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IMJ Archives - 003

Mahjong club - Lifetime Ranking Measure
(Initiated message 10 Sep 1999 - Newsgroups: rec.games.mahjong / File [maiarchives003])

PREFACE:

A system to measure a player's "Lifetime Ranking" is one of the long term development of International Mahjong ("IMJ"). The following recorded the messages once posted at the newsgroup rec.games.mahjong. Obviously the topic was not of interest of the majority of the NG readers. This page is to record the event and is for future reference should anyone come across this topic and wish to contribute their opinions (or want to make use of the ideas contained herein). Should you wish to contribute your ideas/suggestions to the IMJ development you are welcome to email to the author.

Cofa Tsui, author
International Mahjong Rules
email: imj@cofatsui.com
September 24, 1999
<><><><><><><><><><><><><>

From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Input requested: Lifetime Ranking Measure
Date: 10 Sep 1999 00:00:00 GMT
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Hi Group,

I have been working on a system that is used to measure the Ranking of a
player in his lifetime playing of mahjong. (Obviously the job is
initiated for International Mahjong. The Ranking involving different
types of mahjong would not be ideal for comparison purposes. The system
once established, however, may be used to measure the Ranking of ANY
type of mahjong IF only one type of game is involved.)

The following paragraphs are marked (A), (B), (C)... for reference
purposes and are the initial ideas I have worked out (so far) for the
proposed system. For definition of terminology used please refer to the
bottom of this message.

(A) Initially in my mind, each measure shall involve two sets of number:
(a) Number of Events played to date;
(b) Average Scores Per Event to date.

(B) For example, Player A in his lifetime may have played 3 Events of
mahjong games, each Event has the following scores recorded ("+" means
Scores won, "-" means Scores lost):
Event 1 = +5,000;
Event 2 = -800;
Event 3 = +3,000.
His lifetime Ranking measure is obtained by simple calculations, as follows:
(Number of Events played to date) / (Average Scores of All Events played) =
3 / {[(+5000)+(-800)+(+3000)]/3} = 3/{[+7200]/3} =
3/800
[Correction 9/24/99: The correct result should be 3/2400]

(C) As a result, the Lifetime Ranking Measure of the player is 3/2400,
which means he has played 3 Events in his lifetime to date and the
average Scores of all Events played is 2,400 Scores.

(D) Eventually the Lifetime Ranking Measure may be obtained with the
following formula:
n / [(S1+S2+S3+...+Sn)/n] where:
The first "/" is a separator not a calculator;
n = Number of Events played to date;
S1, S2, S3... Sn = Scores recorded for Event 1, Event 2, Event 3, ... up
to Event n.

(E) For the updated Lifetime Ranking Measure after each additional Event
played, the following formula may be used:
(n+1) / { [(S1+S2+S3+...+Sn)/n]*n + S(n+1) } / (n+1)

The input I request from you folks may be summarized as follows:

For Paragraph (A):

(a)- Would these two factors good enough to determine a player's
lifetime rank?

(b)- If not, what other factors would you suggest?

(c)- Initially in my mind I have set 8 Rounds to be played for each
Event to be qualified for the purposes of reaching a Lifetime Ranking
Measure, not more or not less. Would this number of Rounds per Event
good enough?

(d)- I also have set the minimum and maximum numbers of Folds to be won
in each Game (Art. 7.3 of the IMJ Rules). I have set the Agreed Lowest
Rank to be 3 Folds and the Agreed Highest Rank to be 13 Folds (not
higher, not lower). Any input? (Note: Beginners normally play with games
allowing any rank to be won. The lifetime ranking system is obviously
NOT intended to record scores of players at their entry levels.)

(e)- Whether the Full Scoring System or the Semi Scoring System should
be used. (Note: In Full Scoring System the Scores of a Rank are double
of the preceding Rank. In Semi Scoring System the Scores of a Rank are
less than double of the preceding Rank.)

(f)- Any other suggestions not mentioned above?

For Paragraph (B) ~ Paragraph (E):
I will post other requests later and one group at a time, if
participation indicates it to be appropriate. For the meantime let's
concentrate on Paragraph (A) only.

