«1. Purpose The purpose of this particular project is to create a handicap system which - ...»
Project 52 – Handicap
050605 Per Jernberg
070510 Translated Åke Sjöberg
The purpose of this particular project is to create a handicap system which
- shall rank all the members within the Swedish Bridge Federation
- shall be official, fair, robust and individual
- facilitate the arrangement of fair handicap tournaments irrespective of the tournament is individual, pairs or teams The handicap system shall record all reported top‐score competitions, imp across the field competitions (IAF) and teams (with or without IAF or TAF1). The handicap shall reflect the existing level of skill in such a way that no or insignificant consideration will be made in respect of old tournaments. Another purpose with the handicap system is to use the system to rank all the members of the Swedish Bridge Federation.
2. The handicap system The handicap varies as from 0 to 52, where 0 corresponds the best players in the country and 52 is the starting point for a beginner. A player’s handicap will be adjusted when a competition is reported and the adjustment is depending on the player’s performance since the last adjustment. The performance will be marked through a comparison between the achieved result and the expected result. The achieved result means the result without any handicap adjustments. The expected result is based on the handicap for the pair/team where the player participates and also the handicaps for all the other players in the field. The same procedure applies in an individual bridge tournament. For tournaments calculated with topscore or with the IAF the following shall apply:
• the difference between the handicap for the pair and the average handicap for all other players in the field constitutes the base for the expected result. In respect of team tournaments, the IAF/TAF results will be used if available, otherwise each match will be handled separately. If the IAF/TAF are available the following shall apply:
• the difference between the pairs handicap and the average handicap of all pairs in the opposite direction and the sum of the handicap of the players you actually played against and the average
1 TAF = Topscore Across the Field is the same as IAF at the Board – a – Match team competition and is the same as the topscore calculation in a pairs tournament 1 | H a n d i c a p i n B r i d g e handicap of all the pairs playing in the same direction shall be the base for the expected result for each pair. If each match is handled separately the following shall apply:
• the difference between the two pairs handicap and the sum of the two opponent pairs handicap is the base for the expected result of a pair. If the achieved result exceeds the expected result each player in the pair shall lower the handicap proportionally to the difference between the achieved and the expected result. Accordingly, the handicap will be increased if the achieved result is poorer than the expected one. Thus, the handicap system is therefore a game where wins and losses take out each other. The exception from this can sometimes occur, for example when a player should have a handicap exceeding 52, which will be corrected to 52. The handicap system is designed in such a way that older performances will diminish in value when new competitions are played. The decrease of old results is therefore soft and is not based on time, but on the number of boards played.
3. Basic algorithm
In respect of topscore‐competitions the achieved result r (m ) and the expected result r (m ) is calculated in percent over or below average. Other competitions are calculated in imps± per board. Please observe that all variables above and those defined below is depending on the specific n competition Tm, which is not clearly indicated with the purpose to make the formulas more clear. The equations (1) and (2) are valid for every type of competitions. Below will those factors and variables which differ between different types of competitions be discussed in respect of:
b) type of tournament r (m ) •
22.214.171.124 Duplicate teams IAF/TAF If all the teams have played the the whole tournament with the same pairs and also subject to that no change is made between open and closed rooms, a simplified calculation can be made. Preferably, all the teams have played against each other, but if it can be assumed that a good balance exists the simplified calculation can be made.
4. Certain aspects on the function of the algorithm
4.1 Impact The impact, i.e. which effect a single tournament shall have on the handicap is interesting. Another way to see it is how fast the impact of old performances are cancelled. 1 In equation 2, the factor , is found, which is decisive for the impact. This particular factor could be 480 established on another level. However, It should not be changed after the start of the handicap system ( see however,chapter 6.2 ) To get a feeling for the impact of one separate tournament on the handicap the following example can be studied. If anyone exceeds the expected result with 10 per cent in a topscore tournament with 24 boards, this will at the next adjustment, decrease the handicap with approx. one handicap unit. How fast the impact of old results is diminished can be shown by the following. After 480 boards ( i.e. the inversion of the impact factor ) or 20 normal evening tournaments, approx. 33% of the handicap is from older results and 67% is a result from last 20 tournaments. After 1152 boards or 48 normal evening tournaments ( which is a normal annual play for a club player ), 7% of the handicap is from older performances and 93% of the handicap is from the last 48 tournaments.
