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Technical
Who Should Qualify for the Knock-Out?

by Louis Nel

Qualification for the Knock-Out (KO) stage of a tournament is often primarily based on the number of games won in the preceding Block Play stage. In case of a single block this works well when supplemented by a satisfactory tie-breaking method. If more than one block is present, then the fairness becomes dependent on how equally challenging the blocks are. The greater the number of blocks, the more difficult it becomes to ensure fairness in this respect.

In the 2007 World Championships, 8 blocks were used. In that situation equally strong blocks are virtually impossible to obtain. The element of unfairness that creeps into the proceedings this way (despite the sincerest efforts to minimise it) has been accepted as inevitable. It is indeed inevitable if no practical and credible alternative is available. The purpose of this article is to bring to light such an alternative. It also addresses a more hidden issue of inherent unfairness illustrated by a case in the most recent World Championship.

The Concept of Event Performance Grade (EPG)

How could the performance of a player in a qualifying event be measured so as to allow fair comparison of all the players? The EPG algorithm does this through successive approximations. Start by simply guessing a performance Grade for the player. Call it a Trial Grade. Using this Trial Grade and the actual Grade of each opponent, calculate an adjustment for every game, much as is done in the World Ranking system. The adjustment is positive (upwards) for a game won, negative for a game lost. After doing this for all block games of the player, we end up with a total Net Adjustment. One Trial Grade is deemed better than another if its resulting Net Adjustment is closer to zero. The EPG of a player is defined to be that Trial Grade that gives a Net Adjustment exactly equal to 0. But how on earth will we find that unique real number? Actually we don’t have find it precisely. We merely need to find a good approximation – for example, one within the Tolerance of 0.01 could be deemed good enough. That can readily be done by using the following three facts: (1) a Trial Grade that is too low gives a positive Net Adjustment; (2) one that is too high gives a negative Net Adjustment; (3) the midpoint between two such Trial Grades will always be better than the worst one of the two. By taking a sequence of successive midpoints as described, the computer can find a good enough approximation typically within about six trials and can do that in just a fraction of a second.

EPG is nothing but a reincarnation of the Period Performance Grade (PPG) introduced in section 2 of my recent article “Bayesian Ranking for Croquet”. So those who may want to know more computational details will find them in that article. One noteworthy difference between PPG and EPG is that it would be unpractical to demand five Moderate Disparity wins as well as five such losses for calculation of EPG. We have to make do with the games at our disposal. That calls for an adaptation in the case of players who either won no games or lost no games. Fortunately, such players are not really the focus of our present scrutiny – they either obviously qualify or obviously don’t qualify for the KO, so the adaptation (details below) is largely a formality.

Note that EPG does not compare a player only with those in the same block. It compares all players involved in the block play stage with each other. This feature puts it in a good position to address inherent unfairness arising from unequal blocks.

An Illustration of EPG at Work

Let us turn to the historic data of the most recent World Championship and look at the EPG of the players after the block play stage. Players without losses were simply assigned an EPG of 50 more than the highest calculated EPG in existence; those without wins were assigned 50 below the lowest calculated EPG (the number 50 is chosen as a matter of arbitrary convenience).

In the table to follow, GW = Games Won, GL = Games Lost and the entry “qualified” in the last column indicates a player who qualified for the KO under the official wins-in-block criterion (in some cases after a play-off game as tie-breaker). The top 32 listed would have qualified under EPG ranking as criterion. One player qualified officially despite an EPG ranking of 47.

2005 World Championship Block Play

Ranking by EPG

       

Rnk

Player

EPG

GW

GL

KO

1

Robert Fulford

2821

9

0

qualified

2

Reg Bamford

2821

9

0

qualified

3

Chris Clarke

2821

9

0

qualified

4

Keith Aiton

2771

8

1

qualified

5

James Death

2740

8

1

qualified

6

David Maugham

2729

8

1

qualified

7

Matthew Burrow

2719

8

1

qualified

8

Jonathan Kirby

2717

8

1

qualified

9

Ken Bald

2583

7

2

qualified

10

Rutger Beijderwellen

2577

7

2

qualified

11

Ed Duckworth

2570

7

2

qualified

12

Kevin Beard

2566

7

2

qualified

13

Ian Dumergue

2560

7

2

qualified

14

Mark Avery 

2549

7

2

qualified

15

 Aaron Westerby        

2526

7

2

qualified

16

 Ronan McInerney       

2518

7

2

qualified

17

 Robin Brown           

2445

6

3

qualified

18

 Mike Jenner           

2438

6

3

qualified

19

 Leo McBride            

2424

6

3

 

20

 Graeme Roberts        

2413

6

3

 

