Ratings Bureau
Rating Regulations
Adopted at the 01 February 2018 Chess SA AGM.
1 INTRODUCTION
1.1 Following are the Rules and Regulations for the calculation and updating of South African
ratings and performance ratings, which will come into force on 01 January 2018.
1.2 In this document, any gender reference (e.g. his, him, etc.) also refer to the female equivalent.
1.3 These regulations are the only and official regulations which determine the manner in
which South African ratings are managed and calculated and these Regulations
overwrite any regulations existing elsewhere in whatever/whichever form and/or
format.
2 DEFINITIONS & ABBREVIATIONS
2.1 Definitions
2.1.1 Event: A competition where players participate in one or more sections, and is
Chess SA and/or FIDE rated.
2.1.2 Section: Sub-group of an event, and is Chess SA and/or FIDE rated.
2.1.3 Province: One of the 9 provinces of the Republic of South Africa.
2.1.4 Region: An area within a Province and which is a member of that Provincial Body,
functions independently from other Regions within the same Provincial
Body, and which have been constituted by Chess SA.
2.2 Abbreviations
2.2.1 Chess SA: Chess South Africa.
2.2.2 AOC: Arbiters and Organisers Commission.
2.2.3 FIDE: Federation Internationale des Echecs.
2.2.4 RSA: Republic of South Africa.
3 ARBITERS AT TOURNAMENTS
3.1 During each and every round of an event, a qualified arbiter (as approved by the AOC and/or
FIDE) must be present (in an appointed capacity) for the duration of the round.
3.2 A RSA arbiter officiating at an event (regardless of where the event is held) must have paid his
AOC membership fees for the year in which the event is hosted and must have done so before
the start of the event, otherwise the tournament will not be rated.
Ratings Bureau
How South African Ratings are Calculated
2 | P a g e
3.3 Excluding Club events, no arbiter will be allowed to participate in an event (not even as a filler)
where he has been appointed in an official capacity, otherwise the event will not be rated.
4 EVENTS TO BE RATED
4.1 Events played within the borders of RSA.
4.2 Events played outside the borders of RSA
Must comply with the regulations stated within this document. It will be the responsibility of the
player (or team manager) who participated in such an event to submit his results of the event
(preferably a link to a website where his results can be obtained and verified) no later than 21
calendar days after the event has ended otherwise the event will not be accepted for rating and
will not count towards the updating of his rating, activity and calculation of performance rating
for Grand Prix Points. Once details of the event have been submitted and processed, it may not
be unrated upon request by either a player, team manager or anyone else.
4.3 The Ratings Committee reserves the right to refuse to rate an event (or one or more sections of
that event) regardless if the event was played within/outside the borders of RSA. In the event of
refusal to rate and event (or section/s) the Ratings Committee will provide reasons why the event
(or section/s) is not to be rated. The aggrieved party may appeal this decision (lodge an appeal
with Chess SA) but no later than 21 calendar days after receiving notification of refusal.
4.4 The Ratings Committee reserves the right to rate any event (regardless of where it was played)
that was not submitted for rating purposes and/or registered to be rated.
5 EVENT DETAILS REQUIRED
The following information must be indicated in each tournament file. Files without these details will not
be processed and sent back to the relevant region for updating the files and submitting them again.
5.1 Event/Section details
5.1 Complete event name, including section name (if applicable).
5.2 Start and end dates of the event/section.
5.3 Date on which each round was played.
5.4 Code of the region physically hosting the event.
5.5 Name, surname and Chess SA id of the Chief Organiser.
5.2 Player details
5.2.1 Surname, Initials and First name (no nicknames).
5.2.2 Date of birth (but at least indicating the year-of-birth).
5.2.3 Gender.
5.2.4 Chess SA id (where applicable).
5.2.5 Code of the region the player is a member of. If no code is provided, the player will be
assigned the code of the host region.
Ratings Bureau
How South African Ratings are Calculated
3 | P a g e
5.3 Arbiter details
5.3.1 Name and surname (no nicknames).
5.3.2 Chess SA id number.
5.3.3 Title.
5.3.4 The names of the arbiters must be indicated in order of appointed position. The 1st name
must be the Chief Arbiter, the 2nd and 3rd names the Deputy Chief Arbiters, then all other
arbiters.
6 AGE GROUPS
A player’s age (and thus age group) is calculated by subtracting his year-of-birth (regardless of
the day-on and month-in which he was born) from the year in which the FIDE event (for which he
qualifies or is to qualify) is hosted.
Example 1: A player was born in 2006. The FIDE event will be hosted in 2018. His age is 12 (2018-
2006). His age group is U12.
Example 2: A player was born in 2005. The FIDE event will be hosted in 2018. His age is 13 (2018-
2005). His age group is U14.
7 NUMBER OF PLAYERS & ROUNDS PER SECTION
A section of an event will only be rated if:
7.1 For Individual Swiss-, Individual Single Round-Robin- and Team- sections (Swiss and Round-
Robin): there are at least 6 players participating AND at least 5 rounds are completed.
7.2 For Individual Double Round-Robin sections: there are at least 4 players participating AND at
least 6 rounds are completed.
7.3 For Team Scheveningen sections: there are at least 5 players per team participating AND at
least 5 rounds are completed.
7.4 For disabled (e.g. Braille) events (or sections) only (regardless of format): there are at least 6
players participating AND at least 4 rounds are completed.