4.2 The consideration of the number of boards
6 | H a n d i c a p i n B r i d g e N B −1 The factor in equation 2 is a weight factor which corrects the statistical significance of the NB + S number of boards in a tournament. This factor is based on a pattern which shows how the randomized spread of results (random samples of results ) varies as a function of number of boards. The term S has been established thru statistical analyzes of results from tournaments played (variance calculations from different data’s). Observe that S varies depending on type of tournament.
4.3 The relations between handicap units, topscore och imp There is also a relation factor Cr which depends on the type of tournament. In a topscore tournament factor Cr is 2, which means that a handicap unit is recalculated to 0,5 % when calculating the expected result. Another way to see it is that a player with a handicap of ten units below another player is expected to have a result 4% better, if those two are playing with partners with the same handicap as themselves. In respect of IMP – tournaments the Cr factor is 12, i.e. 6 times more than the top score factor. To ensure this particular relation, an analyze of results from tournaments played (variance calculations) has been used.
4.4. Special handicap tournament When reporting a special handicap tournament ( see chapter 8 ), the results must be recalculated to the result without any handicap adjustments at all.
5. Special establishment of handicap
5.1 Placing of a player at the beginning The start handicap will, in accordance with the discussion above, pretty soon be “forgotten”, especially those who play much and often, so the handicap is not technically of any decisive importance. However, in order to be able to “sell” the system, it could be important. The best way to place the players into the system at the beginning is to use the master points. The easiest way is to give every master class a certain starting value, but on the one hand to achieve correct placements and on the other it should psychologically be advantageous if the spread works from the start my suggestion is as follows: 52 H0(m) = (10) 1 + C ⋅ MP (m ) where C is fixed and MP(m) is m:s master points at the beginning (mutual start for all members). Approximately can C = 0,01 be suitable. Using this, the following rough starting values will be: MP = 0 → H0 = 52,0 MP = 10 → H0 = 47,3 MP = 30 → H0 = 40,0 MP = 50 → H0 = 34,7 MP = 100 → H0 = 26,0 7 | H a n d i c a p i n B r i d g e MP = 300 → H0 = 13,0 MP = 1000 → H0 = 4,7 MP = 3000 → H0 = 1,68 The reader should estimate if this seems to be reasonable. For instance, in a starting field where all pairs except one are reasonable club players with roughly 50 master points, a pair of higher standard where both have 300 master points should reach (34,7‐13,0)/ Cb = +10,8 %, which means 60,8 % to keep the handicap ( Cb = 2). After testing it is easily possible, if needed, to adjust both the size of the interval ( if the handicap should, for instance, spread you over 65 units instead of 52 ) by changing the relationship between the result and the handicap, and the level ( if, the lowest handicap after a while will be – 10 instead of 0 ) through adjusting the scale upwards or down.
5.2 Placing of players afterwards Beginners will be ranked in accordance with the equation above in 5.1, which most oftenly means a handicap of 52. However, the beginner will not be part of the system until he or she will be registered for the first masterpoints or participates in a competition which is registered at the Swedish Bridge Federation. Players, which make a comeback after an interruption of playing bridge, will regain the handicap they had when they stopped playing bridge. However, if they stopped playing before the handicap system starts, they will be ranked in accordance with the 5.1 equation. Players from abroad could be ranked after a estimated size of master points which should reflect the level of play or use the 5.1 equation or also directly be given an estimated handicap in relation to the level of play.
5.3 The ranking of foreign guest players Sometimes foreign guest players participate in official tournaments in Sweden, for instance in OBS – tournaments or the Chairman´s Cup. Those players could be treated as follows:
1. Give all such players a temporary identification number;
2. Give those players/pairs a temporary handicap for the tournament. The handicap can be established thru one of the following methods:
a) be based on the reported level of play
b) be the same handicap as his partner if he is ranked in the system
c) estimate, for every pair where one player lacks a handicap, the pairs handicap: hn −1 (m1,m 2 ) based on the performance of the pair in the particular tournament, in P
8 | H a n d i c a p i n B r i d g e At an individual tournament or teams the corresponding estimation can be made.
5.4 The handling of players without a membership Unfortunately unlicensed players are allowed to participate in competitions arranged by clubs belonging to the Swedish Bridge Federation. We should be able to handle the reporting of such a competition, unless the competition should be declared invalid in respect of handicap. In my opinion such a treatment would be unfair in respect of players who have paid the member fee and cannot be blamed for the participation of “free‐ players”. Hence, I suggest the following approach:
1. when a member and a non‐member play together, the whole pair shall be regarded as non‐ members;
2. at the calculation of the tournament those two should be assigned temporarily member numbers;
3. establish for each non‐member pair an occasional handicap, as a suggestion in accordance with