points system technical note

ColinJenkins · 27 August 2004 15:34

http://www.sailwave.com/index.php?page=tnote&num=4

draft

CJ

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Geoff_Burrell · 25 August 2004 20:39

Hi Colin et al
You may be interested in my comments on the Rinderle B System.
The table commonly quoted as being gospel for Rinderle B has some anomalies
in it and if inspected closely it does not actually reflect the values that
were derived some long time ago using Jim Rinderle's original formula.
There is clearly an advantage for a system such as Sailwave if a formula is
used rather than a look-up table. So I have derived such a formula, which
matches the principles of Rinderle B but with some very minor improvements.
One such improvement is to make the score for a win against an infinite
number of boats = 100.
(In practice my formula gives a score of 99.9 for a win in a 25 boat race.
(The current Rinderle B table gives 100.5 instead of 100 for an infinite
number of boats. The extra 0.5 seems a bit pointless.)
At the other end I have set it so that a win in a 3 boat race gives
approximately 80 points (actually 79.8).
The score for last place in any size of race remains at 10.5 with the score
for a retirement being 5.
I believe this is a more understandable and useful way of applying the
Rinderle B principles - but of course that is only my personal view.
Rather than present the formula here I have attached a spreadsheet for the
table for races of between 3 and 25 boats. The formula is of course present
in each cell and it also includes the fiddly bits that round all scores to
one decimal place and avoids putting rubbish in non-used cells.
Best regards,
Geoff B
Sailing Secretary, Chipstead SC

[Non-text portions of this message have been removed]

ColinJenkins · 28 August 2004 09:29

Hi Geoff,

Would you be prepared to let me know the formula - I would prefer to
implement that, rather then use a table.

I have emailed Jim R a few times asking the same, but he does not respond.

Regards,
Colin J
www.sailwave.com

···

-----Original Message-----
From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
Sent: 25 August 2004 21:40
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Colin et al
You may be interested in my comments on the Rinderle B System.
The table commonly quoted as being gospel for Rinderle B has some
anomalies
in it and if inspected closely it does not actually reflect the
values that
were derived some long time ago using Jim Rinderle's original formula.
There is clearly an advantage for a system such as Sailwave if a
formula is
used rather than a look-up table. So I have derived such a formula, which
matches the principles of Rinderle B but with some very minor
improvements.
One such improvement is to make the score for a win against an infinite
number of boats = 100.
(In practice my formula gives a score of 99.9 for a win in a 25 boat race.
(The current Rinderle B table gives 100.5 instead of 100 for an infinite
number of boats. The extra 0.5 seems a bit pointless.)
At the other end I have set it so that a win in a 3 boat race gives
approximately 80 points (actually 79.8).
The score for last place in any size of race remains at 10.5 with
the score
for a retirement being 5.
I believe this is a more understandable and useful way of applying the
Rinderle B principles - but of course that is only my personal view.
Rather than present the formula here I have attached a spreadsheet for the
table for races of between 3 and 25 boats. The formula is of
course present
in each cell and it also includes the fiddly bits that round all scores to
one decimal place and avoids putting rubbish in non-used cells.
Best regards,
Geoff B
Sailing Secretary, Chipstead SC

[Non-text portions of this message have been removed]

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Geoff_Burrell · 28 August 2004 10:30

Hi Colin
OK here is the CSC-modified Rinderle formula presented in the form entered
into Excel:

Points
=IF(N>=P,ROUND(89.5*(1-EXP(-(0.8+0.23*N)))*(IF(N=1,1,(N-P)/(N-1))),1)+10.5,"
")

where N is the Number of Starters and P is the Position.

In addition for RTD, DNF, etc, then Points = 0.5
And for a DSQ, DNC (and in my view also for a DNS) then Points = 0

This is exactly the form of Jim Rinderle's original formula but with the
parameters 89.5, 0.8 and 0.23 changed a bit. Clearly one can dream up other
variations by changing the parameters, including also changing the 10.5 if
one wishes to apply something different for last position. .
Although I have not seen any presentation of the formula used for Cox
Sprague there are obvious similarities with that but, in that case, the last
place value is a function of the number of participants. But I guess
someone must know the Cox Sprague formula (rather than having to use the
look up table). I have not checked in detail but it may be possible to add
a further element to my formula to make it equivalent to Cox Sprague or at
worst a close approximation, you would then only need to choose the
parameters to match whatever scoring system is desired.
I hate look-up tables and I always go for a formula to simplify things and
give maximum flexibility.
Hope this is useful.
Best regards,
Geoff B

···

-----Original Message-----
From: Colin Jenkins [mailto:colin@sailwave.com]
Sent: 28 August 2004 10:29
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Geoff,

Would you be prepared to let me know the formula - I would prefer to
implement that, rather then use a table.

I have emailed Jim R a few times asking the same, but he does not respond.

Regards,
Colin J
www.sailwave.com

-----Original Message-----
From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
Sent: 25 August 2004 21:40
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Colin et al
You may be interested in my comments on the Rinderle B System.
The table commonly quoted as being gospel for Rinderle B has some
anomalies
in it and if inspected closely it does not actually reflect the
values that
were derived some long time ago using Jim Rinderle's original formula.
There is clearly an advantage for a system such as Sailwave if a
formula is
used rather than a look-up table. So I have derived such a formula, which
matches the principles of Rinderle B but with some very minor
improvements.
One such improvement is to make the score for a win against an infinite
number of boats = 100.
(In practice my formula gives a score of 99.9 for a win in a 25 boat race.
(The current Rinderle B table gives 100.5 instead of 100 for an infinite
number of boats. The extra 0.5 seems a bit pointless.)
At the other end I have set it so that a win in a 3 boat race gives
approximately 80 points (actually 79.8).
The score for last place in any size of race remains at 10.5 with
the score
for a retirement being 5.
I believe this is a more understandable and useful way of applying the
Rinderle B principles - but of course that is only my personal view.
Rather than present the formula here I have attached a spreadsheet for the
table for races of between 3 and 25 boats. The formula is of
course present
in each cell and it also includes the fiddly bits that round all scores to
one decimal place and avoids putting rubbish in non-used cells.
Best regards,
Geoff B
Sailing Secretary, Chipstead SC

[Non-text portions of this message have been removed]

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ColinJenkins · 29 August 2004 09:51

Hi Geoff,

Thanks. Can I publish this formula in the points system technical note?
with a credit of course.

