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Round Robin Drop Out

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Terry Faust

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Jan 14, 2012, 12:50:29 PM1/14/12
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How would you handle this situation and would it be handled
differently in a very high level event.

This occured in our extend teams even in ACBL land (one match played
about one per month).

There is a round robin phase of six matches and top 4 or 8 teams make
it into the KO phase.

In the first RR match team A plays team B in a normal match. Then
team A completely drops out of the event (no ethical problem, they
just can't make the rest of their matches).

Does the result of the A vs. B match count or is it thrown out since A
cannot play their remaining five matches?

If it stays, what result do you give to the other five teams that team
A was scheduled to play. There are more than six teams in the RR. The
Conditions of Contest has a clear default formula. (Of course the
result of A vs. B was lopsided or we probably would not be asking.)

Thanks.


Travis Crump

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Jan 14, 2012, 1:12:25 PM1/14/12
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If it were really a round robin format I would just not count the
result. Since it doesn't in fact seem to be a round robin I would count
the result and give the other teams the equivalent of their average result.

Mark Brader

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Jan 14, 2012, 1:14:01 PM1/14/12
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Terry Faust:
> How would you handle this situation and would it be handled
> differently in a very high level event.
>
> This occured in our extend teams even in ACBL land (one match played
> about one per month).
>
> There is a round robin phase of six matches and top 4 or 8 teams make
> it into the KO phase.
>
> In the first RR match team A plays team B in a normal match. Then
> team A completely drops out of the event (no ethical problem, they
> just can't make the rest of their matches).
>
> Does the result of the A vs. B match count or is it thrown out since A
> cannot play their remaining five matches?
>
> If it stays, what result do you give to the other five teams that team
> A was scheduled to play. There are more than six teams in the RR.

If the RR phase is 6 matches, then presumably there are 7 teams --
A, B, and 5 others.

> The Conditions of Contest has a clear default formula.

Then that answers the question, doesn't it? The played match stands,
and the other 5 teams get the prescribed default-win score.

> (Of course the result of A vs. B was lopsided or we probably would
> not be asking.)

Well, these things happen.
--
Mark Brader, Toronto "Remember that computers are very,
m...@vex.net very fast..." -- Steve Summit

My text in this article is in the public domain.

David Stevenson

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Jan 14, 2012, 5:29:33 PM1/14/12
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Terry Faust wrote
Of course the simple answer is that the CoC should cover this specific
case. But here have been arguments about this sort of thing for years,
yet even so, organisers fail to allow for it.

In my opinion once a contestant has a legitimate result against
another contestant, that result should not be taken away from them.

Following the EBU's approach [no reason why you should, of course!]
let the result stand, and give everyone else the VPs for 1.5 imps per
board in their match.

--
David Stevenson Bridge RTFLB Cats Railways
Liverpool, England, UK bluejak on BBO Mbl: +44 7778 409 955
<webj...@googlemail.com> EBL TD Tel: +44 151 677 7412
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Steve Foster

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Jan 15, 2012, 8:04:15 AM1/15/12
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I hesitate to argue with David, but according to the EBU White Book:

"145.2 All-Play-All event – withdrawal
If a contestant withdraws before half of the event is
completed, all scores obtained
against that contestant are cancelled. "

And

"145.4 Not All-Play-All – withdrawal part way through a session
If a contestant withdraws before half of the session is completed,
all scores obtained
against that contestant are cancelled. "

So the standard action in an EBU event would appear to be to cancel the
score for A v B.

(when you say a RR phase that produces 8 leading teams, I assume you
mean the field is divided into groups that play RR within the group, so
not an all-play-all event)

--
Steve Foster
For SSL Certificates, Domains, etc, visit.:
https://netshop.virtual-isp.net

Henk Uijterwaal

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Jan 16, 2012, 5:10:16 AM1/16/12
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On 14/01/2012 18:50, Terry Faust wrote:

> There is a round robin phase of six matches and top 4 or 8 teams make
> it into the KO phase.
>
> In the first RR match team A plays team B in a normal match. Then
> team A completely drops out of the event (no ethical problem, they
> just can't make the rest of their matches).
>
> Does the result of the A vs. B match count or is it thrown out since A
> cannot play their remaining five matches?

If this event was played here, the result of the A-B match would be thrown
out, effectively reducing the round-robin to an event with a team less
than originally planned.

