A tad too much McMahon?

[Schachus]

I have actually had the same idea that you call layered McMahon and I think it would be better, but I have no way to know, as there ist no such tournament.

It just makes so much sense: you have McMahon, to guarantee appropriate opposition, then you have the top bar to give all strong players a chance for tounament victory, because standings are otherwise unfair against lower ranked players. Now, why should this be limited to the top. Why shouldnt someone in the lower ranks be given a fair chance to place above the guy who is ranked two stones higher and a real risk to place below who is two stones lower by making them play similar opposition(at least from the start, they might diverge if they really do better/worse then you, as expected) by basically having a bar every couple of stones? Its not like high-dans would sudenly need to play mid-kyus, so games would still be interesting for everyone.

[Pio2001]

Realistically speaking in big tournaments like Euro go congress where you have 400+ players with 5 rounds if you are a 10 kyu who plays on high dan level you can win all 5 games only to end up on 10th place or something.

The problem is that it is also true if you play at your 10 kyu level. You might well win your 5 games, meeting only players as strong as yourself, while the 7-9 dan players, all meeting each other, have 4 wins only.

To fairly get the first player right among 400, you need at least 9 rounds.
To fairly rank everybody according to their number of victories alone, you need 399 rounds.

[Javaness2]

To be valid, the McMahon system should be able to place above the bar only those players with a chance of winning. It can't really well cope with 6-dans declaring as 1-kyu. I suppose that another option for Elom to avoid the regular McMahon would be for him to organise a league on KGS / IGS / OGS for BGA members (and recognised by the BGA). Such a league could have stronger players in it, and could be submitted for rating with the EGD.

[Uberdude]

There is already the BGA online league: http://britgo.org/bgaleague.html. Maybe Elom would like to play in that? Its teams are usually geographic, but I'm sure Elom could find a place to play (I once played for Belfast when Cambridge had no team). There's also a youth team, for which he would probably be first board so get to play lots of stronger players.

[Elom0]

Ironically, the year i mentioned this, Sandy Taylor was unfairly robbed of his win in the London open due to the McMahon System. So I've been vindicated? And maybe the solution is that when using McMahon, the final result should be based on your score combined with your SOS for a S+SOS score.

[Fenring]

When someone does not start in the top group, he has weaker opponents.
So there will always be a difference in SOS.
So the score+SOS would not change anything.
I find it funny to say that someone has been unfairly robbed, and to propose a fairer system that leads to exactly the same result.

I'm not sure that the system of one Mcmahon point for 3 levels is better, for me it is too random.
Let's imagine that the 7,8 and 9k have the same macmahon score.
Then in a 4 round tournament an 8k who would win everything could have faced,
in the best case:

a 7k,a 4k with 0 wins, a 1k with 0 wins, a 1k with a win.
in the worst case:
a 9k,a 9k with 1 win, a 9k with 2 wins, a 9k with 3 wins.
for a less unlikely case:
a 9k, a 9k with 1 win, a 6k with 1 win, a 6k with 1 win(after round 3 in this system, 1v for a 6k is most likely).

3 very different cases, for the same player with the same results.


I totally agree with Pio2001 ,it's not possible to have a perfect system.


In my opinion, two things could be improved:
-in addition to a majority of McMahon tournaments, make sure there are a minority of Swiss tournaments(championships).

-Make sure that the ranking system works well. Specifically, we sometimes see players who after winning everything don't get the GOR of their strongest opponent. To me, these are the players who are penalized, because not only did they not play balanced games, but they still don't have the rank for which they performed.
The French ranking system use a specific calculation for this.
If a player wins more than X points at a tournament, the whole tournament is recalculated by giving this player his initial GOR+X.

Not only does the under-randed player win more points, but his opponents lose less

And i don't know why this system is not in the european rating system.

[pwaldron]

When I played in Canadian tournaments the practice was to cluster players into McMahon bands that were separated by 2 points. For tournaments of moderate size (~30-50 people) there tended to be breaks in the distribution of players that facilitated natural bands.

The effect of the larger gap between adjacent groups was that players tended to play more games within their group before being paired up.

I can't comments on the theoretical merits, but it certainly produced a good series of games and I never felt disadvantaged. Tournaments run like this tended to run over two days and have six rounds. I'm not sure what the practice elsewhere in the world.

[Elom0]

When someone does not start in the top group, he has weaker opponents.
So there will always be a difference in SOS.
So the score+SOS would not change anything.
I find it funny to say that someone has been unfairly robbed, and to propose a fairer system that leads to exactly the same result.