Greg Bemis, in "Yacht Race Scoring" says that the Cox-Sprague formula is:-

Points = 1311 - 100 * CubeRoot(20*P + 11)

But I don't see how, because the number of starters is not in there... the
20 could be it.. The points have to be divided by the winners points as
well.

It might be a good idea to dream up a simple equation (no if's) of our own
that achieves the same thing. i.e. making the assumption that it's harder
to win when there are more boats in the race and it's harder in any race to
move up a place near the front of the fleet.

See also this:-

"The following is an abstracted/paraphrased/quoted copmpendium taken
from Chapter 17 of Win More Sailboat Races by C. Stanley Ogilvy, (W.W.
Norton, 1976) (and edited by me); Geoff Newbury".

*****************
In or about 1970, William S. Cox and Henry Sprague became interested
in devising a 'best possible' scoring system to overcome the
inequities they observed in then current scoring systems:

1. Unrealistic award of points in any one race.
2. Incorrect weighting of the fleet size in a race.
3. Disregard of the disastrous effects of dnf/dns.

Cox-Sprague works best in a long series of races where a boat is
allowed a high percentage of absenteeism. Once a threshold number of
qualifying races is sailed, the presence or absence of a yacht in a
particular race is irrelevant to its score, which is based solely on
its placings in the races it sailed, and the number of boats it sailed
against in each race.

With low-point systems, (including Bonus-point or "Olympic") a DNS,
DNF, retirement or DSQ scores one more than the number of boats
entered. This is acceptable for a short regatta where all yachts
entered are expected to sail all the races, but does not work over a
summer, as one weekend missed is an insurmountable obstacle.
High-point systems are susceptible to the opposite effect, and can
also be sensitive to the fleet size.

Cox-Sprague ignores the races which a boat does not sail. It is only
interested in the races actually sailed. Cox-Sprague varies the points
awarded in relation to the fleet size. It addresses the inequities
listed above as follows:

1. Most systems allow equal points for equal changes of position, but
it is not as easy to move from 5th to 3rd as from 15th to 13th. In
Cox-Sprague the points are not linear but on a curve that says it is
twice as hard to go from 2nd to 1st as from 5th to 4th, and three
times as hard as from 10th to 9th.

Cox-Sprague is not linear, nor quite as non-linear as the Olympic
scoring curve. More importantly, the difference in points between
boats similarly placed is the same, whatever the fleet size. What
differs is that the number of points awarded differs with fleet size.
First always gets 6 more points than second, but first gets 43 in a
fleet of 4 and 100 in a fleet of 20 or more.

2. A boat's score for a race is obtained by dividing the points earned
*by the possible points she coud have earned*. If a boat finished 3rd
among 18 starters, then she earns 88 of 98 possible points (or .898).
This is almost as good as 3rd in 20 (.900) and much better than 3rd
among 4 boats (.767).

The boat's overall score is kept not by averaging the points for each
day (which would equally weight all races notwithstanding the
different fleet size), but by totalling the points earned and dividing
that total by the sum of all possible points for the races sailed. A
running fraction is maintained so that after each race points are
added to both the numerator and denominator, and the resulting new
fraction is the score to date. This procedure automatically gives
lesser weight to smaller races.

Together with item 1 this means that as between boats who are always
out sailing, the point scores for their relative positions is
dependant solely on their results, and completely independant of the
fleet size. If A gets first to B's third in a large fleet on Saturday
and they then sail to a 3-1 on Sunday in a small fleet, their results
are the same. They earn the same number of points, which should be the
case for a 'fair' system.

3. Under traditional systems, a DSQ or DNF puts a boat out of
contention. A worst race exemption mitigates this but is not effective
for season-type championships where there may be any number of races
not sailed. With a drop race, each boat's score is unknown until the
end and the calculations must be done twice on a running basis.
Cox-Sprague makes the penalty much less severe, about 58/100 instead
of 0/100 and no drop is necessary. A DNS is irrelevant to the system,
neither adding nor subtracting points.
**************

Regards,
Colin
www.sailwave.com

-----Original Message-----
From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
Sent: 28 August 2004 11:30
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Colin
OK here is the CSC-modified Rinderle formula presented in the form entered
into Excel:

Points
=IF(N>=P,ROUND(89.5*(1-EXP(-(0.8+0.23*N)))*(IF(N=1,1,(N-P)/(N-1)))
,1)+10.5,"
")

where N is the Number of Starters and P is the Position.

In addition for RTD, DNF, etc, then Points = 0.5
And for a DSQ, DNC (and in my view also for a DNS) then Points = 0

This is exactly the form of Jim Rinderle's original formula but with the
parameters 89.5, 0.8 and 0.23 changed a bit. Clearly one can
dream up other
variations by changing the parameters, including also changing the 10.5 if
one wishes to apply something different for last position. .
Although I have not seen any presentation of the formula used for Cox
Sprague there are obvious similarities with that but, in that
case, the last
place value is a function of the number of participants. But I guess
someone must know the Cox Sprague formula (rather than having to use the
look up table). I have not checked in detail but it may be
possible to add
a further element to my formula to make it equivalent to Cox Sprague or at
worst a close approximation, you would then only need to choose the
parameters to match whatever scoring system is desired.
I hate look-up tables and I always go for a formula to simplify things and
give maximum flexibility.
Hope this is useful.
Best regards,
Geoff B

-----Original Message-----
From: Colin Jenkins [mailto:colin@sailwave.com]
Sent: 28 August 2004 10:29
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Geoff,

Would you be prepared to let me know the formula - I would prefer to
implement that, rather then use a table.

