**Arbiter Grand Prix**

The following is a proposal for the changing of the current AOC’s Arbiter Grand Prix System (AGPX).

Some benefits of the new system are:

1The “gap” between arbiters is smaller it’s easier for arbiters to “pass one another”.

2It gives a more fair and realistic opportunity to all arbiters to be considered for selection.

3It combines a linear and geometrical approach whereas it only used to be the latter.

4Tournament sections are now evaluated individually instead of the whole tournament as an “average”. Only the top 3 sections per tournament is considered, dropping the lower sections thereby eliminating diluting an arbiter’s points.

5No penalties applied for not submitting reports. But bonus points awarded for submitting reports.

General

1An arbiter will be considered active if he/she has arbitrated in at least one tournament in a calendar year.

2An arbiter’s Total AGPX Points (TAGPX) will be calculated by summing his/her top 5 tournament AGPX points.

Formulae

The following formulae will be used for the calculation of an arbiter’s tournament AGPX.

**Grand Prix Point for each section of a tournament (Ai)**

where:

Ai=Tournament section points

K1=Weighed factor depending on the type/status of the tournament/section

R=Points for the average rating of the section

P=Points for the number of players in the section

T=Points for the title of the arbiter (during the tournament)

S=Points for the status of the arbiter (during the tournament)

The weighed factor of the event is determined by the type/status of the event and is the following.

-International tournaments:K1 = 1.0

-National tournaments:K1 = 0.9

-Provincial tournaments:K1 = 0.8

-Regional tournaments:K1 = 0.7

**Points for the average rating of the section (R)**

where:

R=Points for the average rating of the section

r=Average rating of the section

If r>=1065 then the formula has a positive (+) sign, otherwise negative (-).

r-max: 2000

r-min: 130

See the graph (below) for full details.

**Points for the number of players per section (P)**

where:

P=Points for the number of players in the section

p=Number of players in the section.

If p>=60 then the formula has a positive (+) sign, otherwise negative (-).

p-max: 114

p-min: 6

See the graph below for full details.

**Points for the title of an arbiter (T)**

1International Arbiter (IA):T = 7

2FIDE Arbiter (FA):T = 6

3National Arbiter (NA):T = 5

4Provincial Arbiter (PA):T = 4

5Candidate Provincial Arbiter (CPA):T = 3

6Tournament Supervisor (TS):T = 2

7School Supervisor (SS):T = 1

**Points for the status of the arbiter (S)**

1Chief Arbiter (CA):S = 4

2Deputy Chief Arbiter (DCA):S = 3

3Arbiter/Match-Arbiter (SA/A/MA):S = 2

4Assistant Arbiter (AA):S = 1

The above formulae can be combined to give the following:

**Arbiter tournament Grand Prix Points (AGPX)**

AGPX is determined by calculating the weighted average of the top 3 sections of the tournament (the 3 sections producing the highest Ai values).

where:

Ai=Tournament section points

i=Section number (lower means higher placed section)

N=Number of top sections (either 3, 2 or 1)

Ni=Rank number of the specific section (1, 2 or 3)

K2=Number-of-sections weight

B=Bonus points

AGPX is calculated and is dependent on there being at least 3 sections. If there are less sections (either 1 or 2 only) and to prevent lob sided results (more points for less work), AGPX is weighed as if there existed additional sections.

K2 = 1.0 (3 or more sections)

K2 = 1.1 (only 2 sections)

K2 = 1.2 (only 1 section)

Bonus points will be awarded if an arbiter submits his/her report within the stipulated time frame after the tournament has ended:

B = 5 (if report was submitted in time)

B = 0 (if no report was submitted or report submitted late)

Graph

The following graph was used to determine the formulae for R and P.

The green line is used. Basically the graph consists of two parabolas with their turning points meeting at a common point. For the top parabola, the left half is ignored (red dotted line) and for the bottom parabola, the right half is ignored (red dotted line). This thus produces the green section.

For both R and P, a maximum of 10 points is awarded. This is indicated by the coordinates:

2000,10:For R

114,10:For P

The coordinates in the middle (2000,5 and 60,5) indicate the absolute centre if a section complies with the following:

-Average rating is 1065

-Number of players is 60

If the average rating of the section is greater than 2000, it is capped at 2000. And if it is less than 130 it is capped at 130.

If the number of players in a section is greater than 114, it is capped at 114. 6 is the minimum number of players allowed per section (as per the Rating Regulations).

Average rating

-1065 (as the average rating) was chosen based on the highest average rating of all tournaments per region for 2015.

-2000 was chosen as the maximum allowed average rating (as few tournaments ever go beyond this number as well as to prevent runaway Ai values).

-The difference between 2000 and 1065 is 935. Therefor the minimum allowed average is 130 (1065-935).

Number of players

-60 (as the number of players) was chosen based on the highest average number of players of all tournaments per region for 2015.

-6 is the minimum number of players allowed per section.

-The difference between 60 and 6 is 54. Therefor the max limit for the number of players is set at 114 (60+54).

The formula for a parabola is:

where:

y=y-axis value (Ai points)

x=x-axis value (average rating or number of players)

h=x-axis value for the turning points of the parabola

k=y-axis value for the turning point of the parabola

a=Gradient of the parabola

By substituting the coordinates of the turning point of the parabola as well as the coordinates of the maximum allowed values, the following values are obtained for “a” (after simplifying):

Example

Calculating Ai

The following example has been constructed to demonstrate the various possible scenarios of calculating Ai.