I'm not sure that the system of one Mcmahon point for 3 levels is better, for me it is too random.
Let's imagine that the 7,8 and 9k have the same macmahon score.
Then in a 4 round tournament an 8k who would win everything could have faced,
in the best case:

a 7k,a 4k with 0 wins, a 1k with 0 wins, a 1k with a win.
in the worst case:
a 9k,a 9k with 1 win, a 9k with 2 wins, a 9k with 3 wins.
for a less unlikely case:
a 9k, a 9k with 1 win, a 6k with 1 win, a 6k with 1 win(after round 3 in this system, 1v for a 6k is most likely).

3 very different cases, for the same player with the same results.

Heh, my bad! I clearly meant SODOS in my head but typed SOS. I'm such a duh-brain. Sandy Taylor beat the winner Sai Sun and runner up Andrew Kay. S+SODOS respectively is 41, 43, 36 so it would put him in second place which seems more accurate to what the right result should be! 2015 london open https://britgo.org/results/2015/london

I totally agree with Pio2001 ,it's not possible to have a perfect system.


In my opinion, two things could be improved:
-in addition to a majority of McMahon tournaments, make sure there are a minority of Swiss tournaments(championships).

-Make sure that the ranking system works well. Specifically, we sometimes see players who after winning everything don't get the GOR of their strongest opponent. To me, these are the players who are penalized, because not only did they not play balanced games, but they still don't have the rank for which they performed.
The French ranking system use a specific calculation for this.
If a player wins more than X points at a tournament, the whole tournament is recalculated by giving this player his initial GOR+X.

Not only does the under-randed player win more points, but his opponents lose less

And i don't know why this system is not in the european rating system.

If a person wins consecutive games, then their McMahon score increases by the number of consecutive wins they've had up to that point plus one. So when they lose it resets to zero plus one and they need to win consecutive. If a person skipped a game then tthey'll still get the consecutive win points if all the games they last played were won games, but of course they would be behind by the number of rounds they skipped. This seems fairer.

Another solution might be to start of tournaments with a series of fast games worth fractional McMahon points, for the first third or so of the tournament by total time. For example, three fast games each worth a third of a McMahon point, and then two games three times slower each worth a whole point!

[Fenring]

Heh, my bad! I clearly meant SODOS in my head but typed SOS. I'm such a duh-brain. Sandy Taylor beat the winner Sai Sun and runner up Andrew Kay. S+SODOS respectively is 41, 43, 36 so it would put him in second place which seems more accurate to what the right result should be! 2015 london open https://britgo.org/results/2015/london

Your system work better in that particular case, but he is very unfair in a lot of other cases.
For example, in the Open London, if we have one undefeated player,the victory vs the 2th give him only a +8 S+SODOS score, so it means it is possible the only undefeated player of the top group lose the tournament if his early opponents do a bad tournament.
Not fair.

If a person wins consecutive games, then their McMahon score increases by the number of consecutive wins they've had up to that point plus one. So when they lose it resets to zero plus one and they need to win consecutive. If a person skipped a game then tthey'll still get the consecutive win points if all the games they last played were won games, but of course they would be behind by the number of rounds they skipped. This seems fairer.

Not really.
The systems seems totally unfair for the top-group if there is no undefeated players.
For the non-top there can be other problems too.
We can imagine a 5k,after 3 rounds he did 1win-1 loss-1win. So he play like a good 5k.
His opponent can be a 10k who did 3 wins, and for the moment just play like a 7k.
So its not fair for the 5k player, with his results, he should have oportunity to play agaisnt stronger player,we give hima opponent who most probably is 2k lower.

Another solution might be to start of tournaments with a series of fast games worth fractional McMahon points, for the first third or so of the tournament by total time. For example, three fast games each worth a third of a McMahon point, and then two games three times slower each worth a whole point!

As said Pio2001,we are limited by number of rounds. Yes, with a full blitz tournament we have better rankings.
But this mix-system seems totally bullshit.
What happens if the best 2 players of the tournament play each other at the 3th round, then have no defeat, we consider it is fair, to decide the result of a slow tournament on a blitz?

[Elom0]

Heh, my bad! I clearly meant SODOS in my head but typed SOS. I'm such a duh-brain. Sandy Taylor beat the winner Sai Sun and runner up Andrew Kay. S+SODOS respectively is 41, 43, 36 so it would put him in second place which seems more accurate to what the right result should be! 2015 london open https://britgo.org/results/2015/london

Your system work better in that particular case, but he is very unfair in a lot of other cases.
For example, in the Open London, if we have one undefeated player,the victory vs the 2th give him only a +8 S+SODOS score, so it means it is possible the only undefeated player of the top group lose the tournament if his early opponents do a bad tournament.
Not fair.

If a person wins consecutive games, then their McMahon score increases by the number of consecutive wins they've had up to that point plus one. So when they lose it resets to zero plus one and they need to win consecutive. If a person skipped a game then tthey'll still get the consecutive win points if all the games they last played were won games, but of course they would be behind by the number of rounds they skipped. This seems fairer.