I have emailed Jim R a few times asking the same, but he does not respond.

Regards,
Colin J
www.sailwave.com

> -----Original Message-----
> From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
> Sent: 25 August 2004 21:40
> To: sailwave@yahoogroups.com
> Subject: RE: [sailwave] points system technical note
>
>
> Hi Colin et al
> You may be interested in my comments on the Rinderle B System.
> The table commonly quoted as being gospel for Rinderle B has some
> anomalies
> in it and if inspected closely it does not actually reflect the
> values that
> were derived some long time ago using Jim Rinderle's original formula.
> There is clearly an advantage for a system such as Sailwave if a
> formula is
> used rather than a look-up table. So I have derived such a
formula, which
> matches the principles of Rinderle B but with some very minor
> improvements.
> One such improvement is to make the score for a win against an infinite
> number of boats = 100.
> (In practice my formula gives a score of 99.9 for a win in a 25
boat race.
> (The current Rinderle B table gives 100.5 instead of 100 for an infinite
> number of boats. The extra 0.5 seems a bit pointless.)
> At the other end I have set it so that a win in a 3 boat race gives
> approximately 80 points (actually 79.8).
> The score for last place in any size of race remains at 10.5 with
> the score
> for a retirement being 5.
> I believe this is a more understandable and useful way of applying the
> Rinderle B principles - but of course that is only my personal view.
> Rather than present the formula here I have attached a
spreadsheet for the
> table for races of between 3 and 25 boats. The formula is of
> course present
> in each cell and it also includes the fiddly bits that round
all scores to
> one decimal place and avoids putting rubbish in non-used cells.
> Best regards,
> Geoff B
> Sailing Secretary, Chipstead SC
>
>
>
>
> [Non-text portions of this message have been removed]
>
>
>
>
> -!- http://www.fastmail.fm/ -!- http://www.spampal.org/ -!-
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ColinJenkins · 30 August 2004 16:11

Hi Geoff,

re: rinderle

Points
=IF(N>=P,ROUND(89.5*(1-EXP(-(0.8+0.23*N)))*(IF(N=1,1,(N-P)/(N-1)))
,1)+10.5,"
")

I've been plotting this function wrt x:-

y = a * (1 - exp(-(b + c*k))) * (k-x)/(k-1) + d

abcd as per your email, k is the number of starters and x is the place, and
it comes out as a straight line, do I have it correct? It matches the end
values OK but doesn't bend at all I suspect a k needs to be an x
somewhere or something like that.

For example, for the k=25 case, the above curve exactly matches:-

y = 103.596 - 3.72383*x

Tech note 4 updated a bit with some graphs on web site - which is v slow
today.

Regards,
Colin
www.sailwave.com

···

-----Original Message-----
From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
Sent: 28 August 2004 11:30
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Colin
OK here is the CSC-modified Rinderle formula presented in the form entered
into Excel:

Points
=IF(N>=P,ROUND(89.5*(1-EXP(-(0.8+0.23*N)))*(IF(N=1,1,(N-P)/(N-1)))
,1)+10.5,"
")

where N is the Number of Starters and P is the Position.

In addition for RTD, DNF, etc, then Points = 0.5
And for a DSQ, DNC (and in my view also for a DNS) then Points = 0

This is exactly the form of Jim Rinderle's original formula but with the
parameters 89.5, 0.8 and 0.23 changed a bit. Clearly one can
dream up other
variations by changing the parameters, including also changing the 10.5 if
one wishes to apply something different for last position. .
Although I have not seen any presentation of the formula used for Cox
Sprague there are obvious similarities with that but, in that
case, the last
place value is a function of the number of participants. But I guess
someone must know the Cox Sprague formula (rather than having to use the
look up table). I have not checked in detail but it may be
possible to add
a further element to my formula to make it equivalent to Cox Sprague or at
worst a close approximation, you would then only need to choose the
parameters to match whatever scoring system is desired.
I hate look-up tables and I always go for a formula to simplify things and
give maximum flexibility.
Hope this is useful.
Best regards,
Geoff B

-----Original Message-----
From: Colin Jenkins [mailto:colin@sailwave.com]
Sent: 28 August 2004 10:29
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Geoff,

Would you be prepared to let me know the formula - I would prefer to
implement that, rather then use a table.

I have emailed Jim R a few times asking the same, but he does not respond.