Organisers, arbiters, etc. must always try to ensure that all points (above) are adhered to,
even if it means merging age and/or gender groups, etc. However, if this is/was not
possible (e.g. there were only 5 players in the Section due to a player withdrawing before
the start of the tournament), the Chief Organiser and/or Chief Arbiter must contact the
Ratings Bureau no later than 1 (ONE) calendar day after the event has ended asking
permission if the affected section(s) can be rated. If granted, each Province (if the event is
organised via the Provincial Committee), Region (if the event is organised via the Regional
Committee) or Chess Academy (as recognised by and in good standing with CHESS SA) will
only be granted 1 (ONE) such request per year. NB! The sections must still have at least 5
rounds.
Ratings Bureau
How South African Ratings are Calculated
4 | P a g e
8 TIME CONTROL AND TYPE OF RATING
8.1 The time control for a game is defined as: the base time (original time on the clock) plus 60
times any increment per move.
8.2 There are 3 types of ratings. The minimum time control for each is:
8.2.1 Standard: At least 60 minutes per player.
8.2.2 Rapid: At least 10 minutes but less than 60 minutes per player.
8.2.3 Blitz: Anything less than 10 minutes per player.
8.3 For u8 sections only (all players in that section is u8), the minimum time control for Standard
ratings will be 30 minutes per player.
8.4 Where a section has multiple time controls for different rounds, they must all fall within the same
rating type. If not, then the fastest of these will be used to determine the type of rating to be
updated.
9 K-FACTOR
9.1 K-factor is a number which determines the degree (by how much) a player’s rating will change.
The higher the K-factor, the greater the rating change (and vice versa).
9.2 An unrated player does not have a K-factor and it is only determined once he receives his first
official rating.
9.3 A player’s K-factor (standard rating only and applicable for the whole event) depends on his
activity and is based on his number of games (standard only) played during the past year where
a year is calculated as the date of his first game played in a tournament minus 365 days.
Example: If a player participates in an event and the date of the first game he plays is
2017/07/18, then the “one year cycle” (which is then used to calculate his number of games
played) is from 2016/07/17 to 2017/07/17.
9.4 The formula for K is the following:
𝐾 = (𝐿 × 700
𝐺 + 𝑁) × (1 − 0.01
1𝐿)
or
𝐾 = (8400
𝐺 + 𝑁) × (1 − 0.01
112)
where: K = K-factor (rounded to 1 decimal place).
K may never be more than 50. If so then it’s set equal to 50.
K may never be less than 10. If so then it’s set equal to 10.
L = Number of rating lists published per year (in this case it’s 12).
Ratings Bureau
How South African Ratings are Calculated
5 | P a g e
N = Number of games played in the one-year cycle.
G = Base value depending on number of historical games (H) played (excluding N).
- If H>=31 → G=80.
- If 21<=H<=30 → G=70.
- If 11<=H<=29 → G=60.
- If 0<H<=10 → G=50.
- Regardless of H, G is automatically set at 80 if a player’s highest rating achieved has
been at least 1500.
9.5 Rapid ratings: K=30 (regardless of a player’s rating and activity).
9.6 Blitz ratings: K=40 (regardless of a player’s rating and activity).
10 RATING FLOOR
10.1 No player’s rating will be allowed to drop below 500. If it does then it will be adjusted to
500.
10.2 No player’s performance rating will be allowed to drop below 500. If it does then it will be
adjusted to 500.
11 80% RULE
11.1 A player will only gain rating points, a performance rating (applicable for Grand prix) and
possible Weighed Performance Rating if he has played at least 80% (rounded upwards) of the
total number of scheduled section rounds.
Meaning, if the player’s rating change is positive, he will only receive these points if he has
played at least 80% of the total number of rounds, otherwise not.
11.2 If a player’s rating change is negative, he will be rated, regardless of the number of
games/rounds he has played.
11.3 Rounds where a player won on default (opponent did not arrive in time for the game) or
received a bye (as determined by the pairing software), will not be rated (not taken into
account for updating rating) but taken into account for activity (number of rounds played in
that tournament).
11.4 Games where the player won on default. These games will count towards calculation of his
tournament performance rating as if they were “real games”. Games where a player lost
on default will not count towards activity and calculation of tournament performance
rating.
11.5 The 80% rule is not applicable to team events/sections when a player will be rated
regardless of the number of games played. However, the player’s tournament performance
will only be calculated (and applicable for Grand Prix) if he has played at least 50% (rounded
upwards) of the total number of rounds.
11.6 Excluding round 1, any player who defaults a game (did not inform the Chief Organiser and/or
Ratings Bureau
How South African Ratings are Calculated
6 | P a g e
Chief Arbiter that he will not be participating in that round) and also including players arriving
late for a game, will have 20 rating points deducted for each such game/round. This will not
affect the opponent (who will not be rated and receive rating points for that game).
11.7 Any player who withdraws from the event without informing the Chief Organiser and/or Chief
Arbiter in writing, and without a valid reason (according to the Chief Organiser and/or Chief
Arbiter) will have 20 rating points deducted for that round and each subsequent round, even
though the player is not participating in the event anymore.
12 ACTIVITY
The following games will count towards activity (number of games played) for the purpose of updating
ratings and Grand Prix standings:
12.1 Games vs. rated/unrated opponents.
12.2 Games where a player won on/by default.
12.3 Games where a player received a bye (as determined by the pairing software – for activity
only).
Games where a player did not play (gave notice of absence) and/or lost by default (did not
arrive on time for the game or was not present for the game) and/or requested a ½-point
bye, will not count towards activity, updating of rating and calculation of performance
rating.
13 FIRST OFFICIAL RATING FOR AN UNRATED PLAYER
13.1 A player will receive his first official (initial) rating (and K-factor) as soon as he has
played 5+ games (per rating type).
13.2 All games, regardless if the opponents are rated or not, will count towards the calculation of
his first rating.
