if I beat you twice?

Added after 1 minute
You could calculate it like in Formula 1, where first place is worth a certain number of fixed points, second place is worth another, and so on. But, I guess, since there's already a rating for the race, you should focus on that, it's the fourth stage after all...