Regards,
Colin J
www.sailwave.com

> -----Original Message-----
> From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
> Sent: 25 August 2004 21:40
> To: sailwave@yahoogroups.com
> Subject: RE: [sailwave] points system technical note
>
>
> Hi Colin et al
> You may be interested in my comments on the Rinderle B System.
> The table commonly quoted as being gospel for Rinderle B has some
> anomalies
> in it and if inspected closely it does not actually reflect the
> values that
> were derived some long time ago using Jim Rinderle's original formula.
> There is clearly an advantage for a system such as Sailwave if a
> formula is
> used rather than a look-up table. So I have derived such a
formula, which
> matches the principles of Rinderle B but with some very minor
> improvements.
> One such improvement is to make the score for a win against an infinite
> number of boats = 100.
> (In practice my formula gives a score of 99.9 for a win in a 25
boat race.
> (The current Rinderle B table gives 100.5 instead of 100 for an infinite
> number of boats. The extra 0.5 seems a bit pointless.)
> At the other end I have set it so that a win in a 3 boat race gives
> approximately 80 points (actually 79.8).
> The score for last place in any size of race remains at 10.5 with
> the score
> for a retirement being 5.
> I believe this is a more understandable and useful way of applying the
> Rinderle B principles - but of course that is only my personal view.
> Rather than present the formula here I have attached a
spreadsheet for the
> table for races of between 3 and 25 boats. The formula is of
> course present
> in each cell and it also includes the fiddly bits that round
all scores to
> one decimal place and avoids putting rubbish in non-used cells.
> Best regards,
> Geoff B
> Sailing Secretary, Chipstead SC
>
>
>
>
> [Non-text portions of this message have been removed]
>
>
>
>
> -!- http://www.fastmail.fm/ -!- http://www.spampal.org/ -!-
> http://www.sailwave.com/ -!-
>
> Convert to daily digest of emails send blank email to:
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>
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>
>
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ColinJenkins · 30 August 2004 17:12

Hi Geoff,

re: rinderle again

I think I'm beginning to understand - I should have read the whole of your
post first!. Rinderle is a linear points system (differentiate your fn wrt
place and you get a horizontal line); the non-linearness is related to how
the points for the same place change as the fleet size changes... So we can
start to categorise systems in terms of linearity in at least two
dimensions, wrt fleet size and wrt place.

cj

···

-----Original Message-----
From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
Sent: 29 August 2004 23:49
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Colin
Yes I am happy for you to publish the formula. You will need to clarify
that this is not exactly the same as in the Rinderle B table but it does
however follow the same principles.
A simpler presentation for publication (without the IFs) might be:
Points = a*[1 - exp -(b + c*N)]*(S - P)/(S - 1) + d
Where my recommended values are:
a = 89.5
b = 0.8
c = 0.23
d = 10.5
S is the Number of Starters in the race
P is the Position

When presenting the results to participants I recommend rounding to one
decimal place.
DSQ/OCS/DNC = 0
Please excuse the typo in my previous message: RTD/DNF = 5 (not 0.5).

As regards Cox-Sprague I agree with you that the formula quoted does not
make sense and any amount of fiddling does not put it right!
Anyway I really do not like the Cox-Sprague method for several reasons.
First the range of points attributed to a win is (in my view) far to
extreme, ranging from 10 (for a 2 boat race) to 100 (for a 20+ boat race).
It is more complicated than Rinderle in that the points scored are divided
by the maximum number of points that could have been scored in
the series to
date, and this is converted to a running fraction.
Races with fewer participants contribute far less to the overall
score than
is justified and this is made even worse by adding the points into the
numerator and denominator by the method described. (The stated
principle in
which the system automatically gives lesser weight to the smaller races
would be OK were it not for the fact that the C-S scheme takes this to an
excessive, unfair extreme).
The complexity of the system (especially the running fraction feature) is
such that participants cannot readily keep track of how well they
are doing
through the race series - the issue of ease of understanding is one of the
biggest criticisms I have experienced for this type of system and
one has to
be sympathetic to this when introducing any such scoring scheme.
The scores for a last place do not work in a logical sequence.
I have a personal objection to giving beneficial scores to DSQ boats.
The system runs off the end of the scale at 80+ boats.
Although not stated in the abstract I assume that everyone who
uses the C-S
system would require a qualifying number of races to be sailed
and counted -
so that the worst scores are discarded if one does more than the
qualifying
number. I think this is an essential element of a high point scoring
system. However this is yet a further complication of C-S which is much
easier to implement and for sailors to comprehend in a Rinderle type of
system.
As you can see my view is that Cox Sprague has very little to recommend it
except for one thing. That is the non-linear nature of the scores - in
which the differences are larger for positions nearer the front of the
fleet - this is a good feature.

Were there to be an interest I could add a couple of further modifications
to my formula:
(a) include the above non-linear feature
(b) make the scores for last place dependent on the number of
participants.
But so many people have played with scoring methods in the past I
am not too
sure whether I should bother to do this or not.
Best regards
Geoff B

-----Original Message-----
From: Colin Jenkins [mailto:colin@sailwave.com]
Sent: 29 August 2004 10:51
To: sailwave@yahoogroups.com
Subject: RE: [sailwave] points system technical note

Hi Geoff,

Thanks. Can I publish this formula in the points system technical note?
with a credit of course.

Greg Bemis, in "Yacht Race Scoring" says that the Cox-Sprague formula is:-

Points = 1311 - 100 * CubeRoot(20*P + 11)

But I don't see how, because the number of starters is not in there... the
20 could be it.. The points have to be divided by the winners points as
well.

It might be a good idea to dream up a simple equation (no if's) of our own
that achieves the same thing. i.e. making the assumption that it's harder
to win when there are more boats in the race and it's harder in
any race to
move up a place near the front of the fleet.

See also this:-

"The following is an abstracted/paraphrased/quoted copmpendium taken
from Chapter 17 of Win More Sailboat Races by C. Stanley Ogilvy, (W.W.
Norton, 1976) (and edited by me); Geoff Newbury".

*****************
In or about 1970, William S. Cox and Henry Sprague became interested
in devising a 'best possible' scoring system to overcome the
inequities they observed in then current scoring systems:

1. Unrealistic award of points in any one race.
2. Incorrect weighting of the fleet size in a race.
3. Disregard of the disastrous effects of dnf/dns.

Cox-Sprague works best in a long series of races where a boat is
allowed a high percentage of absenteeism. Once a threshold number of
qualifying races is sailed, the presence or absence of a yacht in a
particular race is irrelevant to its score, which is based solely on
its placings in the races it sailed, and the number of boats it sailed
against in each race.

