[blml] Thai braking [SEC=UNOFFICIAL]

[richard.hills at immi.gov.au]

This weekend's Trials to select the ACT Open Team for the Aussie
Interstate Open Teams will be 12 pairs playing 11 rounds of 14-
board matches in a round robin, with the top three pairs forming
the team.  The scoring will be Butler against a datum (yes, I
know that cross-imps is a slightly superior method), with the
datum an average of the middle four scores, with the two extreme
scores excluded (yes, I know that some have strong objections to
excluding scores when striking a datum).

The question I am posing to blml is which VP scale of the two
proposed by BFACT Tournament Secretary Griff Ware is superior
(see attached)?

Best wishes

Richard James Hills, amicus curiae
National Training Branch, DIAC
02 6223 9052

*     *     *

Griff Ware (BFACT Tournament Secretary):

[snip]

Option (i)
Essentially forget VP scales and score by net IMPs with upper and
lower caps -- what we've done for the past two years -- with the
following slight improvement:

A pair's VP score will be equal to the net IMPs scored in a round,
excepting that positive scores are capped above by X, and each
negative imp below -X is worth -0.7VPs until a pair's VP score
reaches a lower limit of -Y.

X and Y vary depending on the number of boards played in a match.

For a 14-board butler-scored pairs event appropriate values are X
= 38 and Y = -56.2

To prevent ugly looking negative scores we could add a placebo
60VPs per match, so that scores are equal to 60 + net imps [x0.7
for each imp below -38] up to a maximum of 98VPs and a minimum of
3.8VPs; this is roughly a 0 to 100 range which is aesthetically
attractive.

Option (ii)
Use the standard 12-board VP scale (12-board scale despite 14-
board match length because in butler-scored pairs events wins are
statistically smaller than in teams matches, so a shorter scale
should be used).

[snip]

Part (C): Analysis of the two options

I reiterate the point that the *average* difference between these two
scoring options is very minimal.  The numbers look totally different, but
the underlying relativity of pairs' scores is not significantly different
when moving between option (i) and (ii), particularly due to the 0.7
factoring of scores between -X and -Y in option (i).  When compared to the
standard VP scale, option (i) does NOT fundamentally change the nature of
the scores or the general outcome of events -- it just fixes some fuzzy
boundaries, which may or may not be critical in a given instance.

What changes is that option (i) is a finer and more accurate scale, and
hence removes elements of luck caused by the coarseness of the standard VP
scale.  In short, option (i) is statistically fairer than option (ii).  I
will give an example of this effect to illustrate:

Suppose a 4-round event scored on the standard WBF 12-board VP scale takes
place.
Pair 1 wins its matches by +6, +10, +6 and +6.  All smallish wins of
comparable size, for a net IMP score of +28 and a VP score of 16+18+16+16 =

66VPs.
Pair 2 wins its matches by +7, +7, +7 and +6.  All smallish wins of
comparable size, for a net IMP score of +27 and a VP score of 17+17+17+16 =

67VPs.

That is, 28 IMPs for pair 1 scored 66 VPs, while 27 IMPs for pair 2 scored
67 VPs.  Does this seem fair to you?

Pair 1 scored more IMPs than Pair 2 (NB without maxing out any of its
opponents), averaging 7IMPs a match, yet Pair 2 with its less-than-7IMP per

match average scored more VPs.  Why?  Pair 2 was lucky enough that three of

its IMP scores just cusped into the 17-13 VP range while only one of its
scores was just outside, at the maximum of the 16-14 range.  Meanwhile,
Pair
1 had only one of its IMP scores 'just cusp' into the 18-12 range while
three of its scores were at the very maximum of the 16-14 range.

The question should be asked: was this due to a lack of skill on the part
of
Pair 1 or an exhibition of a greater degree of skill by Pair 2?  Certainly
not.  In IMPed duplicate bridge you can never be sure how well you are
doing
with a precision better than about 5IMPs, and hence it is certainly not
possible to, for instance, tell on the final board of a match that a
specific extra overtrick will give you the IMP needed to cross into a new
VP
bracket. You simply can not have that level of control. It’s not even the
same as being lucky that a 13% grand slam you bid happens to make: in that
case you chose to take the chance by bidding the grand; here the dice are
being thrown in the air for you. When using a standard VP scale, where your

score falls within your eventual VP bracket is almost entirely due to
chance
and beyond your influence. All you can do is try to maximise your IMPs on
each given board and hope that you will benefit from good cusps.  In the
above example, the IMPs indicate that Pair 1 and Pair 2 had very similar
results, but provide an effective, adequate and fair tie-break between the
two: Pair 1 did ever so slightly better than Pair 2.  By filtering the
results with a VP-scale whose theoretical value is questionable, the
opposite result is randomly produced: Pair 2 gets one more VP than Pair 1.

This sort of occurrence is not uncommon. Several years ago Mark and I did a

theoretical analysis of the 8-board VP scale and found that in a standard
6-round congress event, if you assume two teams are on the same IMP total
at
the end of it, have not had any maximum wins or losses and (for the sake of

statistical independence) did not play each other, then the chance of them
being on the same VP total is only 14%.  Now in congress and other minor
events this isn't really a problem and it's OK by me for luck to play its
part.  But when it comes to a state-level/selection event I personally
don't
want to take the chance that we have a narrow VP margin for a critical
place
and it turns out that the margin is less than the random difference thrown
up by beneficial/detrimental cusping of scores on the VP scale used.  Hence

why a fractional VP scale (somewhat complex but more familiar to people) or

just simply using net IMPs with appropriate (dampened) caps is my strongly
preferred option for major BFACT tournaments.

Why does the standard VP scale exist? I guess I should give a couple of
words about its merits.  Firstly, as alluded to above, it provides a
benchmark scale that can be used to compare results between matches of
differing lengths.  But such a luxury is still available with fractional VP

scales, and is of benefit only because people are not used to using net
IMPs.  Secondly, small fluctuations in VP bracket size over the span of the

scale provide some dampening effects that were presumably deemed beneficial

by the creators of the scales (eg the 16-14 bracket is always broader than
the 15-15 and 17-13 brackets either side of it; why this is the case is
beyond me).  These effects are very minor and of no immediately obvious
value, however, and again fractional VP scales can mimic these properties.

More important and valuable are the dampening effects at the extreme end of

the scales: these have a significant statistical impact, which is why I
suggest applying this aspect to straight net-IMPs, as in option (i).

But as far as I can tell the main reason that the VP scales were introduced

is due to the now out-dated need to deal in smaller, regulation size
scores.
  Before computers, having a standard VP scale that ranged from 0 to 25 (or

-5 to 20 or whatever) led to faster mental arithmetic by the scorers and a
faster turnaround for results.  This reason no longer applies, however,
because with an appropriately programmed computer any vaguely appropriate
algorithm for scoring that we like can be implemented.  My opinion is that
the standard WBF scales are reaching the end of their usefulness and should

be replaced with a more precise, fairer, more modern alternative.  It is my

hope that BFACT can lead the way by scoring its events with such
alternatives, eg option (i).

Propaganda over.

Important Notice: If you have received this email by mistake, please advise
the sender and delete the message and attachments immediately.  This email,
including attachments, may contain confidential, sensitive, legally
privileged and/or copyright information.  Any review, retransmission,
dissemination or other use of this information by persons or entities other
than the intended recipient is prohibited. DIAC respects your privacy and
has obligations under the Privacy Act 1988. The official departmental
privacy policy can be viewed on the department's website at www.immi.gov.au
See: http://www.immi.gov.au/functional/privacy.htm