21

 David Goacher         

2410

6

3

qualified

22

 Simon Williams        

2408

6

3

qualified

23

 John Gibbons          

2405

6

3

qualified

24

 Andrew Johnston       

2405

6

3

qualified

25

 Leslie Watson         

2405

6

3

qualified

26

 Peter Landrebe        

2401

6

3

qualified

27

 Marcus Evans          

2400

6

3

qualified

28

 Jeff Dawson           

2399

6

3

qualified

29

 Tim Wilkins           

2397

6

3

 

30

 Ian Lines             

2394

6

3

qualified

31

 Paddy Chapman         

2393

6

3

qualified

32

 David Openshaw        

2387

6

3

qualified

33

 Trevor Bassett        

2374

6

3

qualified

34

 Peter Trimmer         

2365

6

3

 

35

 Kenster Rosenberry    

2327

5

4

 

36

 Jenny Williams         

2314

5

4

 

37

 Chris Williams        

2313

5

4

 

38

 Stephen Mulliner      

2305

5

4

 

39

 Stewart Jackson       

2297

5

4

 

40

 Jerry Guest           

2295

5

4

 

41

 Toby Garrison         

2287

5

4

 

42

 Peter Batchelor       

2286

5

4

 

43

 Sam Tudor             

2278

5

4

 

44

 Jerry Stark           

2271

5

4

qualified

45

 Robert Lowe           

2265

5

4

 

46

 Colin Irwin           

2261

5

4

 

47

 Mark McInerney        

2255

5

4

qualified

48

 Roger Jenkins         

2172

4

5

 

49

 Liz Fleming           

2156

4

5

 

50

 Alan McInerney        

2065

3

6

 

51

 William Louw          

2064

3

6

 

52

 Alan Sands            

2058

3

6

 

53

 Brian Cumming         

2056

3

6

 

54

 Doug Grimsley         

2050

3

6

 

55

 Alex Leggate          

2046

3

6

 

56

 Mark Prater           

2018

3

6

 

57

 Paul Bennett          

2016

3

6

 

58

 Simon Hockey          

1997

3

6

 

59

 Ian Burridge          

1979

3

6

 

60

 Ahmed El Mahdy        

1978

2

7

 

61

 Bruno Hess            

1964

2

7

 

62

 Kevin Wells           

1939

2

7

 

63

 Curtis Drake          

1914

2

7

 

64

 Rodolphe Dourthe      

1886

2

7

 

65

 Paul Smith            

1875

2

7

 

66

 Ian Sexton            

1870

2

7

 

67

 Dennis Bulloch        

1865

2

7

 

68

 Stephen Forster       

1862

2

7

 

69

 Ailsa Lines           

1860

2

7

 

70

 Ben Ashwell           

1841

2

7

 

71

 Juan Ojeda            

1780

1

8

 

72

 Rhys Thomas           

1658

1

8

 

73

 David Foulser         

1598

1

8

 

74

 Jane McIntyre         

1596

1

8

 

75

 Masaaki Yamada        

1546

0

9

 

76

 Thomas Magin          

1546

0

9

 

77

 Andres Alvarez Sala   

1546

0

9

 

78

 Walid Wahban          

1546

0

9

 

79

 Judith Hanekom        

1546

0

9

 

80

 Anton  Varnas         

1546

0

9

 

Any two different qualification criteria can be expected to produce different outcomes, especially for players near the cut-off point. However, the players far from this point that ended on different sides of the cut-off under the two systems ask for closer inspection. So let us look at the detailed records of these players. The table to follow shows for each player his EPG followed by the Bayesian Grades of opponents encountered in his Wins followed by those encountered in his Losses.

McBride

Roberts

Stark

McInerney

2424

2413

2271

2255

WINS vs

WINS vs

WINS vs

WINS vs

2398

2501

2330

2270

2284

2257

2117

2147

2130

2194

2110

2063

2098

2112

1993

1910

2047

1937

1467

1564

1436

1661

LOSSES vs

LOSSES vs

LOSSES vs

LOSSES vs

2571

2503

2626

2470

2450

2410

2420

2365

2290

2370

2325

2362

2283

2286

Is there anybody out there who would argue that qualifiers Stark or McInerney performed better in block play than either of the non-qualifiers McBride or Roberts?

Let me emphasise that I am not complaining about what was done in the past. Indeed, were I to do that, I would in a sense be complaining against myself, as I chaired the International Seeding Method Committee whose recommendations were adopted by the WCF. There is always room for improvement and that is the spirit in which I am writing. Note however, that the mentioned committee did not invent the idea of block-by-block promotion to the KO. That practice was inherited from earlier years and left unchanged - at the time there was no feasible alternative in sight. The committee introduced a number of other changes, all aimed at assuring fairness to all players.