With low-point systems, (including Bonus-point or "Olympic") a DNS,
DNF, retirement or DSQ scores one more than the number of boats
entered. This is acceptable for a short regatta where all yachts
entered are expected to sail all the races, but does not work over a
summer, as one weekend missed is an insurmountable obstacle.
High-point systems are susceptible to the opposite effect, and can
also be sensitive to the fleet size.

Cox-Sprague ignores the races which a boat does not sail. It is only
interested in the races actually sailed. Cox-Sprague varies the points
awarded in relation to the fleet size. It addresses the inequities
listed above as follows:

1. Most systems allow equal points for equal changes of position, but
it is not as easy to move from 5th to 3rd as from 15th to 13th. In
Cox-Sprague the points are not linear but on a curve that says it is
twice as hard to go from 2nd to 1st as from 5th to 4th, and three
times as hard as from 10th to 9th.

Cox-Sprague is not linear, nor quite as non-linear as the Olympic
scoring curve. More importantly, the difference in points between
boats similarly placed is the same, whatever the fleet size. What
differs is that the number of points awarded differs with fleet size.
First always gets 6 more points than second, but first gets 43 in a
fleet of 4 and 100 in a fleet of 20 or more.

2. A boat's score for a race is obtained by dividing the points earned
*by the possible points she coud have earned*. If a boat finished 3rd
among 18 starters, then she earns 88 of 98 possible points (or .898).
This is almost as good as 3rd in 20 (.900) and much better than 3rd
among 4 boats (.767).

The boat's overall score is kept not by averaging the points for each
day (which would equally weight all races notwithstanding the
different fleet size), but by totalling the points earned and dividing
that total by the sum of all possible points for the races sailed. A
running fraction is maintained so that after each race points are
added to both the numerator and denominator, and the resulting new
fraction is the score to date. This procedure automatically gives
lesser weight to smaller races.

Together with item 1 this means that as between boats who are always
out sailing, the point scores for their relative positions is
dependant solely on their results, and completely independant of the
fleet size. If A gets first to B's third in a large fleet on Saturday
and they then sail to a 3-1 on Sunday in a small fleet, their results
are the same. They earn the same number of points, which should be the
case for a 'fair' system.

3. Under traditional systems, a DSQ or DNF puts a boat out of
contention. A worst race exemption mitigates this but is not effective
for season-type championships where there may be any number of races
not sailed. With a drop race, each boat's score is unknown until the
end and the calculations must be done twice on a running basis.
Cox-Sprague makes the penalty much less severe, about 58/100 instead
of 0/100 and no drop is necessary. A DNS is irrelevant to the system,
neither adding nor subtracting points.
**************

Regards,
Colin
www.sailwave.com

> -----Original Message-----
> From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
> Sent: 28 August 2004 11:30
> To: sailwave@yahoogroups.com
> Subject: RE: [sailwave] points system technical note
>
>
> Hi Colin
> OK here is the CSC-modified Rinderle formula presented in the
form entered
> into Excel:
>
> Points
> =IF(N>=P,ROUND(89.5*(1-EXP(-(0.8+0.23*N)))*(IF(N=1,1,(N-P)/(N-1)))
> ,1)+10.5,"
> ")
>
> where N is the Number of Starters and P is the Position.
>
> In addition for RTD, DNF, etc, then Points = 0.5
> And for a DSQ, DNC (and in my view also for a DNS) then Points = 0
>
> This is exactly the form of Jim Rinderle's original formula but with the
> parameters 89.5, 0.8 and 0.23 changed a bit. Clearly one can
> dream up other
> variations by changing the parameters, including also changing
the 10.5 if
> one wishes to apply something different for last position. .
> Although I have not seen any presentation of the formula used for Cox
> Sprague there are obvious similarities with that but, in that
> case, the last
> place value is a function of the number of participants. But I guess
> someone must know the Cox Sprague formula (rather than having to use the
> look up table). I have not checked in detail but it may be
> possible to add
> a further element to my formula to make it equivalent to Cox
Sprague or at
> worst a close approximation, you would then only need to choose the
> parameters to match whatever scoring system is desired.
> I hate look-up tables and I always go for a formula to simplify
things and
> give maximum flexibility.
> Hope this is useful.
> Best regards,
> Geoff B
>
>
>
> -----Original Message-----
> From: Colin Jenkins [mailto:colin@sailwave.com]
> Sent: 28 August 2004 10:29
> To: sailwave@yahoogroups.com
> Subject: RE: [sailwave] points system technical note
>
>
> Hi Geoff,
>
> Would you be prepared to let me know the formula - I would prefer to
> implement that, rather then use a table.
>
> I have emailed Jim R a few times asking the same, but he does
not respond.
>
> Regards,
> Colin J
> www.sailwave.com
>
>
> > -----Original Message-----
> > From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
> > Sent: 25 August 2004 21:40
> > To: sailwave@yahoogroups.com
> > Subject: RE: [sailwave] points system technical note
> >
> >
> > Hi Colin et al
> > You may be interested in my comments on the Rinderle B System.
> > The table commonly quoted as being gospel for Rinderle B has some
> > anomalies
> > in it and if inspected closely it does not actually reflect the
> > values that
> > were derived some long time ago using Jim Rinderle's original formula.
> > There is clearly an advantage for a system such as Sailwave if a
> > formula is
> > used rather than a look-up table. So I have derived such a
> formula, which
> > matches the principles of Rinderle B but with some very minor
> > improvements.
> > One such improvement is to make the score for a win against
an infinite
> > number of boats = 100.
> > (In practice my formula gives a score of 99.9 for a win in a 25
> boat race.
> > (The current Rinderle B table gives 100.5 instead of 100 for
an infinite
> > number of boats. The extra 0.5 seems a bit pointless.)
> > At the other end I have set it so that a win in a 3 boat race gives
> > approximately 80 points (actually 79.8).
> > The score for last place in any size of race remains at 10.5 with
> > the score
> > for a retirement being 5.
> > I believe this is a more understandable and useful way of applying the
> > Rinderle B principles - but of course that is only my personal view.
> > Rather than present the formula here I have attached a
> spreadsheet for the
> > table for races of between 3 and 25 boats. The formula is of
> > course present
> > in each cell and it also includes the fiddly bits that round
> all scores to
> > one decimal place and avoids putting rubbish in non-used cells.
> > Best regards,
> > Geoff B
> > Sailing Secretary, Chipstead SC
> >
> >
> >
> >
> > [Non-text portions of this message have been removed]
> >
> >
> >
> >
> > -!- http://www.fastmail.fm/ -!- http://www.spampal.org/ -!-
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> >
> >
> >
> >
> >
> >
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Geoff_Burrell · 31 August 2004 00:12

