Annex 5 Appendix D (TPR) Tournament performance rating

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clp
Posts: 127
Joined: Tue Jul 10, 2018 14:28
Real name: Kees Pippel
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Annex 5 Appendix D (TPR) Tournament performance rating

Post by clp » Fri Jun 18, 2021 12:41

From annex 5 Swiss system, Appendix D.Tournament performance rating we read:
Introduction
The tournament performance rating may be used as tie-break criterion between players with the same score, or even as first criterion more important than the final score, to decide about the final result.The easy way to calculate the tournament performance rating is by using the average rating of the opponents but given the theory of probability behind the ELO rating system it is mathematically not fully correct way to do this. The performance belonging to an average rating may be something a bit different from the average performance, especially when there is a large variation in the ratings of the opponents.The tournament performance rating should be calculated on a game by game basis.
Definition
The tournament performance rating is that rating for which the expected result of the player, calculated opponent by opponent,equals the realized result of the player.
The TPR could replace many tie-break criteria. The chance that after a few rounds the TPR for two players will be equal is negligible. However, the TPR is not yet available in, for example, Draughts Arbiter Pro. I think there are good reasons for that.
  1. The tournament performance ratings are unique up to a factor iff the game results at hand are connected and indivisible. That is, there must always be a non-losing results path between any two players. This is not the case if one player has won or lost all his games. This is easy to see; but it can also be much more complicated as in this chess tournament: iv memorial-lobaziewicza 2007. To calculate the TPR, the underlying structure of the strongly connected components must be determined.
  2. Within a strongly connected component the TPR constitutes the roots of the function We(x) - W, where x is a vector of ratings, We(x) is the expected score given rating vector x, and W is the actual score.
    Finding the TPR comes down to solving a system of non-linear equations as noted by
    Bert Zwart wrote:
    Mon Aug 06, 2007 14:44
    Wouter,

    Heb je aangetoond dat TPR* uniek is? Het lijkt me een vast punt van een niet-lineair stelsel vergelijkingen...

    Het is natuurlijk duidelijk dat TPR* niet uniek is, omdat in ratings alleen verschillen van belang zijn. Dus laten we zeggen uniek op een constante na.
---> In short: determining the "real" TPR is not straight forward.

The problem can be greatly simplified by replacing the S-shaped expectation function with a linear relationship between the rating difference (D) and the score percentage (P):
  • P(D) = D / 800 + 50%
This simplified performance rating (AVG400), based on the "rule of 400", exists on any universal score results domain.
This performance rating can be computed by solving a set of lineair equations.
When computed, it is easy to verify manually.
The rating is equivalent to the recursive Buchholz tie-break.

The above could be implemented as a first step.

clp
Posts: 127
Joined: Tue Jul 10, 2018 14:28
Real name: Kees Pippel
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Re: Annex 5 Appendix D (TPR) Tournament performance rating

Post by clp » Sun Nov 14, 2021 11:43

clp wrote:
Fri Jun 18, 2021 12:41

The above could be implemented as a first step.
TPRe - TPR extended
  • First criteria. If all players with the highest score are strongly connected, then calculate the TPR for all players belonging to this component.
  • Second criteria. The simplified TPR (AVG400) as described above.
The players are ranked according to (Score, TPR, simplified TPR). In the first rounds of a Swiss tournament, the simplified TPR will dominate as a tie-breaker. As the game results become more connected, the "real" TPR comes into play.
Last edited by clp on Tue Nov 16, 2021 22:08, edited 1 time in total.

clp
Posts: 127
Joined: Tue Jul 10, 2018 14:28
Real name: Kees Pippel
Location: IJmuiden

Re: Annex 5 Appendix D (TPR) Tournament performance rating

Post by clp » Tue Nov 16, 2021 22:02

clp wrote:
Sun Nov 14, 2021 11:43
As the game results become more connected, the "real" TPR comes into play.
Example: Golden Prague 2020 after round 4