13.3 If he plays 5+ games in his first tournament, then all these games will be used to calculate his
initial rating.
13.4 His initial rating will be set equal to his performance rating for that tournament (based on his
first 5+ games) and is calculated using the performance formula (see below).
14 GAMES VS UNRATED OPPONENTS
14.1 Rated/Unrated vs. Unrated
Games against unrated players will be taken into consideration for the updating of ratings,
calculation of performance ratings and activity.
14.2 An unrated player will first be assigned a temporary rating which is equal to his tournament
performance rating. This temporary rating will then be used for all calculation purposes.
Ratings Bureau
How South African Ratings are Calculated
7 | P a g e
15 ACCEPTANCE OF EVENTS FOR RATING
Each region must have one appointed Regional Administrator who will be tasked with the following.
Only events complying with the points below will be accepted for the updating of ratings and
calculation of performances (for Junior and Senior Grand Prix Points). When uploading a
tournament file, the Region acknowledges that all information indicated in the file is 100%
correct.
15.1 Each event must be registered via the CHESSA website at least the following
number of days before the start of the event. Events which have been registered late or not
registered at all will be subjected to a penalty fee (see below).
15.1.1 CHESSA rated only: 3 days
15.1.2 FIDE (no player norms available) & CHESSA rated: 9 days
15.1.3 FIDE (player norms available) & CHESSA rated: 32 days
15.1.4 For all FIDE rated events/sections, the appropriate documentation (as provided by
the CHESS SA Qualifications Commission) must be completed and submitted to the
CHESS SA Ratings Bureau and CHESS SA Qualifications Committee no later than
the number of days before the start of the event/section, as per these documents.
PLEASE NOTE: FIDE does NOT accept any events/sections that are
registered late. They also do NOT accept any changes made to
event/section details once the event/section has started (e.g. arbiters,
organisers, time controls, etc.). It is thus IMPORTANT that all Organisers
make sure that the data they supply are CORRECT as changes cannot be
made at a later stage.
15.2 Once the event has finished, the event files (file per section) must be uploaded to the CHESS
SA website within 14 days after the event has ended to avoid any penalty fees (see below).
No events submitted via email or any other way, except for uploading, will be accepted unless
permission has been granted by the Ratings Bureau.
15.3 All event files must be uploaded together (same session) so that they can all be incorporated
into the same rating list. If submitted in different rating periods, then they will all be
incorporated into the latter rating period.
CHESS SA INSTRUCTIONS 15.4 Events that are submitted late distort the accuracy of the rating system, especially if they are
submitted in a latter month to the month in which the event was hosted. This causes unfair
rating changes (increase/decrease) and too-high/too-low performance ratings of the players,
which affect their positions on the various Grand Prix lists.
15.5 The following penalties (in the form of a financial penalty), as decided by Chess SA
Management Committee, will be applied to all events that are submitted late. The number of
days indicated below refers to the number of days after the event has ended. The penalty
indicates the amount to be paid PER PLAYER THAT PARTICIPATED (any player who has played
at least 1 game in the event, excluding players who received a Bye/Default-win in round 1 but
subsequently withdrew).
Ratings Bureau
How South African Ratings are Calculated
8 | P a g e
15.5.1 Submitted 0-14 days: No penalty
15.5.2 Submitted 15-21 days: R10/player
15.5.3 Submitted 22-28 days: R15/player
15.5.4 Submitted 29-35 days: R20/player
15.5.5 Submitted 36-42 days: R25/player
15.5.6 Submitted 43+ days: WILL NOT BE RATED
15.6 Any Province, Region or Chess Academy who submits events late, will be contacted and an
invoice will be sent to the relevant Body. Any such penalty will also be loaded to the Region’s
online account. The Body must do the following:
15.6.1 deposit the fee into the CHESS SA bank account, and
15.6.2 submit proof of payment to the CHESS SA Financial Director and CHESS SA Ratings
Bureau no later than 7 calendar days after receiving the invoice otherwise the event
will be unrated.
15.7 Any event which is registered contrary to Point 15.1 above or which was not registered at
all, will incur an additional “Late Registration Penalty”/”Not Registered Penalty” of R500
which must be paid into the CHESS SA bank account before submitting the event for rating.
Proof of payment must be sent to the CHESS SA Financial Director and the CHESS SA Ratings
Bureau, otherwise the event will not be rated.
16 CHANGES MADE TO SECTIONS ALREADY RATED
16.1 Making changes to sections already rated necessitates un-rating and rerating the section. It is
not a problem if the changes are made to sections which are still to be incorporated into the
next published rating list as it does not affect current published ratings.
16.2 No changes will be made (e.g. correcting player results, removing penalty rating
points, etc.) once a section has been incorporated into the new rating list. It is the
responsibility of the Chief Arbiter, Chief Organiser and Regional Administrator to
ensure that all data is 100% correct before the files are uploaded to be rated.
17 HOW UNRATED PLAYERS WILL BE TREATED BEFORE RATING A SECTION
17.1 Before a section is rated, all unrated players will be assigned a temporary rating which will be
200 less than the highest rated player in that section but capped at 1000 (max) and 500
(min). This is not an official rating and is only used to calculate the temporary performance
ratings of other unrated players.
17.2 Calculate the temporary performance rating (see performance rating calculation below) of an
unrated player by taking into account the rating of his rated opponents and the temporary
value of his unrated opponents. The temporary performance rating calculated this way will
Ratings Bureau
How South African Ratings are Calculated
9 | P a g e
then be used to update the ratings and calculate the actual tournament performance ratings of
all players.