Henk

--
------------------------------------------------------------------------------
Henk Uijterwaal Email: henk(at)uijterwaal.nl
http://www.uijterwaal.nl
Phone: +31.6.55861746
------------------------------------------------------------------------------

There appears to have been a collective retreat from reality that day.
(John Glanfield, on an engineering project)

Frances

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Jan 17, 2012, 7:56:46 AM1/17/12
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Well as everyone has already said, and you already know, it's much
better to define what will happen in advance because otherwise you
have a very difficult decision and there will be accusations of bias.

The general approach tends to be that
- If someone drops out 'very early' having played 'very few' matches,
then you throw out the results
- If someone drops out 'very late' having played 'most of' the
matches, then you include all the results so far and use your CoC's
default formula for the remaining matches.

The problem comes with the definition of 'early' and 'late': the EBU,
as quoted by Steve, usually split at the half way point.


p.s. I like our county league's default formula: with a 20-VP scale,
you get the highest of:
1. 12 VPs
2. Your average over all the other matches
3. 20 - the defaulting team's average over the matches it has played

Steve Foster

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Jan 18, 2012, 5:27:08 AM1/18/12
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Frances wrote:

> p.s. I like our county league's default formula: with a 20-VP scale,
> you get the highest of:
> 1. 12 VPs
> 2. Your average over all the other matches
> 3. 20 - the defaulting team's average over the matches it has played

Which we have, of course, adopted from the EBU.

Frances

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Jan 18, 2012, 7:48:37 AM1/18/12
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On Jan 18, 10:27 am, "Steve Foster" <stevefos...@invalid.invalid>
wrote:
Interestingly the EBU Premier League gives you something different,
rather than your average or the complement of the opponents' average
you get

Average (e.g. 15 on a 30-VP scale) + {your average - their average}

So on the WBF 30-VP scale, capped at 25 for the winning team, you get
at least 18, but if, say, your average is 19 and theirs is 14 then you
get 15 + (19-14) = 20, rather than the 19 of your average.

Steve Foster

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Jan 18, 2012, 12:47:56 PM1/18/12
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Frances wrote:

> On Jan 18, 10:27 am, "Steve Foster" <stevefos...@invalid.invalid>
> wrote:
> > Frances wrote:
> > > p.s. I like our county league's default formula: with a 20-VP
> > > scale, you get the highest of:
> > > 1. 12 VPs
> > > 2. Your average over all the other matches
> > > 3. 20 - the defaulting team's average over the matches it has
> > > played
> >
> > Which we have, of course, adopted from the EBU.
> >
>
> Interestingly the EBU Premier League gives you something different,
> rather than your average or the complement of the opponents' average
> you get
>
> Average (e.g. 15 on a 30-VP scale) + {your average - their average}

I suppose this might be explained (at least partly) by the Premier
League using the WBF 30 VP scale, whereas the EBU White Book guidance
tends to be working with the 20 & 25 VP scales.

The County is not obliged to follow the EBU White Book - but we see
little point in inventing our own wheels (and it saves us documenting
every little detail)...

Steve Willner

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Jan 19, 2012, 8:45:35 PM1/19/12
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On 2012-01-14 12:50 PM, Terry Faust wrote:
> In the first RR match team A plays team B in a normal match. Then
> team A completely drops out of the event

As others have written, you have to see what the CoC say.

If you are _writing_ CoC, it seems to me the score should not count if
only one match has been played. The problem is that you have no idea
how good or bad team A was, so there's no basis to guess what would have
happened if they had played more matches. If they had played as many as
two matches, you would have some information. Suppose team A loses to B
but wins against C. Then you have some evidence that B is better than
C, and B ought to wind up with more VPs (perhaps not very many more but
some) than C for the matches against A. With only one match played, you
can assume team A was average, but you have no actual data to support
that (and evidence against if the A-B match was lopsided).

Thinking further... if m matches have been played out of N scheduled,
what I'd offer is this:
if m = 1, throw out the score.
if m > 1, give the prescribed artificial scores in the matches not
played, and then weight all the results (both real and artificial)
involving the withdrawn team by m/N. For example, if the withdrawn team
has played half the matches, in effect there are only 10 VPs at stake in
each match.

I'm not sure this is mathematically right, but it seems better than a
sharp cutoff between "no matches count" and "all matches count full weight."