Average rating of the section:1600 (because 1600>1065, the formula for R is +)

Number of players in the section:40 (because 40<60, the formula for P is -)

Tournament type:Provincial (K1 = 0.8)

Arbiter title:PA (T = 4)

Arbiter status:DCA (S = 3)

Thus, the arbiter receives 14.36 points for this section.

Example

**Highest and Lowest possible values for Ai**

Section (max)Section (min)

Average rating:2000Average rating:130

Number of players:114Number of players:6

Tournament type:International (K1 = 1)Tournament type:Regional (K1=0.7)

Arbiter title:IA (T = 7)Arbiter title:SS (T = 1)

Arbiter status:CA (S = 4)Arbiter status:AA (s = 1)

Substituting this data into the formulae (for each section) will yield (IGNORING bonus points):

Ai (max):31.0 points

Ai (min):2.0 points

Thus, an arbiter can never receive more than 31.0 and less than 2.0 points for any section. Subsequently the AGPX (or weighted average - see below) must always be between these two limits.

Example

**Calculating AGPX**

Assume a tournament has 4 sections and the Ai value for each section is the following:

A1=17.0 (position 1)

A2=16.5 (position 2)

A3=15.0 (position 3)

A4=14.0

We only consider the top 3 sections (A1, A2 & A3) and ignore A4 in totality.

N = 3 (the number of sections we are using)

K2 = 1.0 (because we are using 3 sections)

The formula for AGPX can be expanded to the following (to make it easier to understand). For the time being, B (bonus points)isignored.

Substituting the values will yield:

Thus the weighted average of the 3 sections is 16.5 (whereas the plain average would have been 16.17).

If the arbiter submitted his report in time, 5 points are added to 16.5 to give 21.5 which is now the arbiter’s total AGPX points for that tournament. If the arbiter did not submit a report then his/her AGPX for the tournament remains at 16.5.

If the above tournament only had 2 sections (A1 and A2: excluding B for the time being)

The AGPX for the arbiter (without K2) is 16.83. But we now divide this answer by 1.1 to give 15.30.

With the bonus points, the arbiter would receive 20.30 points.

If the above tournament only had 1 section (A1: excluding B for the time being)

The AGPX for the arbiter (without K2) is 17.0. But we now divide by 1.2 to give 14.17.

With the bonus points, the arbiter would receive 19.17 points.

**TOTAL Arbiter Grand Prix Points**

An arbiter’s total Grand Prix Points is calculated by summing his/her top 5 tournaments (top 5 highest AGPX points).

**What is a tournament?**

An event will be considered as a (one) tournament if:

1Regardless of the number of sections.

2Regardless of the number of days over which the tournament takes place (sections may be played over a different number of days. E.g. the A section over 4 days, the B section the latter 2 days, etc.).

3If the same set of players participate.

4If the name of the tournament is the same for all sections (regardless of the individual section names).

Example 1:

A region hosts the ABC High School Championships over 1 day on 01 January.

This is considered ONE tournament.

Example 2:

A region hosts the ABC Primary School Championships over 1 day on 02 January.

This is considered ONE tournament.

Example 3:

A region hosts the above two tournaments on the above given dates (2 different dates) regardless if the same venue is used or not.

These will be considered as TWO separate tournaments.

However (Examples 4 and 5):

Example 4:

A region hosts the above two tournaments on the same date at the same venue (regardless of the tournament schedules).

These will be considered as ONE tournament.

Example 5:

A region hosts the above two tournaments on the same date but at different venues (regardless of the tournament schedules).

These will be considered as TWO tournaments.

**Type of tournaments**

Regardless if a section is FIDE rated or not, and where an arbiter is arbitrating:

International

1Any FIDE sanctioned tournament where a player was selected (or qualified) to represent RSA (either Individual or Team).

2Any FIDE sanctioned tournament where an arbiter was appointed or nominated by FIDE, African Chess Confederation or the AOC.

3Any FIDE rated tournament outside the borders of RSA which is FIDE rated and where at least 4 different federations are represented, regardless of the number of participants, otherwise the tournament will be considered as National.

National

Only the following tournaments (including point 3 above if applicable).

1South African Closed (Open)

2South African Closed (Women)

3South African Senior Closed (Open)

4South African Senior Closed (Women)

5South African Junior Closed

6South African Open

7South African Women’s Open

8South African Junior Nationals (Team Championships)

9South African Junior Nationals (Wild Card/Individual Championships)

10Inter Club Championships

11Inter Regional Championships

12SA Schools Championships (Individual)

13SA Schools Championships (Team)

14USSA Championships (Open)

15USSA Championships (Women)

16South African Braille Championships

17South African Braille Top 8

However (taking “What is a tournament” into account), the following tournaments will be considered as ONE tournament if they are played over the same period at the same venue:

-South African Closed (Open and/or Women and/or Senior and/or additional sections)

-USSA Championships (Open and Women)

-The Inter Regional will always be considered a separate tournament regardless of it is hosted alongside the South African Junior Nationals (Team or Wild Card Championships).

Provincial

-Team tournaments where at least 3 different Regions are represented to vie for the title of “Provincial Champion” or to select a winner to represent the Province in a National event. Examples: Gauteng League, Western Cape Top Schools, etc.

-Individual tournaments where at least 3 regions are represented where players vie for the title of “Provincial Champion” or to select a player or players to represent the Province at a National event. Examples: Eastern Cape Individual Championship, etc.

Regional

Any tournament not mentioned above (most tournaments will fall under this category).