18 CALCULATE THE PERFORMANCE RATING FOR A PLAYER SCORING >0% AND <100%
The following table is used:
Table 1
% Dp % Dp % Dp % Dp % Dp % Dp
100 MAF 83 +273 66 +117 49 -7 32 -133 15 -296
99 +677 82 +262 65 +110 48 -14 31 -141 14 -309
98 +589 81 +251 64 +102 47 -21 30 -149 13 -322
97 +538 80 +240 63 +95 46 -29 29 -158 12 -336
96 +501 79 +230 62 +87 45 -36 28 -166 11 -351
95 +470 78 +220 61 +80 44 -43 27 -175 10 -366
94 +444 77 +211 60 +72 43 -50 26 -184 9 -383
93 +422 76 +202 59 +65 42 -57 25 -193 8 -401
92 +401 75 +193 58 +57 41 -65 24 -202 7 -422
91 +383 74 +184 57 +50 40 -72 23 -211 6 -444
90 +366 73 +175 56 +43 39 -80 22 -220 5 -470
89 +351 72 +166 55 +36 38 -87 21 -230 4 -501
88 +336 71 +158 54 +29 37 -95 20 -240 3 -538
87 +322 70 +149 53 +21 36 -102 19 -251 2 -589
86 +309 69 +141 52 +14 35 -110 18 -262 1 -677
85 +296 68 +133 51 +7 34 -117 17 -273 0 MAF
84 +284 67 +125 50 0 33 -125 16 -284
18.1 Calculate the player’s % score (taking into account actual games played and games won on
default).
18.2 Calculate his average opponent rating (AOR).
18.3 Find Dp in Table 1.
18.4 Calculate his performance by adding Dp to his AOR (Performance = Dp + AOR).
Example 1:
A player scores 5.5/7.
% = 79
AOR = 1500
Dp = +230
Performance = 1500+230 = 1730
Example 2:
A player scores 1/6.
% = 17
AOR = 1500
Dp = -273
Performance = 1500-273 = 1227
Ratings Bureau
How South African Ratings are Calculated
10 | P a g e
19 CALCULATING THE PERFORMANCE RATING OF A PLAYER SCORING 0% OR 100% (MAF)
The following formula is used:
𝑃 =𝑇𝑜𝑟 + 𝑅
𝑛 + 1− 400 [
𝐿𝑛 (𝑛 + 1
𝑠 + 0.5− 1)
𝐿𝑛10] 𝑜𝑟 𝑃 =
𝑇𝑜𝑟 + 𝑅
𝑛 + 1− 400𝐿𝑜𝑔 (
𝑛 + 1
𝑠 + 0.5− 1)
where: P = performance rating
Tor = Total opponent rating
R = Player’s own rating (or temporary performance for unrated players)
n = Number of games played (including default wins and Bye)
s = Score achieved (including default wins and Bye)
Example 1:
A player’s is rated 2000 and scores 5/5 against opponents rated 1400, 1500, 1600, 1700 and 1800.
𝑃 =𝑇𝑜𝑟 + 𝑅
𝑛 + 1− 400𝐿𝑜𝑔 (
𝑛 + 1
𝑠 + 0.5− 1)
=1400 + 1500 + 1600 + 1700 + 1800 + 2000
5 + 1− 400𝐿𝑜𝑔 (
5 + 1
5 + 0.5− 1)
= 1666.67 + 416.56
= 2083
Example 2:
Same as example 1 except that the player scores 0/5.
=1400 + 1500 + 1600 + 1700 + 1800 + 2000
5 + 1− 400𝐿𝑜𝑔 (
5 + 1
0 + 0.5− 1)
= 1666.67 − 416.56
= 1250
20 DIFFERENCE IN RATING
For updating of ratings only. For performances, the actual opponent ratings are used.
20.1 The rating difference (D) is the difference between the player’s own rating and that of his
opponent. Thus, D = Rating (player) - Rating (opponent)
20.2 For the higher rated player, D may not be more than 392 (if it is, set it to 392). Thus, treat
the opponent as if he was rated only 392 rating points less than the player himself.
Ratings Bureau
How South African Ratings are Calculated
11 | P a g e
20.3 For the lower rated player, D may not be less than -736 (if it is, set it to -736). Thus, treat
the opponent as if he was rated only 736 points higher than the player himself.
21 WEIGHED PERFORMANCE RATING (WPR)
21.1 After a section has been rated, a player’s weighed performance will be calculated based on his
tournament just completed and his 4 previous events (thus 5 events in total).
21.2 Only events where a player has participated in 100% of the rounds will be
considered.
21.3 The WPR of a new player can only be calculated once he has completed his 5th tournament.
21.4 If a player’s WPR is higher than his current rating (Rc), then his Rc will be set equal to his WPR
but only up to a maximum of 200 points. Thus, WPR – Rc may not be greater than 200. If his
WPR is lower than his Rc, then his Rc will not be affected.
21.5 WPR is calculated using the following formula:
𝑊𝑃𝑅 =∑ [𝑃𝑖 × (6 − 𝑖) × 𝑄𝑖]
5𝑖=1
15
where: WPR = Weighed Performance Rating
P = Tournament performance
i = the number of the tournament, with 1 being the most recent and 5
the last.
Q = Depreciation factor and depends on the age of the event, where age
is the difference in days between the current date (the event is
processed/rated) and the end-date of the event.
Q = 1.0 when 0<=age<=121
Q = 0.99 when 122<=age<=243
Q = 0.98 when 244<=age<=365
Q = 0.97 when 366<=age<=486
Q = 0.96 when 487<=age<=608
Q = 0.95 when 609<=age
21.6 A player’s rating will be adjusted to his WPR (if applicable) even in the middle of a rating
period. This new rating will be used for his next event (even within the same month) and then
be updated based on his rating changes for any events played in the same month.
