# Do-To-Ho World Ranking List Criteria

Still to be checked !!! - This prototype is released 22.01.1999

Still to be checked !!! - This prototype is released 22.01.1999

Still to be checked !!! - This prototype is released 22.01.1999

(Including the changes from "Der Schelmenstre!ch" (DSS) No.9, 32.1.1998)

### 1. Calculation of the tournament valuation T

The tournament valuation T is given by T = [F.W+0.5], where the tournament factor F depends on the type of tournament, (comp. 1.a.), whereas the world ranking list valuation W is defined by the set of participants (comp. 1.b.).

#### 1.a. Calculation of the tournament factor F

The following numbers have an effect on the tournament factor:

• Tradition and game variant of a tournament;
• (Non-)limitation of participation;
• Type and mode of tournament.

The formula for calculating F is F = t.a.c, where t is the tradition factor, a is the announcement factor and c is the tournament mode factor.

#### i) The tradition factor t

lies between 1.0 and 1.5 for every tournament.

It is calculated according to

t = max {1, (0.02 1/z+ 0.98(10y+1)/z + 1)/2}.

Herein z is the number of years since the tournament was first held, and y is the number of years since, in which it did not take place.

If a tournament is held in one of the Do-To-Ho variants (Stahlkugelhockey or Schelmen-Do-To-Ho), instead of t the factor t' := (t+1)/2 is used for the further calculations.

The second and all further times a tournament is held during a calendar year are counted with a tradition factor of t = 1.

#### ii) The announmcement factor a

It is
 a = 1.3, for open tournaments. These are all tournaments, which are announced in the Schelmenstre!ch, where the number of participants is not limited and which are held on one weekend. a = 1.1, for semi-open tournaments. These are all tournaments, which are announced in the Schelmenstre!ch and where the number of participants is resticted directly or indirectly by objective achievement oriented criteria. a = 1.0, for invitation tournaments. These are all tournaments, which do not fulfill one of the above mentioned criteria.

Limitations of the tournament valuation

The valuation for semi-open tournaments is cut back to 180 points and for invitation tournaments to 120 points.

#### iii) The tournament mode factor c

There are the following tournament modes:
 Pure league: g = 1.000 Pure KO system: g = 0.800 Albei type: g = 0.930

The tournament mode factors of the most common mixed forms are listed in the following table, depending on the part of participants, who are eliminated after the first round:

Part of players eliminated after the first round final round
in one group KO system
First round no KO system First round KO system First round no KO system
[0-25)% g = 0.870 g = 0.810 g = 0.840
[25-50)% g = 0.900 g = 0.805 g = 0.870
[50-100)% g = 0.930 g = 0.800 g = 0.900

If the final round is played with play offs, i.e. at least two games against each opponent are played, the basic tournament factor g is increased by 0.020.

Explanations:

Albei type means that a first round is played in league mode (at least 50% of all possible combinations are played). Thereafter a sliding KO round is held, where the ones placed last after the first round have to qualify in KO rounds for the next round. The two players placed first after the first round are automatically qualified for the semi-finals.

League means that every possible combination is played.

Group means that a proper subset of participants plays a league among themselves.

#### 1.b Calculation of the world ranking list valuation W

In case there were qualification tournaments required in order to participate in the tournament, the valuation according to 1.b.i) or 1.b.ii), respectively, is increased by

30.0.9N(1-0.9Q),

where Q is the number of participants in qualification tournaments, who did not participate in the tournament itself, and N the number of participants of the tournament in question.

#### 1.b.i) Calculation of the world ranking list valuation (of participants) W for simple tournaments

(WRL-) placement (n) basic valuation (g(n))
1 bis 5 20
6 bis 10 18
11 bis 15 16
16 bis 20 14
21 bis 25 12
26 bis 30 10
31 bis 40 9
41 bis 50 8
51 bis 75 7
76 bis 100 6
ab 101 5
not placed (yet) (0) 3

Let N be the number of tournament participants. Further assume that N' of them are listed on the WRL. For n=1,2,...,N' the function  f : {1,2,...,N} -> {0,1,...} shall have the WRL placement of the nth best participant as the value f(n). Further we define f(n)=0 if the participant is not yet listed, i.e. for n=N'+1,...,N. The sequence W(n) is defined by

W(1)=g(f(N))

and

W(n+1)=0.9.W(n)+g(f(N-n))

for n=1,2,...,N-1.

Finally put

W:=W(N).