<><><><><><><><><><><><><>
Terminology: IMJ Rules uses a set of terminology, each of which is
defined by a rule. In most cases, an IMJ term is written with its first
letter in UPPERCASE. For definitions of the terms such as Event, Round,
Game, etc., please visit:
http://www.cofatsui.com/mahjze01a01.html

COFA TSUI
International Mahjong Rules - World's FIRST comprehensive set of
written rules of mahjong, governing every step of play. (tm)
IMJ Rules on PDF file - IT IS NOW SHIPPING!
http://www.cofatsui.com/mahjong.html
imj@cofatsui.com

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From: mrep@telekabel2.nl (Martin Rep)
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 12 Sep 1999 00:00:00 GMT
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On Fri, 10 Sep 1999 19:50:07 GMT, Cofa Tsui <cofatsui@my-deja.com>
wrote:

>
>(A) Initially in my mind, each measure shall involve two sets of number:
>(a) Number of Events played to date;
>(b) Average Scores Per Event to date.
>
>For Paragraph (A):
>
>(a)- Would these two factors good enough to determine a player's
>lifetime rank?
>
>(b)- If not, what other factors would you suggest?
>
>(c)- Initially in my mind I have set 8 Rounds to be played for each
>Event to be qualified for the purposes of reaching a Lifetime Ranking
>Measure, not more or not less. Would this number of Rounds per Event
>good enough?
>
>(d)- I also have set the minimum and maximum numbers of Folds to be won
>in each Game (Art. 7.3 of the IMJ Rules). I have set the Agreed Lowest
>Rank to be 3 Folds and the Agreed Highest Rank to be 13 Folds (not
>higher, not lower). Any input? (Note: Beginners normally play with games
>allowing any rank to be won. The lifetime ranking system is obviously
>NOT intended to record scores of players at their entry levels.)
>
>(e)- Whether the Full Scoring System or the Semi Scoring System should
>be used. (Note: In Full Scoring System the Scores of a Rank are double
>of the preceding Rank. In Semi Scoring System the Scores of a Rank are
>less than double of the preceding Rank.)

Cofa

Three remarks.
1. I welcome this initiative very much. Of course it will meet with
the common problem: what type of mahjong is involved. Since this
posting is from you, there is no doubt that you are talking about IMJ.

Since I fear these rules are not widely-known, not even by the members
of this newsgroup, I suggest you publish them just for free on your
website. Would not that be the best way to spread their popularity?

2. In Japan there is a system of dan; not only for judo and
jiu-jiutsu, but also for mahjong (this has been mentioned earlier in
this newsgroup). Perhaps it is wise first to investigate how this
system works. (Probably that system is about riichi, but perhaps it is
good for you as well.)

3. For the rating, I think not only the number of events and the
results will do, but also the frequency of the games. E.g. a player
who has won three games two years ago, does not deserve a high
lifetime ranking, imho.

Greetings

| Visit the Internet Mahjong Newspaper
| http://www.mahjong-nl.com
| extensive website in Dutch and English
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From: actsearch@aol.com (Tom Sloper)
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 12 Sep 1999 00:00:00 GMT
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I agree with Martin that the Japanese dan system needs to be considered, since
it is already in existence for quite some time.
If there is a system in use in Hong Kong or Taiwan, then those systems should
also be considered.

It would be good to know more about the Japanese dan system and how it works.

Tom Sloper, Activision
Executive Producer, Shanghai
tsloper@activision.com (wkdays)
Actsearch@aol.com (wkends)
The opinions expressed herein are those of the writer, not of Activision.
http://www.activision.com/games/dynasty
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From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 12 Sep 1999 00:00:00 GMT
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Martin wrote:
1. I welcome this initiative very much. Of course it will meet with the
common problem: what type of mahjong is involved. Since this posting is
from you, there is no doubt that you are talking about IMJ.

From Cofa:
The system could be used in ANY mahjong game, if only ONE type of
mahjong is used for that particular ranking. (See my original posting:
"... The system once established, however, may be used to measure the
Ranking of ANY type of mahjong IF only one type of game is involved.")
In face, this discussion is NOT intended to relate to only one or any
specific mahjong type.

Martin wrote:
Since I fear these rules are not widely-known, not even by the members
of this newsgroup, I suggest you publish them just for free on your
website. Would not that be the best way to spread their popularity?

From Cofa:
I had thought of this idea. For many reasons however, this might just
not be a good time to do at this stage (of the overall development of
IMJ). Since this is not related to the topic of a lifetime ranking
system, further discussions on this issue are welcome off-line, by
sending email directly to me - see bottom.