22 WHEN NEW RATINGS ARE CALCULATED
22.1 Ratings will be updated based on the events received for that month and the database
updated
22.1.1 during the month when unrated players are assigned their new ratings, and
22.1.2 during the month when rated players are assigned their WPR, and
22.1.3 on the first day of the next calendar month when all ratings are updated.
Ratings Bureau
How South African Ratings are Calculated
12 | P a g e
22.2 As soon as a new player has played his 5th+ game, the system will automatically
calculate the player’s new rating upon rating the event. The database is updated as soon as a
section has been rated. The next event rated, where that player participates in, will use his
newly calculated rating.
Example: An unrated player plays his 5th+ game on the 7th of the month and receives an
official rating of 750. He also participates in an event on the 14th of the same month. When
rating the 2nd event, his 750 rating will be used to calculate rating changes and tournament
performance ratings, even if both events are submitted on the same day.
NB! It is important for Tournament Organisers and Chief Arbiters to download the
ratings database as close as possible to the start of the event or just before the
pairings for round 1 are calculated and published so as to ensure fair pairings and
results.
22.3 For rated players: A player’s rating (as published on the first day of the month) will be used
to calculate his total rating change for that month, regardless of the number of events he has
participated in. However, if the player receives a WPR then this WPR will be used to calculate
his rating change for all other events within the same month.
Example: If the player’s rating is 1500, then 1500 will be used to calculate his rating change
for each event played that month provided he does not receive a WPR.
22.4 All ratings will be saved to the main database as real numbers (including decimals). Ratings
will be displayed on the Chess SA website up to one decimal place. Ratings will be saved to
the downloadable databases as integers (rounded).
23 PLAYERS WINNING A SECTION
A player ending in 1st position (clear or joint) may not lose rating points provided he has played
100% of the total number of rounds and none of the games involved default wins or byes
(the player has played each and every round with the white/black pieces). If he does, his
rating change for that event will be set to 0. This rule is not applicable to team events/sections.
24 HOW TO CALCULATE A RATED PLAYER’S RATING CHANGE FOR AN EVENT
24.1 Calculate his expected result (We) for each game played and subtract this from his actual
result (S) to obtain Swe (Swe = S - We).
24.2 His total rating change (ΔR) is calculated by summing the Swe (TSwe) scores and multiplying
the answer with his K-factor (ΔR = TSwe x K).
Ratings Bureau
How South African Ratings are Calculated
13 | P a g e
25 HOW TO CALCULATE EXPECTED SCORES (WE)
The following table is used.
Table 2
D H L D H L D H L D H L
0-3 0.50 0.50 92-98 0.63 0.37 198-206 0.76 0.24 345-357 0.89 0.11
4-10 0.51 0.49 99-106 0.64 0.36 207-215 0.77 0.23 358-374 0.90 0.10
11-17 0.52 0.48 107-113 0.65 0.35 216-225 0.78 0.22 375-391 0.91 0.09
18-25 0.53 0.47 114-121 0.66 0.34 226-235 0.79 0.21 392-411 0.92 0.08
26-32 0.54 0.46 122-129 0.67 0.33 236-245 0.80 0.20 412-432 0.93 0.07
33-39 0.55 0.45 130-137 0.68 0.32 246-256 0.81 0.19 433-456 0.94 0.06
40-46 0.56 0.44 138-145 0.69 0.31 257-267 0.82 0.18 457-484 0.95 0.05
47-53 0.57 0.43 146-153 0.70 0.30 268-278 0.83 0.17 485-517 0.96 0.04
54-61 0.58 0.42 154-162 0.71 0.29 279-290 0.84 0.16 518-559 0.97 0.03
62-68 0.59 0.41 163-170 0.72 0.28 291-302 0.85 0.15 560-619 0.98 0.02
69-76 0.60 0.40 171-179 0.73 0.27 303-315 0.86 0.14 620-735 0.99 0.01
77-83 0.61 0.39 180-188 0.74 0.26 316-328 0.87 0.13 736+ 1.00 0.00
84-91 0.62 0.38 189-197 0.75 0.25 329-344 0.88 0.12
25.1 Calculate the difference in rating (D).
25.2 If D is positive, read the value to the immediate right in the “H” column.
25.3 If D is negative, read the value to the immediate right in the “L” column.
Example 1:
A player is rated 1500. His opponent is rated 1700.
D = 1500-1700 = -200.
We = 0.24
Meaning, the player is expected to score 0.24 points from that game.
Example 2:
A player is rated 1200. His opponent is rated 900.
D = 1200-900 = +300.
We = 0.85
Meaning, the player is expected to score 0.85 points from that game.
Ratings Bureau
How South African Ratings are Calculated
14 | P a g e
26 EXAMPLE: CALCULATE A RATED PLAYER’S RATING CHANGE AND PERFORMANCE RATING FOR AN EVENT WHERE HE SCORES >0% BUT <100%
A player is rated 1500 and has a K-factor of 23.4 (K=23.4). His event results are:
Round 1 2 3 4 5 6 7
Opponent 1258 1469 1604 1582 1773 536 2305
D (actual) +242 +31 -104 -82 -273 +864 -805
D (used) +242 +31 -104 -82 -273 +396 -736
Opponent used 1258 1469 1604 1582 1773 1104 2236
Result 1 0.5 0 1 0.5 1 0
We 0.80 0.54 0.36 0.39 0.17 0.92 0.00
SWe 0.2 -0.04 -0.36 0.61 0.33 0.08 0.00
𝑇𝑠𝑤𝑒 = 0.2 − 0.04 − 0.36 + 0.61 + 0.33 + 0.08 + 0 = 0.82
∆𝑅 = 𝑇𝑠𝑤𝑒 × 𝐾 = 0.82 × 23.4 = 19.2
𝑅𝑎𝑜𝑟 =1258 + 1469 + 1604 + 1582 + 1773 + 536 + 2305
7= 1503.86
% =𝑆
𝑁× 100 =
4
7× 100 = 57.14 (57)
𝐷𝑝 = +50 (𝑓𝑟𝑜𝑚 𝑇𝑎𝑏𝑙𝑒 1)
𝑃 = 𝑅𝑎𝑜𝑟 + 𝐷𝑝 = 1503.86 + 50 = 1553.86 = 1554
Thus, the player gained +19.2 rating points and achieved a performance rating of 1554.
