# Inbox: Fwd: The Role of 1.5 in Masterpoint Formulas (1 of 43)

Date:  Fri, 13 Jan 2012 14:31:58 -0500 [02:31:58 PM EST]
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Subject:  Fwd: The Role of 1.5 in Masterpoint Formulas
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---------- Forwarded message ----------
From: William Arlinghaus
Date: Sun, Apr 3, 2011 at 8:39 PM
Subject: The Role of 1.5 in Masterpoint Formulas
To: Bill Arlinghaus <warlingha@ltu.edu>, "BOD#25(Rich DeMartino)" <rademr@optonline.net>, "BOD#3(Joan Levy Gerard)" <joanandron@worldnet.att.net>, "BOD#4(craig robinson)" <4spot@comcast.net>, Claire Jones <stats@accesscomm.ca>, Robert Heller <hellerb@mindspring.com>, The Subecks <stansubeck@prodigy.net>

to the masterpoint committee:

In the grand old days of yesteryear, nobody worried about such things as 12-board sessions, 18-board sessions, etc.  Everybody ran at least 24 boards, and most ran more if they could.  How diefferent life is today, when people want short morning sessions, afternoon sessions that finish well before dinner, 12-board internet sessions, and even dinner bell knockouts with 12-board sesssions.

Nonetheless, I believe history has something to teach us.  In 1993, the masterpoint gurus seemed to be solidly behind the fact that doubling the number of sessions multiplied the award by 1.5. So in that year, two sessions were worth 1.5 times one session, 4 sessions were worth 1.5 times two sessions (or 2.25 times one session), and six sessions were worth 1.5 times three sessions.  This was reflected in the S factors of that time.  Unfortunately, the S factor was 2.0 for three sessions when it should have been 1.90

Mathematical note:  to raise 1.5 to the correct power, for N sessions one should raise 1.5 to the power 2 would have to be raised to to get N.  For instance, for N=4, one should raise 2 to the second power to get 4, so one should square 1.5 to get 2.25, the proper value for S for 4 sessions.  Of course, that number that 2 should be raise to to get N is the logarithm base 2 of N.  1.5 raised to the logarithm base 2 of 3 gives the 1.90 referred to above.

Please feel free to ignore the mathematical note, if you desire.  In any case, someone (I think in 1998) noticed that the S factors were 1,1.5, and 2 for 1,2,3 sessions, so just made them 2.5,3,3.5 for 4,5,6 sessions.  This created the inconsistencies present in the current formulas.  For instance, a 4-session event is now worth 5/3 of a 2-session event, a 6-session event is now worth 1.75 times a 3-sessions event.  This may lend some credence to complaints that KOs pay too much, since they are 10/9 of what they would have been using S=2.25
Another place we still  recognize the 1.5 number is that knockout matches of 48 boards pay 1.5 the value of 24-board knockout matches.(see p. 4 of current regulations.

This suggests that 12-board sessions, being half the length of 24-board sessions, should pay 2/3 of 24-board sessions (or, viewing it the other way, 24-board sessions should pay 1.5 times 12-board sessions.

To me, the way to solve this problem would be to make the formula for 1st overall = B x R x S x M x P x L (remember we are eliminating T), where L is 1.5 to the power log2(#bds/24).  Thus L=1 for 24-board sessions, L=2/3 for 12-board sessions.  Other values of L are in the second sheet of the attached spreadsheet.  (The first sheet contains S factors).

In fact, I think our goal is to replace B x M by a strength of field factor, which I call FS.  Since B X M is almost always between 0 and 2 (it takes more than 400 tables to make B>2), I think FS should be a number between 0 and 2.
There is a discussion of the masterpoint formula in the third sheet of the attached spreadsheet.

The knockout formula was written in 2007 to relect values for 4-session regional knockouts.  I have translated this formula so that it fits into the general masterpoint formula.  When R=14 and S=2.25, the FS factor generated produces exactly 9/10 of the present awards (I chose 9/10 to reflect the change from S=2.5 to S=2.25.  This is in the fourth sheet of the spreadsheet.

The various changes in S make 3-session knockouts worth more than they were.  For this reason, the awards for brackets of sizes less than 16 have to be changed, so the awards are higher than for a 3-session knockout.  This is accomplished by using a non-integer value for the number of sessions in a knockout, again based on logarithms base 2.  These are illustrated in the fifth sheet of the spreadsheet.

The sixth and 8th sheets of the spreadsheet contain examples.  The 7th sheet deals with an anomaly called the D factor, which was artificially created to compute match awards for swiss teams.  The new values for L allow some of that artificiality to be removed.

As I hope you can tell, I have been working for some time to create a cohesive whole on which to base our masterpoint structure for the future.  Like the treatment of club games as tournaments, this seems like a process whose time has come, particularly in light of the development of a more modern ACBLscore.  I know I have given you much to digest.  I hope you will read it carefully, particularly for consistency.

One of my reasons for trying to do so much is my desire for consistency.  I believe some of the discussions about internet games have not taken into account this consistency.  I hope this will put the entire picture on a mathematical basis devoid of emotionl

Thanks for your attention to this long message and even larger spreadsheet.

Bill Arlinghaus

--
William C. Arlinghaus, Ph.D.
Professor Emeritus, Mathematics and Computer Science
Lawrence Technological University
Full Curriculum Vitae
ACBL Board of Directors, District 12

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