Martin wrote:
2. In Japan there is a system of dan; not only for judo and jiu-jiutsu,
but also for mahjong (this has been mentioned earlier in this
newsgroup). Perhaps it is wise first to investigate how this system
works. (Probably that system is about riichi, but perhaps it is good for
you as well.)

From Cofa:
Could someone provide more info on the "system of dan", or direct us to
the sources of such info? Thanks.

Martin wrote:
3. For the rating, I think not only the number of events and the results
will do, but also the frequency of the games. E.g. a player who has won
three games two years ago, does not deserve a high lifetime ranking,
imho.

From Cofa:
This may be an idea that could also be considered. But my current
thinking is, when looking at one's Ranking Measure, the number of Events
played may, indeed, also count. In time, people will justify whether one
will look at the "number of Events" more or at the "overall average
Scores per Event" more, to determine one's Ranking.

Tom Sloper wrote:
I agree with Martin that the Japanese dan system needs to be considered,
since it is already in existence for quite some time. If there is a
system in use in Hong Kong or Taiwan, then those systems should also be
considered.

It would be good to know more about the Japanese dan system and how it
works.

From Cofa:
Yes, more input please!

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From: tarot@notmenetvigator.com (Alan Kwan)
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 13 Sep 1999 00:00:00 GMT
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On Fri, 10 Sep 1999 19:50:07 GMT, Cofa Tsui <cofatsui@my-deja.com>
wrote:

>I have been working on a system that is used to measure the Ranking of a
>player in his lifetime playing of mahjong. (Obviously the job is
>initiated for International Mahjong. The Ranking involving different
>types of mahjong would not be ideal for comparison purposes. The system
>once established, however, may be used to measure the Ranking of ANY
>type of mahjong IF only one type of game is involved.)

It is possible to combine several different types of play under one
rating system, if we have statistical data on "average" scores of a
match for each type of play. ("Average" here means, of course,
something like the "standard deviation" or the "mean of absolute
values", rather than the "arithmatic mean" which is always zero.)

"Live life with Heart." - Alan Kwan / tarot@notmenetvigator.com
http://home.netvigator.com/~tarot (hard-core game reviews)
(please remove anti-spam section "notme" from mailing address)
Dimension S editor: http://209.213.100.47/
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From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 15 Sep 1999 00:00:00 GMT
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In article <37dcd855.436659@news.netvigator.com>,
tarot@notmenetvigator.com (Alan Kwan) wrote:
> On Fri, 10 Sep 1999 19:50:07 GMT, Cofa Tsui <cofatsui@my-deja.com>
> wrote:
>
> >I have been working on a system that is used to measure the Ranking
of a
> >player in his lifetime playing of mahjong. (Obviously the job is
> >initiated for International Mahjong. The Ranking involving different
> >types of mahjong would not be ideal for comparison purposes. The
system
> >once established, however, may be used to measure the Ranking of ANY
> >type of mahjong IF only one type of game is involved.)
>
> It is possible to combine several different types of play under one
> rating system, if we have statistical data on "average" scores of a
> match for each type of play. ("Average" here means, of course,
> something like the "standard deviation" or the "mean of absolute
> values", rather than the "arithmatic mean" which is always zero.)
>

This could be another consideration that may be kept on file. However, I
am afraid it may not be practical as it would be as difficult as
trying to reach a "unified" form of mahjong.

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From: tarot@notmenetvigator.com (Alan Kwan)
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 15 Sep 1999 00:00:00 GMT
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On Wed, 15 Sep 1999 14:38:12 GMT, Cofa Tsui <cofatsui@my-deja.com>
wrote:

>In article <37dcd855.436659@news.netvigator.com>,
> tarot@notmenetvigator.com (Alan Kwan) wrote:

>> It is possible to combine several different types of play under one
>> rating system, if we have statistical data on "average" scores of a
>> match for each type of play. ("Average" here means, of course,
>> something like the "standard deviation" or the "mean of absolute
>> values", rather than the "arithmatic mean" which is always zero.)
>>
>
>This could be another consideration that may be kept on file. However, I
>am afraid it may not be practical as it would be as difficult as
>trying to reach a "unified" form of mahjong.

They are different. There are many obstacles in the way towards
reaching a "unified" style of play: the rules need to be well
presented and readily available, resources need to be spent on
promotion, and the rules must seem reasonably preferable for players
of existing styles (the game must seem at least as fun as the existing
game, and it must be simple enough for the masses to learn or it'll
receive poor propagation).