Hi Colin
OK you have got me going into developing a version of my formula to deal
with the non-linear factors.
The equation below does basically the same as my previous formula but with
two additions -
(1) I have included a non-linearity parameter 'k' which enables larger
differences to be applied to the scores for boats near the front of the
fleet. In practice for large fleets it would not however make sense to make
this factor too large because it would cause the scores for the boats at the
back to be too close together. A figure of 1.5 would be satisfactory. For
the normal linear approach (as Rinderle) k = 1. (NB Cox-Sprague, which is
not a formula based approach at all, has significant problems in dealing
with this and cannot deal with large fleets).
(2) I have also addressed a feature or the Rinderle method that I have
always considered to be something of a slight weakness. That is Rinderle
caters well for the boats near the top of the fleet by giving a slightly
better score if one beats a larger number of boats. But the last boat
always scores the same (10.5) irrespective of how many boats are ahead of
her. So I have included a factor 'F' which adjusts the score for last
position to allow for this and this in turn leads to adjustments for all
boats in the race. My formula is general in that it allows any reasonable
factor to be used. For the normal (previous) formula F is zero. If one
sets F = 1 then this means that the score for being last is increased from
the normal figure of d = 10.5 by the same amount as the winning score is
reduced from 100. It's a little difficult to describe this but what it
means is that the formula then works with equal effectiveness at both ends
of the scale, top and bottom. I have used a value for F of 0.667 in the
Burrell Hi Pt Scoring file I will place on the website, i.e. the effect at
the bottom of the list is then two thirds of that at the top.
There is however a further thing that I would propose if one follows this
approach and that is to also adjust the score for RTD/DNF in synchronism
with the change in score for the last place (which is now different
depending on number of starters). To do this I would propose:
RTD Points = (5 * Last Place Points) / 10.5

So the new formula is:
Points = (100 - d)*{[(S - P)/(S - 1)]^k *[1 - (1 + F)*exp-(b + c*S)] +
F*exp-(b + c*S)} + d

The values for the parameters are:
b = 0.8
c = 0.23
d = 10.5
k = 1.5 (non-linear) or 1 (normal)
F = 0.667 (last place adjustment) or 0 (normal)

Just as with the previous formula the method simply requires the scores for
each race to be added, so that each helm/crew gets a score on the sheet from
the very first race rather than having to wait for sufficient races to be
sailed to qualify. Up to a prescribed maximum number of races are counted
and participants can readily see how well they are doing at all stages of
the series.
If sufficient interest develops in this new formula then it would make sense
for interested clubs to test it by playing with the parameters k and F to
form a consensus as to the optimum values. My personal view is that the
original principles of Rinderle work well without it being necessary to
apply the non-linear factor k at all - in which case this can be retained at
zero.
I think however that there is merit in applying the last place adjustment
and to do this F = 0.667 would be sensible. The absolute maximum value to
consider for F would be 1.

Hope this gives you something to think about!!
Best regards
Geoff B
Sailing Secretary, Chipstead Sailing Club

ColinJenkins · 31 August 2004 15:55

Hi Geiff, Interesting; will get back to you.

I've added some Rinderle graphs to the tech note, showing that the
non-linearity is associated with the points you get for the same place as
the number of starters changes.

http://www.sailwave.com/index.php?page=tnote&num=4

CJ

···

-----Original Message-----
From: Geoff Burrell [mailto:geoff.burrell@btinternet.com]
Sent: 31 August 2004 01:12
To: sailwave@yahoogroups.com
Subject: RE: [sailwave]More on Burrell Hi Pt Scoring

Hi Colin
OK you have got me going into developing a version of my formula to deal
with the non-linear factors.
The equation below does basically the same as my previous formula but with
two additions -
(1) I have included a non-linearity parameter 'k' which enables larger
differences to be applied to the scores for boats near the front of the
fleet. In practice for large fleets it would not however make
sense to make
this factor too large because it would cause the scores for the
boats at the
back to be too close together. A figure of 1.5 would be satisfactory. For
the normal linear approach (as Rinderle) k = 1. (NB Cox-Sprague, which is
not a formula based approach at all, has significant problems in dealing
with this and cannot deal with large fleets).
(2) I have also addressed a feature or the Rinderle method that I have
always considered to be something of a slight weakness. That is Rinderle
caters well for the boats near the top of the fleet by giving a slightly
better score if one beats a larger number of boats. But the last boat
always scores the same (10.5) irrespective of how many boats are ahead of
her. So I have included a factor 'F' which adjusts the score for last
position to allow for this and this in turn leads to adjustments for all
boats in the race. My formula is general in that it allows any reasonable
factor to be used. For the normal (previous) formula F is zero. If one
sets F = 1 then this means that the score for being last is
increased from
the normal figure of d = 10.5 by the same amount as the winning score is
reduced from 100. It's a little difficult to describe this but what it
means is that the formula then works with equal effectiveness at both ends
of the scale, top and bottom. I have used a value for F of 0.667 in the
Burrell Hi Pt Scoring file I will place on the website, i.e. the effect at
the bottom of the list is then two thirds of that at the top.
There is however a further thing that I would propose if one follows this
approach and that is to also adjust the score for RTD/DNF in synchronism
with the change in score for the last place (which is now different
depending on number of starters). To do this I would propose:
RTD Points = (5 * Last Place Points) / 10.5