--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swil...@nhcc.net
Cambridge, MA 02138 USA

Michael Angelo Ravera

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Jan 23, 2012, 2:16:28 AM1/23/12
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I use the overriding principle that "CoCs abhor a forfeit".

If I were creating the CoCs, I'd drop the single result and conduct the league without reference to the team that dropped out.

I might figure out how to give the team that played against the team that dropped out an advanage in the scheduling, not reducing their strength of schedule but some accomodation for the fact that they now might have to make up a match later in the season, but with only one match per week, even that doesn't seem necessary.

If the drop out were for the last match of pool play, a forfeit seems like the only alternative. But, adjudicating a likely result with best advantage going to the team that was available for play seems like the right way not to disadvantage those teams that "earned" their spot in the knockout phase.

My solution would be a 40-40-20 rule or something roughly like it.

If a team has to drop out in the first 40% of pool play, all results obtained against that team are eliminated from the record. Teams scheduled to play against that team get either an open date or play a three-way as necessary to the schedule.

If a team has to drop out after playing at least 3 matches and completing more than 40% of the pool play, matches played against the team that dropped out are counted and the remaining schedule is adjusted to remove the team that dropped out. If this results in an unequal number of matches, postseason eligibllity is determined by percent of available VPs or percent of available wins or net IMPs or total point difference as it would have been on a complete schedule.

If a team has to drop out after completing more than 80% of its scheduled pool play and with at most 2 matches remaining, teams scheduled to play the team that dropped out receive the match result of a forfeit. In the US, that would be a full 20/20 or 30/30VP.

If a team has to drop out during the KO phase before playing any boards against a team, the last team eliminated or the team eliminated in the previous round by the narrowest margin is resurrected. If the round is seeded, reseeding will take place. If a team has to withdraw in the KO phase early in a match, but after playing less that one-forth of the scheduled boards, in the semifinals and earlier, a three way match is formed and two of the three teams advance. Otherwise the team that was playing the team that drops out advanaces.

Dave Flower

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Jan 24, 2012, 6:06:47 AM1/24/12
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On Jan 14, 5:50 pm, Terry Faust <m...@comcast.net> wrote:
There is an interesting position in the Wessex League (EBU). Five
divisions, 8 teams/division (7 in the bottom division). Promotion and
relegation of top 2 and bottom 2 teams. Twenty VPs awarded for each
match.

If a team defaults, they are awarded 0VPs, their opponents the average
of their score over the season, and scores against the defaulting team
over the season. As teams usually enter more than one team, and there
are strict rules about how often individual players can play,
especially if they have played for another of the clubs teams. There
is a risk of having difficulty raising a team at the end of the
season.

These conditions of contest raise two possible problems:

A) The VPs awarded to the non-defaulting team are too close to the
average. Suppose a team averaging 15VPs has their opponents (averaging
5VPs) default. This is (one of) the strongest teams versus (one of)
the weakest, but the stronger team are only awarded 15VPs, their
average over the season. Similarly, had the stronger team defaulted,
the weaker team would have been awarded a generous 5VPs.

B) Suppose, with the only remaining match in the division was between
team X with 90VPs currently 2nd, and team Y, with 80VPs, currently
3rd. If team X defaults, team X (still 90VPs) remains ahead of team Y
(89.17VPs); thus it benefits team X, who may be in a situation where
the only team that thay can raise is very weak, to default. Now,
actually, I do not believe that a team would deliberately default, but
it does create a somewhat undesirable situation.

Dave Flower

Steve Foster

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Jan 24, 2012, 8:56:07 AM1/24/12
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What's the problem here? The stronger team's expectation was to win the
match 15-5, and they get their 15VPs (assuming the other team default).
The converse scenario plays out to expectation too.

Funny how getting your average is mean (sic) for a strong team, yet at
the same time generous for a weak team.


> B) Suppose, with the only remaining match in the division was between
> team X with 90VPs currently 2nd, and team Y, with 80VPs, currently
> 3rd. If team X defaults, team X (still 90VPs) remains ahead of team Y
> (89.17VPs); thus it benefits team X, who may be in a situation where
> the only team that thay can raise is very weak, to default. Now,
> actually, I do not believe that a team would deliberately default, but
> it does create a somewhat undesirable situation.