Combining ratings of different playing styles is merely a simple
statistical process; the above mentioned obstacles are irrelevant.
I'm not intending to impose a 'global, unified' rating system; it can
be used locally, for example for Shanghai Dynasty players who play
multiple styles among those supported by the software.

From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 24 Sep 1999 00:00:00 GMT
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Messages of this thread are now posted at:
http://www.cofatsui.com/mahjze02.html
Under title Mahjong club - Lifetime Ranking Measure.

You can also view previous messages from this NG in an organized form,
at the above URL.

Having Question About Rules?
"International Mahjong Rules" has ALL rules, in same ONE rulebook, which
governs every step of play. Participate in the Contest "Challenge &
Quest To Win" and get yourself a CASH prize (if you could)! Visit the
following web page for details:
http://www.cofatsui.com/mahjzc03.html

P.S.
Although the topic seems was not of interest of the majority of the
readers in this NG, there are still some questions that I would
appreciate some input - Please refer to input request Items (a) through
(f) of my initial posting. i.e., How many Rounds do you normally play in
your regular gatherings? What is the minimum number of Fans allowed in a
winning hand? If possible, with reasons why you think that settings are
appropriate, etc. Your input is highly appreciated!

COFA TSUI
International Mahjong Rules - World's FIRST comprehensive set of
written rules of mahjong, governing every step of play. (tm)
IMJ Rules on PDF file - Now available for sale via Email.
http://www.cofatsui.com/mahjong.html
imj@cofatsui.com

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From: Jesper Harder <jesper_harder@hotmail.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 26 Sep 1999 00:00:00 GMT
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Cofa Tsui <cofatsui@my-deja.com> writes:

> Although the topic seems was not of interest of the majority of the
> readers in this NG,

Well, I found it interesting - I was especially looking forward to
hearing some more about the Japanese Dan system.

> there are still some questions that I would appreciate some input [..]
> i.e., How many Rounds do you normally play in your regular gatherings?

We usually try to play at least 16 turns, i.e. until the prevailing wind
is to become East again - of course the exact number depends on how many
times East goes out.

> What is the minimum number of Fans allowed in a winning hand?

We don't have a minimum fan requirement, instead ordinary mahjong hands
have to be cleared, i.e. one suit only.

> If possible, with reasons why you think that settings are
> appropriate, etc. Your input is highly appreciated!

IMHO your scheme looks very reasonable. Instead of average score per
event you could use average score per turn, I don't know which number is
most appropriate. Also, the standard deviation of the score would be an
interesting number.

--
Jesper Harder, <URL: http://purl.org/harder/ >
S?es: Bolig i ?hus pr. 1. oktober. Max kr. 3000.
*************************************End of message

From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 26 Sep 1999 00:00:00 GMT
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In article <wkg102eict.fsf@ifa.au.dk>,
Jesper Harder <jesper_harder@hotmail.com> wrote:
> Cofa Tsui <cofatsui@my-deja.com> writes:
>
> > Although the topic seems was not of interest of the majority of the
> > readers in this NG,
>
> Well, I found it interesting - I was especially looking forward to
> hearing some more about the Japanese Dan system.

So am I - Any input about the Japanese Dan system from anyone please?

>
> > there are still some questions that I would appreciate
> > some input [..] i.e., How many Rounds do you normally
> > play in your regular gatherings?
>
> We usually try to play at least 16 turns, i.e. until the
> prevailing wind is to become East again - of course the
> exact number depends on how many times East goes out.

How long do you normally need to finish 16 turns? What if East does not
go out? Would you estimate such time to be normally adequate for the
beginner/intermediate/advanced players?

(Sorry but I don't mean to ask for any personal info here - Please
consider these to be info of the average players in general, for the
purposes of establishing the "Lifetime Ranking" system.)

For your info: Long ago I/my groups of players used to play at least 8
Rounds - one Round is roughly 4 turns. Because we were playing minimum 4
Fold and maximum 13 Fold hands and for real money, it took 45 minutes to
an hour to finish one Round (if I recall it correctly).

Today, in my small groups of players by the IMJ Rules, we play for
Scores not for money. We play maximum 8 Rounds per Event. Since our
minimum Fold requirements vary from time to time (depends on who is
participating), I do not have yet had any time recorded for all the
Events. Usually we spend 2.5 ~ 4 hours in mahjong playing before the
dinner is served. (We normally play at a Chinese restaurant, which
provides the mahjong facilities and set dinner menu, as a package. Try
this out in your local Chinese restaurants!)