So the new formula is:
Points = (100 - d)*{[(S - P)/(S - 1)]^k *[1 - (1 + F)*exp-(b + c*S)] +
F*exp-(b + c*S)} + d

The values for the parameters are:
b = 0.8
c = 0.23
d = 10.5
k = 1.5 (non-linear) or 1 (normal)
F = 0.667 (last place adjustment) or 0 (normal)

Just as with the previous formula the method simply requires the
scores for
each race to be added, so that each helm/crew gets a score on the
sheet from
the very first race rather than having to wait for sufficient races to be
sailed to qualify. Up to a prescribed maximum number of races are counted
and participants can readily see how well they are doing at all stages of
the series.
If sufficient interest develops in this new formula then it would
make sense
for interested clubs to test it by playing with the parameters k and F to
form a consensus as to the optimum values. My personal view is that the
original principles of Rinderle work well without it being necessary to
apply the non-linear factor k at all - in which case this can be
retained at
zero.
I think however that there is merit in applying the last place adjustment
and to do this F = 0.667 would be sensible. The absolute maximum value to
consider for F would be 1.

Hope this gives you something to think about!!
Best regards
Geoff B
Sailing Secretary, Chipstead Sailing Club

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Ocean_Racing_Club_o1 · 1 September 2004 00:06

Geoff,

The main resistance we have for implementing these systems is that
the guy in the water needs a spreadsheet to work out how many points
they are going to get for a race. This makes the tactical poistion
almost impossible to work out.

The Cox-Sprague has a feature that you may have missed that makes it
attractive from this point of view.

The difference in points between places is
always the same, no matter what size the fleet is. So
1st will always make 6 points over 2nd and 5th will make 3 points
over 6th.

As a tactician, I need to know, for any boat on the water, how many
places I need to beat them by to lead the series. Cox-Sprague is the
only variable spread system that gives me this.

So, if you can come up with a system with a variable spread but fixed
difference between places, you'll make a lot of people happy and
it'll work on the water too.

You'll probably qualify for sainthood as well.

--- In sailwave@yahoogroups.com, "Geoff Burrell" <geoff.burrell@b...>
wrote:

···

(NB Cox-Sprague, which is not a formula based approach at all,
has significant problems in dealing with this and cannot deal
with large fleets).

ColinJenkins · 1 September 2004 08:02

Hi Mike,

WRT Cox-Sprague and it's percentage of perfection final series total.
Looking at the shape of C-S, RinderleB and Austrian, they all do the same
sort of thing(ish), so presumably they could all be scored as just points or
percentage of perfection. i.e. what I'm getting as is could PoP be added as
a series scored method (along with points accumulation and averaging which
are already there), rather than hard-wire it to C-S only.

Colin
www.sailwave.com

···

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Ocean_Racing_Club_o1 · 1 September 2004 11:17

Colin,

I'me really just being a devil's advocate here. As I do scoring as
well, Cox-Sprague sucks from that point of view.

I'm just concious of the fact that there are two sides to scoring a
series:
* fairness
* tactical

Most of the methods discussed address the fairness part. Indeed,
Geoff and others are talking about putting in tweaks to the formulae
so that people can make it "more fair" for their own particular
circumstances. This is brilliant for the "art" of race scoring and
I'm watching all of this with great interest.

In terms of the second side of things, it is easy (and I'm guilty of
this as well) to get caught up in the "art" and lose side of the
tactical nature of series scoring.

Take our Winter Series which is coming to a close. The last short
race is critical for positioning before the ocean race. We still use
Bonus High Point Scoring here - chiefly because of its
understandability.

Personally, I despair over its shortcomings as a series scoring
method but, for the tacticians, it is easy for them to say before the
race...

"We need to beat Yoko by 2 places and Ruthless by 1 place to be first
in the series. That means we have to beat Yoko by about 3 seconds
every minute and be within 2 seconds of Ruthless."

As a tactician, that gives me some options for fighting a race to win
the series.

This makes for close racing folks.

We can make scoring a series fairer but to make it a great series, it
has to be competitive and that means making the numbers easy to work
with.

Mike

Geoff_Burrell · 1 September 2004 11:27

I do agree that an ability to easily determine ones required tactical
relationship against the opposition is extremely important. Ease of
understanding is also a particularly important feature of any scoring system
and introduction of any such scheme tends to be faced with some resistance
for that reason.
The Cox-Sprague system is actually significantly more difficult than a
Rinderle approach in this respect, assuming of course that the C-S method is
being used in the way originally prescribed. Because C-S calculates a boat
s score in the series as a percentage of perfection over the whole series it
is extremely difficult to work out the required tactical approach to the
(final) race. The fact that the intervals between positions are whole
numbers and the same for all races gives a misleading view that one can
easily work out the tactics. In practice the non-constant intervals makes
this even more difficult and while one may be able to determine what score
one would get for the individual race, the calculation for the whole series,
and hence ones final standing against the opposition, is substantially more
difficult. Clearly one might use the Cox-Sprague table and simply add the
points together but, first, that is not what is intended for the method and,
secondly, that leads to a pretty unfair scoring system with no logical
justification.
It all depends on how the organising club judges the relative importance of
fairness of results versus ease of (tactical) understanding. The trick
is to get what is considered to be the optimum combination based largely on
subjective grounds.
On both grounds for my money I think a Rinderle approach has a significant
edge but to ease the understanding aspect I would choose the simpler
linear method where all the intervals between positions in a race are the
same. If one knows within a boat or two the number of participants in a
race then it is straightforward to work out what to do tactically. And
because ones score is simply added to the previous total (possibly
discarding the worst score) then you are not faced with a second stage
horrible calculation to work out percentage of perfection (which is what
C-S sets out to do).
For example, in a 10 boat race and using my formula with F = 0.667 and K = 1
then one knows that each position improved is worth 9.2 points and for 9
boats it is 10.1 and for 11 boats 8.4. (If one wishes to only use whole
numbers then the whole table can be multiplied by 10).
At the end of the day its simply a matter of preference.
Best regards
Geoff