Code: Select all

Rk Title               Name Cn  Rtg N + = - P ± | Rk  TPR| Rk   A400|Wpl
 1  mi      Boudewijn Derkx nl 2297 4 3 1 0 7 2 |  1 2604|  1  508.4| 16
 2          Foeke Tiemensma nl 2197 4 2 2 0 6 0 |  2 2556|  4  422.7| 18
 2  mi       Bas Messemaker nl 2257 4 2 2 0 6 2 |  3 2508|  3  456.3| 17
 2 gmi            Pim Meurs nl 2366 4 2 2 0 6 2 |  4 2423|  2  477.3| 17
 2 gmi          Jos Stokkel nl 2243 4 2 2 0 6 0 |  5 2216|  5  388.7| 17
 2  mf      Anton Schotanus nl 2130 4 3 0 1 6 0 |  6 2100|  9  194.4| 16
 2  mf          Kees Romijn nl 2131 4 2 2 0 6 0 |  8 2025| 10  186.0| 14
 2 cmf  Sebastian Wieczorek pl 2111 4 3 0 1 6 0 |        |  6  294.4| 13
 2 gmi        Kees Thijssen nl 2335 4 3 0 1 6 0 |        |  8  247.6| 13
10 gmi          Hein Meijer nl 2261 4 2 1 1 5 0 |  7 2042|  7  272.6| 17
10                 Rik Smit nl 2041 4 1 3 0 5 0 |  9 2009| 11  164.3| 16
10             Filip Kareta cz 1979 4 2 1 1 5 0 | 10 2005| 12  133.0| 15
10  mi        Vaclav Krista cz 2054 4 2 1 1 5 1 | 11 1974| 13   96.1| 14
14           Harry de Groot nl 1946 4 1 2 1 4 1 | 12 1777| 15   63.4| 16
14  mf       Erwin Heslinga nl 2153 4 0 4 0 4 0 | 13 1665| 18   26.8| 15
14              Wim Koopman nl 1954 4 1 2 1 4 1 | 14 1659| 17   29.3| 15
14            Petra Duskova cz 2013 4 1 2 1 4 1 | 15 1658| 14   69.8| 14
14        Herm Jan Brascamp nl 1976 4 2 0 2 4 0 |        | 16   51.6| 14
14  mf    Roep Bhawanibhiek nl 2101 4 2 0 2 4 0 |        | 19    5.2| 12
14          Jan van de Veen nl 2049 4 2 0 2 4 0 |        | 21  -50.1| 12
14     Radjendrenath Kalloe nl 2004 4 2 0 2 4 0 |        | 23 -131.6| 12
22           Douwe Hokwerda nl 2084 4 1 1 2 3 2 | 16 1568| 22  -55.5| 15
22                Tom Meurs nl 1948 4 1 1 2 3 0 |        | 20  -23.9| 15
22      Francesco Militello it 1938 4 1 1 2 3 0 |        | 24 -146.3| 14
22            Robert Töpfer cz 1950 4 1 1 2 3 0 |        | 25 -181.3| 13
22              Jeanet Stel nl 1853 4 1 1 2 3 0 |        | 26 -184.5| 11
22            Ondrej Sikora cz 1900 4 1 1 2 3 0 |        | 29 -346.5| 11
22          Martin Plesnivy cz 1814 4 1 1 2 3 0 |        | 30 -381.1| 11
29             Michal Vitek cz 1860 4 1 0 3 2 0 |        | 27 -254.3| 13
29         Nicholas Novelle cz 1871 4 1 0 3 2 0 |        | 28 -263.9| 13
29           Jana Schmidova cz      4 1 0 3 2 0 |        | 32 -420.4| 11
29         Sofia Iljinskaja cz 1860 4 1 0 3 2 0 |        | 33 -435.7| 11
33              Denis Cerny cz 1900 4 0 0 4 0 0 |        | 31 -417.0| 15
33                    Dummy nl      4 0 0 4 0 0 |        | 34 -795.9|  8
See:
Discussion Swiss system (in Dutch).