Ratings Bureau
How South African Ratings are Calculated
15 | P a g e
27 EXAMPLE: CALCULATE A RATED PLAYER’S RATING CHANGE AND PERFORMANCE RATING FOR AN EVENT WHERE HE SCORES 100%
A player is rated 1500 and has a K-factor of 23.4 (K=23.4). His event results are:
Round 1 2 3 4 5 6 7
Opponent 1258 1469 1604 1582 1773 536 2305
D (actual) +242 +31 -104 -82 -273 +864 -805
D (used) +242 +31 -104 -82 -273 +396 -736
Opponent used 1258 1469 1604 1582 1773 1104 2236
Result 1 1 1 1 1 1 1
We 0.80 0.54 0.36 0.39 0.17 0.92 0.00
SWe 0.2 0.46 0.64 0.61 0.83 0.08 1.00
𝑇𝑠𝑤𝑒 = 0.2 + 0.46 + 0.64 + 0.61 + 0.83 + 0.08 + 1.0 = 3.82
∆𝑅 = 𝑇𝑠𝑤𝑒 × 𝐾 = 3.82 × 23.4 = 89.2
𝑇𝑜𝑟 = 1258 + 1469 + 1604 + 1582 + 1773 + 536 + 2305 = 10527
𝑃 =𝑇𝑜𝑟 + 𝑅
𝑛 + 1− 400𝐿𝑜𝑔 (
𝑛 + 1
𝑠 + 0.5− 1) =
10527 + 1500
7 + 1− 400𝐿𝑜𝑔 (
7 + 1
7 + 0.5− 1) = 1503.4 + 470.4 = 1974
Thus, the player gained +89.2 rating points and achieved a performance rating of 1974.
Ratings Bureau
How South African Ratings are Calculated
16 | P a g e
27 EXAMPLE: CALCULATE A RATED PLAYER’S RATING CHANGE AND PERFORMANCE RATING FOR AN EVENT WHERE HE SCORES 0%
A player is rated 1500 and has a K-factor of 23.4 (K=23.4). His event results are:
Round 1 2 3 4 5 6 7
Opponent 1258 1469 1604 1582 1773 536 2305
D (actual) +242 +31 -104 -82 -273 +864 -805
D (used) +242 +31 -104 -82 -273 +396 -736
Opponent used 1258 1469 1604 1582 1773 1104 2236
Result 0 0 0 0 0 0 0
We 0.80 0.54 0.36 0.39 0.17 0.92 0.00
SWe -0.8 -0.54 -0.36 -0.39 -0.17 -0.92 0
𝑇𝑠𝑤𝑒 = −0.8 − 0.54 − 0.36 − 0.39 − 0.17 − 0.92 − 0 = −3.18
∆𝑅 = 𝑇𝑠𝑤𝑒 × 𝐾 = −3.18 × 23.4 = −74.4
𝑇𝑜𝑟 = 1258 + 1469 + 1604 + 1582 + 1773 + 536 + 2305 = 10527
𝑃 =𝑇𝑜𝑟 + 𝑅
𝑛 + 1− 400𝐿𝑜𝑔 (
𝑛 + 1
𝑠 + 0.5− 1) =
10527 + 1500
7 + 1− 400𝐿𝑜𝑔 (
7 + 1
0 + 0.5− 1) = 1503.4 − 470.4 = 1033
Thus, the player lost 74.4 rating points and achieved a performance rating of 1033.
Ratings Bureau
How South African Ratings are Calculated
17 | P a g e
28 EXAMPLE: CALCULATE THE FIRST OFFICIAL RATING OF AN UNRATED PLAYER WHO PLAYED 5+ GAMES IN HIS FIRST TOURNAMENT
The tournament details of a player are the following:
Round 1 2 3 4 5 6
Opponent 1258 Did not play 1158 1056 997 888
Result 1 X 0 0.5 0.5 1
𝑅𝑎𝑜𝑟 =1258 + 1158 + 1056 + 997 + 888
5= 1071.4
% =𝑆
𝑁× 100 =
3
5× 100 = 80
𝐷𝑝 = +240 (𝑓𝑟𝑜𝑚 𝑇𝑎𝑏𝑙𝑒 1)
𝑃 = 𝑅𝑎𝑜𝑟 + 𝐷𝑝 = 1071.4 + 240 = 1311.4 = 1311
His first official rating is 1311.
Because the player has only played 5 historical games, his first K-factor (that will be used for his next
tournament) is:
𝐾 = (8400
𝐺 + 𝑁) × (1 − 0.01
112) = (
8400
50 + 5) × 0.3187 = 48.7
Ratings Bureau
How South African Ratings are Calculated
18 | P a g e
29 EXAMPLE: CALCULATE THE FIRST OFFICIAL RATING OF AN UNRATED PLAYER
The tournament details of a player are the following:
Tournament 1
Round 1 2 3 4 5
Opponent 1258 Did not play 1158 1056 997
Result 1 X 0 0.5 0
Tournament 2
Round 1 2 3 4 5 6 7
Opponent 845 765 934 1106 645 765 1000
Result 1 1 1 0.5 1 0 0.5
Because the player did not play 5 games in his first tournament, the results of his first two
tournaments are combined. If the player played 5 games in his first tournament then the results of
only that tournament would have been used.