Not really.
The systems seems totally unfair for the top-group if there is no undefeated players.
For the non-top there can be other problems too.
We can imagine a 5k,after 3 rounds he did 1win-1 loss-1win. So he play like a good 5k.
His opponent can be a 10k who did 3 wins, and for the moment just play like a 7k.
So its not fair for the 5k player, with his results, he should have oportunity to play agaisnt stronger player,we give hima opponent who most probably is 2k lower.

Another solution might be to start of tournaments with a series of fast games worth fractional McMahon points, for the first third or so of the tournament by total time. For example, three fast games each worth a third of a McMahon point, and then two games three times slower each worth a whole point!

As said Pio2001,we are limited by number of rounds. Yes, with a full blitz tournament we have better rankings.
But this mix-system seems totally bullwaste.
What happens if the best 2 players of the tournament play each other at the 3th round, then have no defeat, we consider it is fair, to decide the result of a slow tournament on a blitz?

Well, if a player is undefeated only because they played weaker players, then I'm not sure how that's unfair! And also, if two players meet in the blitz phase of a tournament, that shouldn't necessarily stop them from meeting again in the slow phase.

Hmm, regarding the 10k and 5k, it can easily be set up so that among players with the same McMahon score, those with the most similar initial McMahon score--kyu/dan--are paired against each other. So it doesn't seem like a big deal! I guess.

[Fenring]

I probably didn't make myself clear. So I'll detail an example to make it clearer:
Imagine a tournament:
We named the best player A, the second best player B. Both in top-group
At round 1, A won against C and D, B won against E and F.
A and B won all their others games until last round.
At last round, A won against B and A is the only player of the top-group to be undefeated.

With classic McMahon System, A won the tournament.
With your system(score+SODOS), if C and D do a worst tournament than E and F, it can be enough to have player B ranked first(B who lose vs A)
It means, a member of the top-group can't win the tournament even he won all his games, and won against his direct opponent.

This is not fair.

Same for blitz phase, even if you allow them to meet against, this may not be the case.

"those with the most similar initial McMahon score kyu/dan are paired agaisnt each other", it solve nothing,when you play a guy with same initial rank than you, it is the classic Mcmahon pairing. But with unfair ranking.
the 10k won against a 10k in round 1, a 10k in round2, a 10k in round 3, and a 9k in round4(no more 10k undefeated),so he will have a 1k Mcmahonscore?
And will be same score than a 3k,who did 2 won and 2 defeats against 3kyu?

All theses ideas seems to have very big flaws.

[kvasir]

I think the McMahon troubles at the 2015 London Open shouldn't be blamed on the players that won most of their games. If it is anyone's fault then it would be the four players in the top group that won two or less games in a seven round tournament. Another reason is the small top group, this is a BGA policy that I can't explain. I know there was a simulation study into the size of the top group but I only remember that the results were controversial, not if they recommended a larger or a smaller top group but I think it was done before this event.

Basically, you can get into trouble because of the composition of the top group. If the top group is very big there is a good chance that the top players never meet in the tournament (too few rounds) and if the group is too small it is possible that it is much easier for a player in the second group to win every game in the tournament than it is for a player in the top group. It is also usual for the top players to draw on McMahon points unless a player wins every game. More trouble ensues when many players in the top group underperform, in this case the ranking of the top players may effectively be decided by a small number of games, assuming we can discount any games with the underperforming players as automatic wins but this is maybe only our perception in hindsight when we already know how these players performed.

[Elom0]

Well, E and F will have to win over twice as many games as C and D overall, and being above the bar D must've won to have played A so they already have the same number of games after 2 rounds. I'm not sure if that's more or less likely than the situation I'm trying to solve, so. But if it's changed to S+(SODOS/2) or even recursively S+(SODOS/2)+(SODODOS/4) . . . then that seems to solve the problem

Pairing people with similar initial McMahons though was just off-the top of my head, and yes, it actually seems terrible. And yes, the original idea doesn't quite work, okay, but again with the same tweaking it may make things better.

So again, halving the weight so that a player gets an extra half a point for each consecutive win.
And instead of those points being added to the McMahon score, they are treated as a separate additional score for determining pairings that have no effect on the final score.

Now if we combine the two systems together, it becomes a lot more unlikely for E and F to win twice as many games as C and D since the difficulty of opponents increases the more you win, which makes counting S+(SODOS) or more preferably S+(SODOS/2)+(SODODOS/4) . . . much better!

[Elom0]

And also this also makes the blitz phase more useful, although it seems it could always be useful!

[Harleqin]

I believe you can try out tournament systems with a rather simple statistical simulation.