#### 1.b.ii) Calculation of the WRL valuation (of participants) for tournaments with more than one league

Let N be the number of tournament participants, L of which play in the first league. Of the latter L' are listed on the WRL. For n=1,2,...,L' the functionf : {1,2,...,N} -> {0,1,...} shall have the WRL placement of the nth best participant of the first league as the value f(n). Further we define f(n)=0 if the participant is not yet listed or does not play in the first league, i.e. for n=L'+1,...,N.
The sequence W(n) is defined by

W(1)=g(f(N))

and

W(n+1)=0.9.W(n)+g(f(N-n))

for n=1,2,...,N-1.

Finally put W:=W(N).

Remark: f(n)=0 for n=L'+1, L'+2,...,N , means that only the WRL placements of players in the first league matter. For all other participants (and for those, who participated only in qualifying tournaments), the basic valuation of 3 is taken.

### 2. Calculation of the participant's valuation

The participant's valuation B(t) of the participant  t is determined by

• the participant's placement Pl(t),
• the number of games he has won in comparison with those he has played (rating) R(t) ,
• the number s(t) of games he has won against opponents placed higher on the WRL,
• the number G(t) of participants with the same placement.

The participant's valuation is calculated according to

B(t) := [T.P(t)1.5+ 10.R(t) + S(t) + 0.5],

where

 (N-Pl(t))G(t)+1- (G(t)-2)(G(t)-1) P(t) = 2 , G(t)N

is his share of won games (rating)

 R(t) = a(t) , b(t)

where b(t) is the number of games and a(t) is the number of won games of t and

S(t) := Min {0.5.s(t), 10}.

N is again the number of participants.

### 3. Small tournaments

For tournaments with only 3 participants 10, 5 and 2 points for the 1., 2. and 3. place can be gained.

For tournaments with only 2 participants 5 and 2 points for the 1. and 2. place can be gained.

### 4. WRL management

The management of the WRL is trusted to the reliable hands of Günter Prschekopowitz.

#### 4.a. Validity of tournaments

If a tournament is held on the d.m.y, it becomes valid on the 1.m+1.y (in case m<12) or on the 1.1.y+1 (in case m=12), supposed the results are submitted in time.

#### 4.b. Generation of the WRL

New WRLs are generated for the deadlines January 1, April 1, July 1 and October 1. For every player the best three results in tournaments with valid-from-date in the last year are counted with their full value. Of the remaining tournaments with valid-from-date in the last two years the best two are counted with half their value.

#### 4.c. Calculation of the starting values

The first WRL was generated from the reported tournaments of the year 1995 and published January 1, 1996. For the calculation it was assumed that all players were placed 16th.

The valuations of all tournaments since 1996 were and are calculated on basis of the so determined WRL.

#### Tournaments up to and including 31.12.1997.

The above rules came into effect January 1, 1998 and include the changes from "Der Schelmenstre!ch" (DSS) No.9, 32.1.1998.

The following variables were changed:

1. The part exceding 1 of the tradition factor t was twice as large,
2. the announcement factor a for open tournamnents was smaller,
3. there was no limitation of valuation and...
4. the tournament mode factor c was to be changed.

#### The tradition factor t (until December 1997)

lies between 1 and 2 for every tournament. Its value is determined as follows:

t = max {1, 0.021/z+ 0.98(10y+1)/z}.

Herein z counts the number of years since the tournament was first held and y the number of those years since when it did not take place.

If a tournament is held in one of the Do-To-Ho variants (Stahlkugelhockey or Schelmen-Do-To-Ho), instead of t the factor t' := (t+1)/2 is used for the further calculations.

The second and all further times a tournament is held during a calendar year are counted with a tradition factor of t = 1.

#### The announcement factor a (before December 1997)

The announcement factor was
 a = 1.0, for invitation tournaments (without announcement); a = 1.1, for tournaments which were limitedly announced (more than 50% of participants were invited participants); a = 1.2, for open tournaments (more than 50% of participants could participate without invitation).

A tournament is called announced, if its date was published in the Do-To-Ho-Magazine "Der Schelmenstre!ch" (DSS).

1. Remark:
The case, that exactly 50% of participants were not formally invited never occurred.

2. Remark:
There was no limitation of valuations before December 1997.

#### The tournament mode factor c (before December 1997)

... is the above described. The current tournament mode factor unfortunately remained top secret, after it was agreed upon by Günter and Joachim.

© 1996 - 2000 Günter Prschekopowitz, Formulation (translation) and typesetting in HTML:

Cordelia Methfessel & Gerd Podszuweit, GerdPodszuweit@CompuServe.com

http://www.dotoho.de