𝑅𝑎𝑜𝑟 =1258 + 1158 + 1056 + 997 + 845 + 765 + 937 + 1106 + 645 + 765 + 1000
11= 957.5
% =𝑆
𝑁× 100 =
6.5
11× 100 = 59.1 = 59
𝐷𝑝 = +65 (𝑓𝑟𝑜𝑚 𝑇𝑎𝑏𝑙𝑒 1)
𝑃 = 𝑅𝑎𝑜𝑟 + 𝐷𝑝 = 957.5 + 65 = 1022.5 = 1023
His first official rating is 1023.
Because the player has only played 11 historical games, his first K-factor (that will be used for his next
tournament) is:
𝐾 = (8400
𝐺 + 𝑁) × (1 − 0.01
112) = (
8400
60 + 11) × 0.3187 = 37.7
Ratings Bureau
How South African Ratings are Calculated
19 | P a g e
30 EXAMPLE: CALCULATING THE WEIGHED PERFORMANCE OF A RATED PLAYER
A player, rated 2000, participates in only 1 tournament that month. His rating change for this
tournament is -10. His new rating (to be published on the 1st day of the next month) will be 1990.
The tournament ended on 2017/10/10 and was submitted and processed/rated on 2017/10/15.
His last 5 tournament performances are the following (including the tournament he has just played):
Tournament Performance Games End date Current date Age Q
1 1936 6 2017/10/10 2017/10/15 4 1.00
2 2201 7 2017/09/14 2017/10/15 30 1.00
3 2186 5 2017/02/05 2017/10/15 251 0.98
4 2297 6 2016/09/10 2017/10/15 399 0.97
5 2385 8 2016/04/16 2017/10/15 546 0.96
𝑊𝑃𝑅 =∑ [𝑃𝑖 × (6 − 𝑖) × 𝑄𝑖]
5𝑖=1
15
=[1936 × (6 − 1) × 1] + [2201 × (6 − 2) × 1] + [2186 × (6 − 3) × 0.98] + [2297 × (6 − 4) × 0.97] + [2385 × (6 − 5) × 0.96]
15
=31656.62
15
= 2110
Because his WPR is greater than his new rating, we first calculate the difference between WPR and his
new rating.
Difference = 2110–1990 = 120
Because the difference is less than 200, the player’s new published rating will be 2110.
If, for example, all the player’s tournaments had an age of 121 or less days, his WPR would have been:
𝑊𝑃𝑅 =[1936 × (6 − 1) × 1] + [2201 × (6 − 2) × 1] + [2186 × (6 − 3) × 1] + [2297 × (6 − 4) × 1] + [2385 × (6 − 5) × 1]
15
=32021
32
= 2135 Difference = 2135-1990 = 145
Because the difference is less than 200, the player’s new published rating will be 2135.
If, for example, the player’s WPR was less than 1990, his new rating would remain at 1990.
Ratings Bureau
How South African Ratings are Calculated
20 | P a g e
31 EXAMPLE: A PLAYER WHO PLAYS MORE THAN 1 TOURNAMENT IN A MONTH AND RECEIVES A WPR DURING THE MONTH.
A player has played the following 3 tournaments during the same month. His most recent tournament
is listed first.
# Rating Rating change WPR
1 2135 -4 2100
2 2135 +28 2045
3 2000 -10 2135
31.1 The player had a 2000 rating at the start of tournament 3.
31.2 His WPR based on his 3rd tournament and the previous 4 tournaments is 2135.
31.3 Because, at this stage, his WPR is greater than his current rating (of 2000), his current rating is
updated to 2135 and this is his starting rating for the 2nd tournament.
31.4 The WPR after the 2nd and 3rd tournaments are not higher than his current rating (his current
rating is therefore not adjusted).
31.5 His new rating is calculated by summing his total rating changes and adding this to his latest
rating. Rnew = 2135-10+28-4 = 2149
Ratings Bureau
How South African Ratings are Calculated
21 | P a g e
32 EXAMPLE: HOW A SECTION IS RATED
The following example (Individual Single Round-Robin) has been constructed (taking all the above into
account) to illustrate the procedure on how a section is rated. The calculations for Individual Swiss
and Team tournaments are exactly the same.
# Player Rating 1 2 3 4 5 6 7 8 Score % K
1 Player A 1200 1 0 ½ 1 1 ½ ½ 4½ 63 23.1
2 Player B 1400 0 0 1 ½ 1 1 1 4½ 63 17.6
3 Player C 0 1 1 0 0 0 1 1 4 57 -
4 Player D 1300 ½ 0 1 0 ½ 0 ½ 2½ 36 32.9
5 Player E 0 0 ½ 1 1 0 1 0 3½ 50 -
6 Player F 0 0 0 1 ½ 1 1 0 3 43 -
7 Player G 1100 ½ 0 0 1 0 0 0 1½ 21 18.4
8 Player H 900 ½ 0 0 ½ 1 1 1 4 57 25.5
32.1 Because unrated players participated, we assign them each a temporary rating of 1000.
# Player Rating 1 2 3 4 5 6 7 8 Score % K
1 Player A 1200 1 0 ½ 1 1 ½ ½ 4½ 63 23.1
2 Player B 1400 0 0 1 ½ 1 1 1 4½ 63 17.6
3 Player C 1000 1 1 0 0 0 1 1 4 57 -
4 Player D 1300 ½ 0 1 0 ½ 0 ½ 2½ 36 32.9
5 Player E 1000 0 ½ 1 1 0 1 0 3½ 50 -
6 Player F 1000 0 0 1 ½ 1 1 0 3 43 -
7 Player G 1100 ½ 0 0 1 0 0 0 1½ 21 18.4
8 Player H 900 ½ 0 0 ½ 1 1 1 4 57 25.5
32.2 For each unrated player, calculate his performance rating, taking into account the actual
ratings of the rated opponents and the 1000 for the unrated opponents.