>
> > What is the minimum number of Fans allowed in a winning hand?
>
> We don't have a minimum fan requirement, instead ordinary mahjong
> hands have to be cleared, i.e. one suit only.

Interesting to learn that - i.e., hands to be "one suit" only. What type
of game do you play? In IMJ Rules system, a winning hand consists of
"one suit" only is already worth 9 Folds (i.e., the Clear Same, Art.
26.5). You must need longer time to complete even 1 turn, must you not?

>
> > If possible, with reasons why you think that settings are
> > appropriate, etc. Your input is highly appreciated!
>
> IMHO your scheme looks very reasonable. Instead of average score per
> event you could use average score per turn, I don't know which number
> is most appropriate.

This is a suggestion that would certainly be kept on file for future
study. However, initially I think the "turn" could be a unit too small
for this purpose. Using the IMJ terminology, 1 turn = 1 Game, in which,

1 Break = 4 Rounds = 4 x (4 Games/turns) = 16 Games/turns (roughly)

It is also practically not recommended to use a Game as a unit for the
results: Players usually do not appreciate players who leave the table
after having only finished few Games.

> Also, the standard deviation of the score would be
> an interesting number.
>

I am not quite understand what you mean by "standard deviation".

Would that mean a standard number to determine the skill level of a
player? I believe once the system is established, a "standard number"
will also be gradually established and recognized for each of the
different types of mahjong games, to indicate the "minimum marks" a
player must achieve before he/she is recognized to have reached a
specific skill level of that particular type of mahjong game.

IMO this could be equally interesting to imagine when this stage of the
mahjong evolution would happen!

By the way, THANKS, Jesper, for your input!

COFA TSUI
International Mahjong Rules - World's FIRST comprehensive set of
written rules of mahjong, governing every step of play. (tm)
IMJ Rules on PDF file - IT IS NOW SHIPPING!
internet: http://www.cofatsui.com/mahjong.html
email: imj@cofatsui.com

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From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 26 Sep 1999 00:00:00 GMT
Message-ID: <7slqg8$h$1@nnrp1.deja.com>
References: <7rbnda$s0a$1@nnrp1.deja.com> <37dcd855.436659@news.netvigator.com> <7rob0i$fs4$1@nnrp1.deja.com> <37dfbd82.746632@news.netvigator.com> <7sgb26$c2q$1@nnrp1.deja.com> <wkg102eict.fsf@ifa.au.dk> <7slmb0$tb9$1@nnrp1.deja.com>
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In article <7slmb0$tb9$1@nnrp1.deja.com>,
Cofa Tsui <cofatsui@my-deja.com> wrote:
> In article <wkg102eict.fsf@ifa.au.dk>,
> Jesper Harder <jesper_harder@hotmail.com> wrote:
> >
> > We usually try to play at least 16 turns, i.e. until the
> > prevailing wind is to become East again - of course the
> > exact number depends on how many times East goes out.
>
> How long do you normally need to finish 16 turns? What if East does
> not go out? ...

Sorry but I mean to ask "What if NO ONE goes out?" Do you change the
Jonga (Dealer) or does the Jonga remain the same?

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From: Jesper Harder <jesper_harder@hotmail.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 28 Sep 1999 00:00:00 GMT
Message-ID: <wkvh8uewkv.fsf@ifa.au.dk>
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Cofa Tsui <cofatsui@my-deja.com> wrote:

> Jesper Harder <jesper_harder@hotmail.com> wrote:

> How long do you normally need to finish 16 turns?

I haven't really thought about it, 5-7 hours I guess.

> What if NO ONE goes out? Do you change the Jonga (Dealer) or does
> the Jonga remain the same?

We change the dealer.

> Would you estimate such time to be normally adequate for the
> beginner/intermediate/advanced players?

I think four rounds (i.e. ca. 16 turns) takes too long when playing
with beginners - two or three rounds is probably more appropriate.

> (We normally play at a Chinese restaurant, which provides the mahjong
> facilities and set dinner menu, as a package. Try this out in your
> local Chinese restaurants!)

Sounds very appealing. Unfortunately, I haven't seen something like that,
probably because the Chinese/Asian community is quite small - most
immigrants around here have a Middle Eastern background.

> > We don't have a minimum fan requirement, instead ordinary mahjong
> > hands have to be cleared, i.e. one suit only.