Now this doesn't look fair. It should not be possible for a team to
lose against a defaulting team.

I do notice that the Wessex League rules don't appear to have been
revised since 2002.

I don't actually see anything in the White Book about defaults, though
I think it would be logical to use the same methodology for calculating
assigned scores as for withdrawals.

Regardless, Oxfordshire have control over their regulations, and I
would suggest raising the matter with them if you're unhappy with the
current rules.

Frances

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Jan 24, 2012, 9:54:17 AM1/24/12
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> Dave Flower- Hide quoted text -
>
> - Show quoted text -

(sorry if this turns out to be a double post)

The problem is that your COC seems to be missing one key rule, which
is that a team who default on a match can't win the event.

Our rule is that if you default on any matches through your own fault,
you certainly don't win the event and the organisers have the right
(i) to stop them entering the following year, or (ii) not allow them
to be promoted.

(some teams default for temporary problems such as illness of a
member's close relative, others because they are just bad at arranging
matches and can't be bothered)

Dave Flower

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Jan 24, 2012, 10:35:42 AM1/24/12
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On Jan 24, 1:56 pm, "Steve Foster" <stevefos...@invalid.invalid>
wrote:
> For SSL Certificates, Domains, etc, visit.:https://netshop.virtual-isp.net- Hide quoted text -
>
> - Show quoted text -

I now have some statistics for the last five years of Division 1 of
the Wessex League, based on matches actually played:

Actual VP score (Number of matches) Mean predicted score

20(17) 13.38
19(10) 12.74
18(17) 12.20
17(25) 11.96
16(12) 11.82
15(10) 10.40
14(18) 10.83
13(8) 11.66
12(8) 9.61
11(9) 9.20
10(4) 10.00
9(9) 10.80
8(8) 10.39
7(8) 8.34
6(18) 9.17
5(10) 9.60
4(12) 8.18
3(25) 8.04
2(17) 7.80
1(10) 7.26
0(17) 6.62

Dave Flower

Dave Flower

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Jan 24, 2012, 10:38:15 AM1/24/12
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On Jan 24, 1:56 pm, "Steve Foster" <stevefos...@invalid.invalid>
wrote:
No, the stronger team's expectation was better than that. If your
average win over all the teams in the dicision is 15-5, then your
expectation against the weakest is greater than that

Dave Flower


>
> Funny how getting your average is mean (sic) for a strong team, yet at
> the same time generous for a weak team.
>
> > B) Suppose, with the only remaining match in the division was between
> > team X with 90VPs currently 2nd, and team Y, with 80VPs, currently
> > 3rd. If team X defaults, team X (still 90VPs) remains ahead of team Y
> > (89.17VPs); thus it benefits team X, who may be in a situation where
> > the only team that thay can raise is very weak, to default. Now,
> > actually, I do not believe that a team would deliberately default, but
> > it does create a somewhat undesirable situation.
>
> Now this doesn't look fair. It should not be possible for a team to
> lose against a defaulting team.
>
> I do notice that the Wessex League rules don't appear to have been
> revised since 2002.
>
> I don't actually see anything in the White Book about defaults, though
> I think it would be logical to use the same methodology for calculating
> assigned scores as for withdrawals.
>
> Regardless, Oxfordshire have control over their regulations, and I
> would suggest raising the matter with them if you're unhappy with the
> current rules.
>
> --
> Steve Foster

Mark Brader

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Jan 24, 2012, 2:24:37 PM1/24/12
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Terry Faust asked:
As a matter of interest, how *did* the league decide to handle this?
--
Mark Brader "I like to think of [this] as self-explanatory."
Toronto "I hope *I* think of [it] that way."
m...@vex.net -- Donald Westlake: "Trust Me On This"

David Stevenson

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Jan 24, 2012, 2:25:16 PM1/24/12
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Frances wrote
>The problem is that your COC seems to be missing one key rule, which
>is that a team who default on a match can't win the event.

We have a Swiss Teams held over 12 months [two matches per evening, so
24 matches] and a Swiss Pairs over 11 months [22 matches]. It is
assumed that some evenings pairs or teams will be absent.

If you do not turn up you get 16 VPs [out of 40] first time, 15 second
time, and so on.

Of course, you could be so far ahead that 16 would guarantee a win in
the last month. So they have a clever rule: not turning up for the last
month gets you 0 VPs!

