Ideally, you would want someone with 1 first, 0 seconds, and 99 thirds to be rated better than someone with 0 firsts, 100 seconds, and 0 thirds; while someone with 99 firsts, 1 second, and 0 thirds is rated better than someone with 99 firsts, 0 seconds, and 1 third.
Look, I know this is just going to be one of those agree-to-disagree type deals, but I feel I have to say something to this lest you think that this is a universally accepted truth.
I think this way of looking at things is fundamentally wrong.
To me, it is really obvious that someone with 1st-2nd-3rd results of 1-0-99 is a much worse player than someone with 0-100-0.
In terms of demonstration of skill, being consistently at the second-place level is a much better indicator of a decent player than being consistently third with a single win.
I would dismiss that single win as a fluke, as would any sort of statistical analysis of those datasets.
For a real world demonstration,
have a look at how international tennis rankings work.To keep it simple, we'll pretend that those are all wins, runners-up and semi-finalist results at the Grand Slam level (and ignore the loss of points over time).
1-0-99 gives 73,280 points, 0-100-0 gives 120,000 points.
Golf is similar.The winner gets 100% of the tournament's ranking value, second place gets 60%, third gets 40% and so on.
So, really, it is absolutely contrary to standard thinking to say that 1st is "infinitely better" than 2nd which is "infinitely better" than 3rd.
Don't get me wrong, I feel very strongly that you should play
as if this is the case, and I am fairly sure that professional athletes would also.
You should always strive to come first and if that's not possible you should try just as hard to come second.
But if the rankings are so heavily weighted in favour of wins that a single win outweighs 100 second-places, where is the incentive to keep trying once the win is impossible?
TL;DR Yes, first is better than second, but consistency is more important than fluking a win.
Also, sorry that this has gotten so far off-topic.