> Interesting to learn that - i.e., hands to be "one suit" only. What type
> of game do you play?

Vanilla Western, specifically Max Robertson's rules with a few slight
variations. I'm not sure if I made it clear, but winds and dragons
*are* allowed in a cleared hand. Also, there are plenty of special hands
where mixing the suits is allowed.

> You must need longer time to complete even 1 turn, must you not?

Yeah. I've tried Chinese Classical a few times, that's definitely a
much faster game.

> > Also, the standard deviation of the score would be
> > an interesting number.
>
> I am not quite understand what you mean by "standard deviation".

I'll skip most of the statistical and niceties: the standard
deviation [1] is basically a statistical measure of much you would
expect a quantity to deviate from its average value. Usually about
two-thirds of the data values will be within a distance of one
standard deviation on either side of the average.

Let us say that a given player has participated in n events with a score
of x_i in event number i. Her average score per event, a, is then

a = (x_1 + x_2 + ... + x_n)/n

and the standard deviation is calculated as

s = squareroot((x_1 - a)^2 + (x_2 - a)^2 + ... + (x_n - a)^2)/(n-1))

> Would that mean a standard number to determine the skill level of a
> player? I believe once the system is established, a "standard number"
> will also be gradually established and recognized for each of the
> different types of mahjong games, to indicate the "minimum marks" a
> player must achieve before he/she is recognized to have reached a
> specific skill level of that particular type of mahjong game.

The most straightforward way of doing this is probably to look at
percentiles. E.g. if a player has a score in the 60th percentile 60% of
the scores are lower than hers are (and 40% are higher). Therefore, you
could for instance define an "expert player" as a player whose score is
above the 80th percentile; a "beginner" as a player with a score below the
20th percentile etc. etc.

[1] To be entirely unambiguous I should probably say "adjusted error of
sample mean"

Cheers,
--
Jesper Harder, <URL: http://purl.org/harder/ >
S?es: Bolig i ?hus pr. 1. oktober. Max kr. 3000.
*************************************End of message

From: Cofa Tsui <cofatsui@my-deja.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 30 Sep 1999 00:00:00 GMT
Message-ID: <7suv7l$dbr$1@nnrp1.deja.com>
References: <7rbnda$s0a$1@nnrp1.deja.com> <37dcd855.436659@news.netvigator.com> <7rob0i$fs4$1@nnrp1.deja.com> <37dfbd82.746632@news.netvigator.com> <7sgb26$c2q$1@nnrp1.deja.com> <wkg102eict.fsf@ifa.au.dk> <7slmb0$tb9$1@nnrp1.deja.com> <wkvh8uewkv.fsf@ifa.au.dk>
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Thanks for the detailed formula leading to the term "standard
deviation". Although I do not understand the formula at all, I will keep
this message in record for future reference - Either for IMJ
developments or for use by other people.

Refer to the web page for the record of messages of this topic (will be
updated from time to time as new messages are posted):
http://www.cofatsui.com/mahjze02a21.html

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From: Jeppe Stig Nielsen <jeppesn@hotpop.com>
Subject: Re: Input requested: Lifetime Ranking Measure
Date: 30 Sep 1999 00:00:00 GMT
Message-ID: <37F3782A.F4828A18@hotpop.com>
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References: <7rbnda$s0a$1@nnrp1.deja.com> <37dcd855.436659@news.netvigator.com> <7rob0i$fs4$1@nnrp1.deja.com> <37dfbd82.746632@news.netvigator.com> <7sgb26$c2q$1@nnrp1.deja.com> <wkg102eict.fsf@ifa.au.dk> <7slmb0$tb9$1@nnrp1.deja.com> <wkvh8uewkv.fsf@ifa.au.dk> <7suv7l$dbr$1@nnrp1.deja.com>
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Cofa Tsui wrote:
>
> Thanks for the detailed formula leading to the term "standard
> deviation". Although I do not understand the formula at all, I will keep
> this message in record for future reference - Either for IMJ
> developments or for use by other people.

Excuse Harder, he's a science nerd ;-)

--
Jeppe Stig Nielsen, <URL:http://www.netby.net/Oest/Europa-Alle/jeppesn/>.

?an ved jo aldrig, hvor godt en Mands Evner havde slaaet til, hvis han
havde arbejdet paa en anden Maade, end det faldt ham naturligt.? - den danske matematiker Zeuthen om den danske matematiker Petersen
*************************************End of message

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