Rink-Hockey Rankings

 

Rules for calculations

 

1.     Basic Theory

 

The Rankings are calculated according to the ELO Rating System[1]. This rating system is applied by several sports to calculate performances of players or teams. This is based on a logistical distribution statistics[2], where, for each difference of points between opponent teams a certain probability of victory is estimated. The table for each probability of victory is the following:

 

 

p

dp

p

dp

p

dp

p

dp

p

dp

p

dp

1.0

?

.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

.09

-383

.93

422

.76

202

.59

65

.42

-57

.25

-193

.08

-401

.92

401

.75

193

.58

57

.41

-65

.24

-202

.07

-422

.91

383

.74

184

.57

50

.40

-72

.23

-211

.06

-444

.90

366

.73

175

.56

43

.39

-80

.22

-220

.05

-470

.89

351

.72

166

.55

36

.38

-87

.21

-230

.04

-501

.88

336

.71

158

.54

29

.37

-95

.20

-240

.03

-538

.87

322

.70

149

.53

21

.36

-102

.19

-251

.02

-589

.86

309

.69

141

.52

14

.35

-110

.18

-262

.01

-677

.85

296

.68

133

.51

7

.34

-117

.17

-273

.00

?

.84

284

.67

125

.50

0

.33

-125

.16

-284

?

?

 

For example (in yellow in the above table), if team  A has more 141 points than team B, this means that it has 69 % probability of victory, and B has 31 %.

 

2.     How it works with Rink-Hockey competitions

 

When applied to Rink-Hockey results, the following calculations are done:

 

  1. For each team an average of points of the opponents during a certain period of time is calculated;
  2. For each team, the average of points obtained is calculated. For this purpose the following rules are applied:

                                                               i.      Victory – 1 point; draw – ½ point; defeat – 0 point

                                                              ii.      Victory after extra-time – 0,75 points; defeat after extra-time- 0,25 points

                                                             iii.      Victory after penalties - 0,60 points; defeat after penalties – 0,40 points

                                                           iv.      Results of games for international official competitions[3] are computed twice

                                                            v.      Results of official games between teams competing in different countries, or different national divisions, or between national selections and club teams are computed twice

                                                           vi.      When eliminating series of games (play-offs, CERS Cup stages, for example), a supplemental game is considered with the overall result[4]. This result should never be considered twice and this rule is valid only for official competitions

                                                          vii.      For games between national teams, except for the cases of teams of Portugal, Spain, Italy, Argentina, Chile, Angola, Netherlands and Brazil, the results are considered also as an additional virtual result between one of the 3 first rated club teams of each opposing nation. This allows, for club teams in countries less active in international club competitions, to evaluate more accurately the strength of the corresponding club teams.

  1. With the scores of b., a performance criteria may be calculated, as the % of points obtained by each team.
  2. Then, the application of the inverse distribution function (points difference = function of %), allows to calculate the ELO rating for each team as:

Rate = Average of opponents ± points difference.

e. When the points difference is greater than ± 366 points (equivalent to 10% or 90 %), then it is considered 366 points for calculation purpose.

f.       An optimisation programme is then employed to calculate the optimised rate values for each team, for the set of results considered.

 

 

  1. Types of Rankings and competitions considered

 

a.      Rankings

 

The Rankings presently calculated and diffused through http://rink-hockey.net/ are:

 

-          World Senior Men Club Teams

-          World Senior Women Club Teams

-          National Men Teams

-          National Women Teams

 

As results of games between club and national teams are considered, men and women rankings are linked and numerical values equivalent.

 

b.      Competitions

 

All results of competitions that are published are considered, on a game by game basis. For some competitions, calculations are done at the end of the competition.

 

World – World Championships, Nations Cup, Friendly Tournaments

Europe – European Championships; Club cups and leagues, Ciudad de Vigo, Friendly Tournaments

South-America – Club and national championships, Friendly Tournaments

Asia – Asian Games, Friendly Tournaments

Africa – African Nations Championship, Friendly Tournaments

Portugal – All official senior competitions + Regional (Açores + women regional’s)

Spain - All official senior competitions + Regional (Catalunya 1.div + 2.div +2.div women, these on a tournament basis)

Italy - All official senior competitions

France - All official senior competitions + Regional (on a tournament basis)

Germany - All official senior competitions (national and regional)

Switzerland - All official senior competitions

Netherlands - All official senior competitions

England - All official senior competitions + Regional (ECRHA div 3)

Austria - All official senior competitions

Argentina - All official senior competitions

Chile - All official senior competitions

Brazil - All official senior competitions

Colombia - All official senior competitions

Mexico - All official senior competitions

USA - All official senior competitions

Uruguay - All official senior competitions

Angola - All official senior competitions

Mozambique - All official senior competitions

South Africa - All official senior competitions

Egypt - All official senior competitions

Israel - All official senior competitions

Japan - All official senior competitions

Macau - All official senior competitions

Australia - All official senior competitions

New Zealand - All official senior competitions

 

For all countries, also friendly tournaments are considered.

 

 

4.     Periods of time to be considered for Rankings calculations

 

  1. National Teams Rankings

 

Last two years (4 half years periods)

 

  1. Club Teams Rankings

 

Last year (2 half years periods).

 

For list published in 1st January:

 

European + African + Asian + North American teams – Results from 1st July to 31th December

Other teams – Results from 1st January to 31 th December

 

For list published in 1st July:

 

European + African + Asian + North American teams – Results from 1st July to 30th June

Other teams – Results from 1st January to 30th June, but considering games against teams from other continents, also from 1st July to 31 th December

 

 

  1. Adjustments of list values

 

When each list is to be published, an adjustment is made, in order that the average of the 100 best rated teams is the same as for the previously diffused list. This allows a more accurate comparison between team’s rates along time.

 

When a second team of the same club appears with more points than the first team of that club (disputing a more important league), virtual results are included between those teams in order to invert the situation. This will adjust the fact that not enough results were considered in the period, opposing teams of the two different competitions.

 

 

  1. Ranking lists

 

Ranking list will be published at the following dates:

 

 

1st January

1st July

After World/ Continental Champs.

Men Club Teams

x

x

 

Women Club Teams

x

x

 

Men National teams

 

 

X

Women National Teams

 

 

X

 

Teams to be included in lists are all that have at least 4 entries (results) calculated to that list.

 

 

10.06.2009


 

[1]  http://en.wikipedia.org/wiki/Elo_rating_system

[2] http://en.wikipedia.org/wiki/Logistic_distribution

[3] European Club League, CERS Cup, European Continental Cup, World Championships, Continental Championships, and similar importance competitions

[4] For example: in a play-off team A wins games 1, 3 and 5, but looses 2 and 4. Besides the consideration of all these results, a 6th virtual result is considered as a victory of A. Another example: in CERS Cup, team A wins first game 6-3, but looses 2nd game 4-2. As A wins the right to continue in competition, a 3rd virtual result is considered as a victory of A.