What happens if you are leading after your 0 VPs? Then you win! The
rule is to stop you failing to turn up tactically, not to stop you
wining when you cannot attend.

Dave Flower

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Feb 6, 2012, 6:17:54 AM2/6/12
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On Jan 24, 1:56 pm, "Steve Foster" <stevefos...@invalid.invalid>
wrote:
> For SSL Certificates, Domains, etc, visit.:https://netshop.virtual-isp.net- Hide quoted text -
>
> - Show quoted text -

Following up, consider the following scenario:

With one match to play, the top of a division is as follows, with two
teams to be promoted:

A 100
B 99
C 90

The remaining match is between A and C; under current Wessex League
rules, if A defaults, the final position would be:

A 100
B 99
C 98.56

This seems harsh on team C, but can any poster suggest a fairer
adjudication ?

Dave Flower

David Stevenson

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Feb 7, 2012, 10:30:46 AM2/7/12
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Dave Flower wrote

>Following up, consider the following scenario:
>
>With one match to play, the top of a division is as follows, with two
>teams to be promoted:
>
>A 100
>B 99
>C 90
>
>The remaining match is between A and C; under current Wessex League
>rules, if A defaults, the final position would be:
>
>A 100
>B 99
>C 98.56
>
>This seems harsh on team C, but can any poster suggest a fairer
>adjudication ?

Sure: do not let a team be promoted who defaults.

Frances

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Feb 8, 2012, 6:16:19 AM2/8/12
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> > For SSL Certificates, Domains, etc, visit.:https://netshop.virtual-isp.net-Hide quoted text -
>
> > - Show quoted text -
>
> Following up, consider the following scenario:
>
> With one match to play, the top of a division is as follows, with two
> teams to be promoted:
>
> A          100
> B            99
> C            90
>
> The remaining match is between A and C; under current Wessex League
> rules, if A defaults, the final position would be:
>
> A           100
> B             99
> C             98.56
>
> This seems harsh on team C, but can any poster suggest a fairer
> adjudication ?
>
> Dave Flower- Hide quoted text -
>
> - Show quoted text -

You've already had replies suggesting alternatives, which include.

- use the EBU rules (in which case team C would get at least 12 VPs at
get promoted). This would solve this problem, but not some other
possible ones.

or the obvious:

- do not let a team which defaults get promoted
- do not let let a team which defaults get promoted UNLESS the scores
are such that it can make no difference to the promotions (e.g. the
scores were A 100 B 99 C 78)

The problem with all of these is that you should have written your
rules before you get to this point. You have to apply the current
rules in the current season, you can't change them half way through.

Even if you say 'a team which defaults cannot be promoted' you still
have a problem if the final 4 scores were

A 100
B 99
D 99
C 90

because C have still missed out on their chance to beat A heavily, and
B & D will be promoted.
However, this type of problem is insoluble. Leagues only work
completely fairly if every team plays every match.


Dave Flower

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Feb 8, 2012, 6:42:03 AM2/8/12
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> > > For SSL Certificates, Domains, etc, visit.:https://netshop.virtual-isp.net-Hidequoted text -
> completely fairly if every team plays every match.- Hide quoted text -
>
> - Show quoted text -

Just for the record, this is a purely hypothetical case.

There certainly seems a strong case to require a defaulting team to
offer alternative dates (Sorry, but we were unsure under which
snowdrift our club was buried), extending the season if necessary, and
only penalising them if they do not do so.

Dave Flower

Frances

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Feb 8, 2012, 9:17:38 AM2/8/12
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> > > > For SSL Certificates, Domains, etc, visit.:https://netshop.virtual-isp.net-Hidequotedtext -
Ah, now we are getting onto a different subject. I had understood
originally that you were discussing what the regulation should be when
a team refuses to play/is unable to organise a team to play a match.

Now we are going backwards a bit, and talking about rules for
rearranging matches/offering extensions. Most leagues have rules
which say (something like) "if you can't play a match according to the
proper schedule, tell the organising committee and we will
adjudicate". The are then possibilities such as
- extending deadlines
- allowing a substitute player(s) (subject usually to them being 'a
similar standard')

However you can't put all possibilities into the CoC because whether
or not you penalise tends to depend on whose fault the default is, and
what sort of fault. A team member dying, or a team member's close
relative dying (sadly a not infrequent occurrence) has more sympathy
than 'we can't arrange the match because we're going on holiday and we
don't care because we're being promoted anyway'. And if it's the
latter, you have to be careful allowing substitutes, because team B
might complain if team A are allowed to play with a much weakened
team, and team C beat them heavily through no fault of B's.