···

-----Original Message-----
From: Ocean Racing Club of Victoria Rudder Cup
[mailto:rudder_cup@orcv.org.au]
Sent: 01 September 2004 01:07
To: sailwave@yahoogroups.com
Subject: Re: [sailwave]More on Burrell Hi Pt Scoring

Geoff,

The main resistance we have for implementing these systems is that
the guy in the water needs a spreadsheet to work out how many points
they are going to get for a race. This makes the tactical poistion
almost impossible to work out.

The Cox-Sprague has a feature that you may have missed that makes it
attractive from this point of view.

The difference in points between places is
always the same, no matter what size the fleet is. So
1st will always make 6 points over 2nd and 5th will make 3 points
over 6th.

As a tactician, I need to know, for any boat on the water, how many
places I need to beat them by to lead the series. Cox-Sprague is the
only variable spread system that gives me this.

So, if you can come up with a system with a variable spread but fixed
difference between places, you'll make a lot of people happy and
it'll work on the water too.

You'll probably qualify for sainthood as well.

--- In sailwave@yahoogroups.com, "Geoff Burrell" <geoff.burrell@b...>
wrote:

(NB Cox-Sprague, which is not a formula based approach at all,
has significant problems in dealing with this and cannot deal
with large fleets).

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Mike_Trish_Butterfie · 1 September 2004 12:10

What formula do you use for the bonus high point scoring?

···

----- Original Message -----
From: "Ocean Racing Club of Victoria Rudder Cup" <rudder_cup@orcv.org.au>
To: <sailwave@yahoogroups.com>
Sent: Wednesday, September 01, 2004 12:17 PM
Subject: Re: [sailwave]More on Burrell Hi Pt Scoring

Colin,

I'me really just being a devil's advocate here. As I do scoring as
well, Cox-Sprague sucks from that point of view.

I'm just concious of the fact that there are two sides to scoring a
series:
* fairness
* tactical

Most of the methods discussed address the fairness part. Indeed,
Geoff and others are talking about putting in tweaks to the formulae
so that people can make it "more fair" for their own particular
circumstances. This is brilliant for the "art" of race scoring and
I'm watching all of this with great interest.

In terms of the second side of things, it is easy (and I'm guilty of
this as well) to get caught up in the "art" and lose side of the
tactical nature of series scoring.

Take our Winter Series which is coming to a close. The last short
race is critical for positioning before the ocean race. We still use
Bonus High Point Scoring here - chiefly because of its
understandability.

Personally, I despair over its shortcomings as a series scoring
method but, for the tacticians, it is easy for them to say before the
race...

"We need to beat Yoko by 2 places and Ruthless by 1 place to be first
in the series. That means we have to beat Yoko by about 3 seconds
every minute and be within 2 seconds of Ruthless."

As a tactician, that gives me some options for fighting a race to win
the series.

This makes for close racing folks.

We can make scoring a series fairer but to make it a great series, it
has to be competitive and that means making the numbers easy to work
with.

Mike

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Mike_Trish_Butterfie · 1 September 2004 12:12

When you sell the scoring systen to the Clubs, they have often heard of the
Names of the scoring system.

If you use your own system then people do not understand and ask for a
deailed explanation. enough said!

Mike Butterfield

···

----- Original Message -----
From: "Colin Jenkins" <colin@sailwave.com>
To: <sailwave@yahoogroups.com>
Sent: Wednesday, September 01, 2004 9:02 AM
Subject: RE: [sailwave]More on Burrell Hi Pt Scoring

Hi Mike,

WRT Cox-Sprague and it's percentage of perfection final series total.
Looking at the shape of C-S, RinderleB and Austrian, they all do the same
sort of thing(ish), so presumably they could all be scored as just points

or

percentage of perfection. i.e. what I'm getting as is could PoP be added

as

a series scored method (along with points accumulation and averaging which
are already there), rather than hard-wire it to C-S only.

Colin
www.sailwave.com

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Ocean_Racing_Club_o1 · 2 September 2004 00:11

The Bonus High Point is actually a fixed point system with a bonus
for 1st to help overcome ties - doesn't always though.

Hence:
  1st - 100
  2nd - 98
  3rd - 97
  4th - 96 ... and so on.

Colin has made it really easy to do this.

In the "Edit" menu select the "Edit Scoring System..." menu item. In
the "Scorring System" dialog box, click on the "Race Scoring" tab.
Under the "High point systems" area, click on the "Custom high point
defined by a list of points" radio button.

Enter the following sequence in the text box: "100,98,97".

That's it. The software works out everything else. You have to tell
it how to do DNF and that which can be a little tricky (think
backwards).

This system will give you the exact same series results as Bonus Low
Point. Try it if you don't believe me.

I once asked our race officials why they used it instead of Bonus Low
Point and was told:

"You get more points the better you do - just like in school".

I had to ask!

Mike

--- In sailwave@yahoogroups.com, "Mike & Trish Butterfield"
<pmbutterfield@e...> wrote:

···

What formula do you use for the bonus high point scoring?