McBride and Roberts each were involved in 3-way tie for two KO places.   From the point of view of EPG both of these two players should easily have qualified.  The procedure prescribed by the present WCF regulations works well only when both of the following two circumstances are present:

  1. All blocks  have equal strength
  2. No crucial ties occur in a block

Unfortunately even the best efforts of organizers cannot guarantee (a) and (b).

This vulnerability  can be addressed by replacing block by block promotion by a procedure, such as EPG,  in which all players are compared together.

Other advantages of EPG

  1. It would eliminate tie-breaking play-off games. This will facilitate the task of the organisers. Occasionally, play-off games can be difficult to accommodate. (In the unlikely event that the rounded EPG of two players result in a tie, one could arrange for every EPG to be printed to with decimal digits. So the possibility of an EPG tie can be virtually eliminated, except at the top and bottom where it does not matter).
     
  2. It would give formatting flexibility. A particular venue may be able to accommodate 7 blocks of 10 players but not 8 blocks of 10, for lack of time and space. The elimination of play-off games will already ease up the time constraint a little. Since it is awkward to let 32 players qualify out of 7 blocks when the qualification is primarily done per block, the venue in question would likely offer to accommodate 8 blocks of 8 under customary qualification but 7 blocks of 10 under EPG (the number of blocks being immaterial under EPG). Given that blocks of 10 are strongly preferable to blocks of 8, this flexibility could occasionally be quite valuable.

The 2006 Australian Open provides an opportunity to see how EPG handles blocks of different sizes. There were 4 blocks of 8 and 1 block of 7. It can be seen that EPG did not favor every 5 – 2 record over every 4 – 2 record, nor vice versa. The qualification list of EPG differs from the official list in only one inconsequential case (McDonald instead of Bailey).

2006 Australian Open Block Play

Ranking by EPG

 

 

 

Rnk

       Fullname           

  EPG

  GW

 GL

KO

1

 Mike Jenner           

2601

6

0

qualified

2

 John Hardy            

2601

7

0

qualified

3

 Stephen Richards      

2551

6

1

qualified

4

 Steve Harden           

2454

6

1

qualified

5

 Jenny Williams        

2450

6

1

qualified

6

 Peter Landrebe        

2428

6

1

qualified

7

 Chris Clarke          

2358

6

1

qualified

8

 Robert Fulford        

2312

6

1

qualified

9

 Ian Lines             

2299

6

1

qualified

10

 Alison Sharpe         

2275

5

2

qualified

11

 Max Donati            

2204

5

2

qualified

12

 Mike Walker           

2144

4

2

qualified

13

 Michael Wright        

2126

5

2

qualified

14

 Anna Miller           

2072

4

2

qualified

15

 Tony Hall             

2053

4

3

qualified

16

 Kevin Beard           

2006

4

3

qualified

17

 Simon Watkins         

1999

4

3

qualified

18

 Claire Gorton         

1976

4

3

qualified

19

 Trevor Bassett        

1975

4

2

qualified

20

 Dennis Bulloch         

1943

4

3

qualified

21

 Gary Fox              

1924

3

4

qualified

22

 Nick Macoun           

1915

3

4

qualified

23

 Eric Miller           

1823

3

4

qualified

24

 Jonathan Bowen        

1821

3

4

qualified

25

 John Levick           

1793

3

4

qualified

26

 Tim Murphy            

1777

3

4

qualified

27

 Martyn Prins          

1710

2

4

qualified

28

 Stephen Howes         

1688

2

5

qualified

29

 Carl Perrin           

1667

2

5

qualified

30

 Nerida Taylor         

1637

2

5

qualified

31

 Ian Bailey            

1467

1

6

 

32

 Alix Verge            

1464

1

6

qualified

33

 Alan Walsh            

1462

1

6

 

34

 Ken Edwards           

1446

1

6

 

35

 Geof McDonald         

1369

1

5

qualified

36

 Mike Hughes           

1319

0

6

 

37

 Christopher Wilson    

1319

0

7

 

38

 Neil Hartley          

1319

0

7

 

39

 Pam Gentle            

1319

0

7

 

Other Potential Uses of EPG

In some tournament formats  particularly a Flexible Swissit  becomes necessary to rank players on the basis of  a different number of games  played  against  opponents of different strengths. EPG is particularly suitable for use in such circumstances, as along as the players to be ranked have played an adequate number of games. So it is potentially of interest to all event organisers.

Software

Obviously, EPG needs to be implemented on a computer.  These days laptops  are frequently seen at tournaments, so that should not be a problem. If the need arises, I would gladly provide the WCF or its event organiser with the required software in the form of an executable file that could run on a Windows XP platform, along with instructions for its use.

Louis Nel
20 January 2007

Author: Louis Nel
All rights reserved © 2007


Updated 28.i.16
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