clp
Posts: 127
Joined: Tue Jul 10, 2018 14:28
Real name: Kees Pippel
Location: IJmuiden

Re: Annex 5 Appendix D (TPR) Tournament performance rating

Post by clp » Thu Nov 18, 2021 13:30

Cross table Golden Prague after round 4
Player ---> SCC ---> Level
Player             Name 1234567891012345678920123456789301234|SCC Level
1   Sebastian Wieczorek x...20..2|..........|.........2|.....|  2  1
2       Boudewijn Derkx .x.....22|1........2|..........|.....|  1  0
3             Pim Meurs ..x1.1...|......22..|..........|.....|  1  0
4        Bas Messemaker ..1x.....|1..2......|2.........|.....|  1  0
5         Kees Thijssen 0...x....|..........|.2.2.2....|.....|  4  2
6           Jos Stokkel 2.1..x1..|..........|......2...|.....|  1  0
7              Rik Smit .....1x..|.11.......|..........|2....|  1  0
8           Hein Meijer .0.....x.|.1......2.|...2......|.....|  1  0
9     Roep Bhawanibhiek 00......x|..........|........2.|..2..|  3  2
10      Foeke Tiemensma .1.1.....|x.........|....22....|.....|  1  0
11          Kees Romijn ......11.|.x........|..2.....2.|.....|  1  0
12       Harry de Groot ......1..|..x.1.0...|.2........|.....|  1  0
13        Vaclav Krista ...0.....|...x.....1|.......2..|.2...|  1  0
14       Erwin Heslinga .........|..1.x..11.|1.........|.....|  1  0
15         Michal Vitek .........|.....x.00.|....0.2...|.....|  7  5
16      Anton Schotanus ..0......|..2...x...|..2.......|...2.|  1  0
17        Petra Duskova ..0......|....12.x..|1.........|.....|  1  0
18       Douwe Hokwerda .......0.|....12..x0|..........|.....|  1  0
19         Filip Kareta .0.......|...1....2x|..........|...2.|  1  0
20          Wim Koopman ...0.....|....1..1..|x.........|..2..|  1  0
21 Radjendrenath Kalloe ....0....|..0.......|.x........|.2.2.| 13  3
22  Francesco Militello .........|.0....0...|..x....1..|2....| 10  7
23    Herm Jan Brascamp ....0..0.|..........|...x2....2|.....|  5  3
24      Jan van de Veen .........|0....2....|...0x.....|.2...|  6  4
25            Tom Meurs ....0....|0.........|.....x12..|.....|  8  6
26        Robert Töpfer .....0...|.....0....|.....1x...|..2..|  8  6
27          Jeanet Stel .........|...0......|..1..0.x.2|.....| 10  7
28        Ondrej Sikora ........0|.0........|........x.|1...2| 12  8
29     Nicholas Novelle 0........|..........|...0...0.x|...2.| 11  8
30      Martin Plesnivy ......0..|..........|..0.....1.|x...2| 12  8
31       Jana Schmidova .........|...0......|.0..0.....|.x..2| 15  5
32     Sofia Iljinskaja ........0|..........|0.....0...|..x.2|  9  7
33          Denis Cerny .........|......0..0|.0.......0|...x.| 14  9
34                Dummy .........|..........|........0.|000.x| 16  9

SCC - Strongly connected components
Level - From top to bottom

Level ---> SCC x Player
0 - "2 3 4 6 7 8 10 11 12 13 14 16 17 18 19 20"
1 - "1"
2 - "9", "5"
3 - "21", "23"
4 - "24"
5 - "15", "31"
6 - "25 26"
7 - "22 27", "32"
8 - "28 30", "29"
9 - "33", "34"


Elo Rating difference between two different levels is infinite.

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