The average opponent rating (Raor) for each unrated player will (obviously) be the same.
𝑅𝑎𝑜𝑟 =1200+1400+1300+1100+900+1000+1000+1000
7= 1271.4 = 1271
Player Raor % Dp Perform
Player C 1271 57 +50 1321
Player E 1271 50 0 1271
Player F 1271 43 -50 1221
These performances are now temporarily assigned to the unrated players and will be used to
update their opponents (both rated and unrated).
Ratings Bureau
How South African Ratings are Calculated
22 | P a g e
# Player Rating 1 2 3 4 5 6 7 8 Score % K
1 Player A 1200 1 0 ½ 1 1 ½ ½ 4½ 63 23.1
2 Player B 1400 0 0 1 ½ 1 1 1 4½ 63 17.6
3 Player C 1321 1 1 0 0 0 1 1 4 57 -
4 Player D 1300 ½ 0 1 0 ½ 0 ½ 2½ 36 32.9
5 Player E 1271 0 ½ 1 1 0 1 0 3½ 50 -
6 Player F 1221 0 0 1 ½ 1 1 0 3 43 -
7 Player G 1100 ½ 0 0 1 0 0 0 1½ 21 18.4
8 Player H 900 ½ 0 0 ½ 1 1 1 4 57 25.5
32.3 Calculate the rating change for each of the rated players taking into account the actual ratings
of the rated opponents and the temporary assigned performance ratings of the unrated
opponents.
PLAYER A (1200)
Opp Rop D We S SWE
B 1400 -200 0.24 1 +0.76
C 1321 -121 0.34 0 -0.34
D 1300 -100 0.36 0.5 +0.14
E 1271 -71 0.40 1 +0.60
F 1221 -21 0.47 1 +0.53
G 1100 +100 0.64 0.5 -0.14
H 900 +300 0.85 0.5 -0.35
SWE +1.20
K 23.1
Total rating change +27.7
PLAYER B (1400)
Opp Rop D We S SWE
A 1200 +200 0.76 0 -0.76
C 1321 +79 0.61 0 -0.61
D 1300 +100 0.64 1 +0.36
E 1271 +129 0.67 0.5 -0.17
F 1221 +179 0.73 1 +0.27
G 1100 +300 0.85 1 +0.15
H 900 +392 0.92 1 +0.08
SWE -0.68
K 17.6
Total rating change -12.0
PLAYER D (1300)
Opp Rop D We S SWE
A 1200 +100 0.64 0.5 -0.14
B 1400 -100 0.36 0 -0.36
C 1321 -21 0.47 1 +0.53
E 1271 +29 0.54 0 -0.54
F 1221 +79 0.61 0.5 -0.11
G 1100 +200 0.76 0 -0.76
H 900 +392 0.08 0.5 +0.42
SWE -0.96
K 32.9
Total rating change -31.6
PLAYER G (1100)
Opp Rop D We S SWE
A 1200 -100 0.36 0.5 +0.14
B 1400 -300 0.15 0 -0.15
C 1321 -221 0.22 0 -0.22
D 1300 -200 0.24 1 +0.76
E 1271 -171 0.27 0 -0.27
F 1221 -121 0.34 0 -0.34
H 900 +200 0.76 0 -0.76
SWE -0.84
K 18.4
Total rating change -15.5
PLAYER H (900)
Opp Rop D We S SWE
A 1200 -300 0.15 0.5 +0.35
B 1400 -500 0.04 0 -0.04
C 1321 -421 0.07 0 -0.07
D 1300 -400 0.08 0.5 +0.42
E 1271 -371 0.10 1 +0.90
F 1221 -321 0.13 1 +0.87
G 1100 -200 0.24 1 +0.76
SWE +3.19
K 25.5
Total rating change +81.3
Ratings Bureau
How South African Ratings are Calculated
23 | P a g e
32.4 Calculate the performance ratings of the rated players.
Player Raor % Dp Perform
Player A (1400+1321+1300+1271+1221+1100+900)/7=1216 63 +95 1311
Player B (1200+1321+1300+1271+1221+1100+900)/7=1188 63 +95 1283
Player D (1200+1400+1321+1271+1221+1100+900)/7=1202 36 -102 1100
Player G (1200+1400+1321+1300+1271+1221+900)/7=1230 21 -230 1000
Player H (1200+1400+1321+1300+1271+1221+1100)/7=1259 57 +50 1309
32.5 Calculate the performance ratings of the unrated players. Note: because they have all played
5+ games, these performances will become their official “new” ratings.
Player Raor % Dp Perform
Player C (1200+1400+1300+1271+1221+1100+900)/7=1199 57 +50 1249
Player E (1200+1400+1321+1300+1221+1100+900)/7=1206 50 0 1206
Player F (1200+1400+1321+1300+1271+1100+900)/7=1213 43 -50 1163
The K-factor for each of these unrated players will be the same (because they have played the
same initial number of games).
𝐾 = (8400
𝐺 + 𝑁) × (1 − 0.01
112) = (
8400
50 + 7) × 0.3187 = 47.0