Bad weather/acts of god cause all sorts of trouble. There was a long
argument about a Gold Cup match a couple of years ago, when the away
team didn't turn up because a truck had run into a shop window on the
North Circular and their car was stuck in a 3 hour traffic jam with
nowhere to go. Had the away team defaulted, or should they try an
rearrange the match? If there is bad weather, what is bad enough to
say it's not their fault: 2 inches of snow but the driver 'doesn't
like' driving in bad weather? 3 feet of now and the house is cut off
for a week?

David Stevenson

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Feb 8, 2012, 10:22:57 AM2/8/12
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Frances wrote

>However you can't put all possibilities into the CoC because whether
>or not you penalise tends to depend on whose fault the default is, and
>what sort of fault. A team member dying, or a team member's close
>relative dying (sadly a not infrequent occurrence) has more sympathy
>than 'we can't arrange the match because we're going on holiday and we
>don't care because we're being promoted anyway'. And if it's the
>latter, you have to be careful allowing substitutes, because team B
>might complain if team A are allowed to play with a much weakened
>team, and team C beat them heavily through no fault of B's.
>
>Bad weather/acts of god cause all sorts of trouble. There was a long
>argument about a Gold Cup match a couple of years ago, when the away
>team didn't turn up because a truck had run into a shop window on the
>North Circular and their car was stuck in a 3 hour traffic jam with
>nowhere to go. Had the away team defaulted, or should they try an
>rearrange the match? If there is bad weather, what is bad enough to
>say it's not their fault: 2 inches of snow but the driver 'doesn't
>like' driving in bad weather? 3 feet of now and the house is cut off
>for a week?

There can be amazing arguments. Many years ago a Gold Cup match was
arranged. On the morning of the match the father of one of the players
died. They were a six man team, but two were unavailable [on holiday in
Switzerland]. However, while this was the third round, neither of the
two had played. So to most people the solution was obvious: allow the
team to produce another member instead of one of the two who had not
played. They found a player who was willing to play and had not played
for another team.

It may seem obvious to you or me, but not to the opponents, who
expected the match to be conceded, and sadly not the authorities of the
day. I was at an EBU Council meeting where there was a three hour
argument over this. I do not remember the final decision.

Frances

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Feb 8, 2012, 12:36:19 PM2/8/12
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> <webjak...@googlemail.com>       EBL TD          Tel: +44 151 677 7412
> bluejak666 on Skype        Bridgepage:http://blakjak.org/brg_menu.htm- Hide quoted text -
>
> - Show quoted text -


We're getting a bit off-topic now, but a couple of years ago we were
due to play a 60-board national KO final. Both teams had to travel 150
miles+ to get to the agreed half-way venue, and both travelled the
night before and paid to stay in a hotel.

The morning of the match one of our team found out that his father had
unexpectedly died that night. We expected to have to concede the
match. The opposing captain very generously said they were happy to
arrange to another date. So our two teams had the opposite of one of
these arguments, we were both arguing for the other side... in the end
our team member said that another few hours would make no difference
and he would prefer to play, so we did.

Steve Willner

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Feb 8, 2012, 8:37:41 PM2/8/12
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On 2012-01-24 6:06 AM, Dave Flower wrote:
> If a team defaults, they are awarded 0VPs, their opponents the average
> of their score over the season, and scores against the defaulting team
> over the season.

_The Bridge World_ 2011 March gives the formula for the expected score
based on available results. (It was actually for an unplayable board,
but the same principles apply to an unplayable match.) If team A wins
on average fraction a of the available VPs, and team B wins on average
fraction b, the expectation is that A would receive fraction
(a-ab)/(a+b-2ab) if the teams had met (and of course B would receive the
rest). (Notice that if a=b, the expectation is equal VPs.)

It seems to me that a formula for assigning scores to a defaulted match
should start with this formula. From there, you could give extra
penalties to the defaulting team and perhaps a bonus to the team willing
to play, but starting from the formula should at least put the result
into the right range.
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