Winner calculation

How does the winner (and 2nd, 3rd, etc.) get calculated in a tournament? Is it by points? Is it by who advances farther in the tournament? Or is it both?

Here's my idea of how it _should_ work. When comparing two players:
1. If one player advanced farther than the other, they win
2. If they advanced to the same round and then were eliminated, then the player who got more points in that round wins.
3. If that ends in a tie, then go back one round and compare those scores.

That seems reasonable except I thought for the 3rd idea that it was determined based on the score of games between each other.

Oh - right, of course. And there are tiebreaks involved too... So here is my new idea:

1. If one player advanced farther than the other, they win
2. If they were eliminated in the same round, then the player who got more points in that round wins.
3. If that is a tie, then the player who has a higher tiebreak score from that round wins.
4. If that is a tie, then go back one round, and repeat steps 2 and 3.

use the binary comparison sort/rank idea - [part of it e.g. finding 3rd highest - is pretty fast.. see Knuth vol 3] - just google 'donald knuth' if you dont know what i am talking about..

funnily, that algorithm was inspired by considering  'how to decide who came at what position in a tournament' --- now I am suggesting reverse-engineering the damn thing!

Sara Baase's algorithms-book had the best concise presentation of this i've seen - it is prob'ly out of print long since.

Normajean: I'm wondering primarily how they have implemented it, and secondarily what is the proper expected behavior. I know all sorts of methods for sorting, I'm not exactly sure how they are relevant though... can you explain further?

So it was a multi-round tournament where none of you (3-4-5) got to the last round? Did only the 1st place from each of the final 2 groups make it?

Can you point me to the tournament homepage? I'm thinking that the sorting algorithm I posted above is in fact the one they use.

That is an interesting handicap that you ended up having - I hadn't thought of it. Thanks for the response. I think it answers my question also, that they use the final round. It's not clear what things would have looked like if there had been a tie -- maybe they just share the place, as things would have looked like if Zug had tied with the other finalist.

Ozzie: I've forgotten :)

After years as a programmer one builds up a library of implemented algorithms: just copiesand pastes them... and for someone *retired* from programming for years - havent written a line of code since 2000...

I have the books at hand so i'll look it up and get back ...

:) <sheepish>

PS ozzie: thats why I said sorting/ranking. Do you know the fastest algorithm for finding the 5th highest of n numbers; (as n -> inf i.e. complexity theorywise)

ranking is what we want, no?

And deciding *all* rankings = sorting! think about it!

Yes, I have no doubt that once we find a method for comparing 2 items that we can sort to our heart's content, but I'm more interested with the binary comparison.

The algorithm for calculating winners doesn't have to be efficient - there are so few winners anyway. They should work on making the algorithms for calculating losers more efficient.

I'm not looking for efficiency, I'm wondering how they do the comparison.

I am currently in 5 tournaments, this includes both the 3rd and 4th chess.com tournaments in my ratings range. If any of them ever finishes I will be interested in who came in 1st, 2nd and 3rd. 

thinking out aloud:

comparing two items is binary comparison. I did NOT imply that binary comparison gives the answer, in fact what criteria are 'appropriate' to say that A < B or A=B or A > B is the *question* here.

So the algorithm is not relevant here - I *said* I'll 'reverse-engineer' the algorithm - not much work - actually only locating one of the two books - i am in the middle of reorganising stuff - just review what they say to justify their comparison criterion.

I remember this much: 'if A lost to the eventual winner C, and B lost to someone other than C, then A>B stands to reason.'

This means: see their [Baase, Knuth] goal was sorting or ranking - and this 'binary comparison' is leading to --- algorithms inspired by KNOCKOUT tournaments! [A plays B - maybe once as white and once as black, whoever has less points at the end is knocked-out; if draw then rematch or other tie-break way..]

So now it is not at all clear that what  I posted before as relevant to this. Okay, rounds and all, so some ideas may be relevant -- but much less than I thought.

So, interesting question -- will research it in due course.

but those two tournaments ARE knockouts, right? So I may be on the right track... anyway I'll post that in my next post and you all decide whether it is also a satisfactory way...and whether is is in fact equivalent to one of the suggested ways there..

[in a staged-league sort of thing - what is it called --- swiss or something -- anyway there are variants --- various rounds, each round is round robin or at least some players play some players -- and in each round the bottom-so-many are eliminated --- in that sort of thing it would be a nightmare to think of a fair way to decide complete rankings!]

Ozzie said in a message to me that

'My entire post has to do with the how the website calculates winners for tournaments. I want to be able to predict how I will do in one specific tournament I am in right now.'

well i copied and pasted that from the message, so it is exactly what he said.

So now it is not clear what are we discussing here -

    how the website does rankings in a knockout,

            or

    what is a fair way to decide rankings in a knockout.

These are two different questions ...

There are examples of non-first place ties determined by the results of the previous round only.

Sort completed tournaments by players then look at the second page.

NID Tournament: The second players in group 1 and group 2 in round 2 shared third place for the tournament.

Fast Play Only: Two players tied for second in group 2 in round 2 and shared third place for the tournament.