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Dr Ian Plummer

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Technical
Yorkshire Variable Base Handicapping System

In normal handicap games the weaker player (with the higher handicap) is given free turns against the stronger player (lower handicap). The number of free turns is the numerical difference in the players' handicaps, e.g. when an 8 handicap plays a four handicap the 8 handicap receives four free turns (known as bisque turns, or more often just bisques).

Another method of arranging handicap play is to give each player a number of bisques equal to their handicap, this is full-bisque play; hence the 8 handicap receives 8 bisques and the 4 handicap four bisques. This can however give the weaker player too many bisques so that they do not have to try very hard. To even out the game further a 'base' can be introduced into the full bisque game where the same number of bisques is subtracted from each player. Hence if the 8 and 4 handicap players played off a base of 3, the 8 handicap player would receive 5 bisques and the 4 handicap player would get only one. If in a game either party's handicap was equal or less than the base, then a normal handicap game would be played.

The purpose of playing games off a base is so that both sides have bisques, but their involvement in the game is increased (i.e. avoiding a whitewash), and hopefully it reduces the time take for the game to be played as bisques encourage hoop making.

The new Variable Base Handicapping System comprises full bisque play to a base which is one quarter of the sum of the two handicaps (rounded down)".

Some examples:

4 vs 8 = base 3
4 vs 12 = base 4
4 vs 16 = base 5 => normal handicap
8 vs 12 = base 5
8 vs 16 = base 6
12 vs 16 = base 7

If you accept the precept that the number of bisques given to each player is approximately that required for them toget both balls to the peg, then the effect of the 'quarter sum' is to give each side the equivalent number of bisques to get one ball to the peg.

A tables for looking up the number of bisques each member of a game should have is given here (base-4).

The table below shows in green the handicap pairs where the variable system applies. The value in each cell is (HA+HB)/4 and hence is the number to be rounded down to give the base. Outside the green area would be played as normal 'bisque difference' play.

    Handicap A (HA)
    -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 11 12 14 16 18 20
H
a
n
d
i
c
a
p
 
B

(H
B)
-2 -1 -0.9 -0.8 -0.6 -0.5 -0.4 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 1 1.3 1.5 1.8 2 2.3 2.5 3 3.5 4 4.5
-1.5 -0.9 -0.8 -0.6 -0.5 -0.4 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1.1 1.4 1.6 1.9 2.1 2.4 2.6 3.1 3.6 4.1 4.6
-1 -0.8 -0.6 -0.5 -0.4 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.3 1.5 1.8 2 2.3 2.5 2.8 3.3 3.8 4.3 4.8
-0.5 -0.6 -0.5 -0.4 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.4 1.6 1.9 2.1 2.4 2.6 2.9 3.4 3.9 4.4 4.9
0 -0.5 -0.4 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.5 1.8 2 2.3 2.5 2.8 3 3.5 4 4.5 5
0.5 -0.4 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.6 1.9 2.1 2.4 2.6 2.9 3.1 3.6 4.1 4.6 5.1
1 -0.3 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.8 2 2.3 2.5 2.8 3 3.3 3.8 4.3 4.8 5.3
1.5 -0.1 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.9 2.1 2.4 2.6 2.9 3.1 3.4 3.9 4.4 4.9 5.4
2 0 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 2 2.3 2.5 2.8 3 3.3 3.5 4 4.5 5 5.5
2.5 0.1 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2.1 2.4 2.6 2.9 3.1 3.4 3.6 4.1 4.6 5.1 5.6
3 0.3 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2 2.3 2.5 2.8 3 3.3 3.5 3.8 4.3 4.8 5.3 5.8
3.5 0.4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2 2.1 2.4 2.6 2.9 3.1 3.4 3.6 3.9 4.4 4.9 5.4 5.9
4 0.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2 2.1 2.3 2.5 2.8 3 3.3 3.5 3.8 4 4.5 5 5.5 6
4.5 0.6 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2 2.1 2.3 2.4 2.6 2.9 3.1 3.4 3.6 3.9 4.1 4.6 5.1 5.6 6.1
5 0.8 0.9 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2 2.1 2.3 2.4 2.5 2.8 3 3.3 3.5 3.8 4 4.3 4.8 5.3 5.8 6.3
6 1 1.1 1.3 1.4 1.5 1.6 1.8 1.9 2 2.1 2.3 2.4 2.5 2.6 2.8 3 3.3 3.5 3.8 4 4.3 4.5 5 5.5 6 6.5
7 1.3 1.4 1.5 1.6 1.8 1.9 2 2.1 2.3 2.4 2.5 2.6 2.8 2.9 3 3.3 3.5 3.8 4 4.3 4.5 4.8 5.3 5.8 6.3 6.8
8 1.5 1.6 1.8 1.9 2 2.1 2.3 2.4 2.5 2.6 2.8 2.9 3 3.1 3.3 3.5 3.8 4 4.3 4.5 4.8 5 5.5 6 6.5 7
9 1.8 1.9 2 2.1 2.3 2.4 2.5 2.6 2.8 2.9 3 3.1 3.3 3.4 3.5 3.8 4 4.3 4.5 4.8 5 5.3 5.8 6.3 6.8 7.3
10 2 2.1 2.3 2.4 2.5 2.6 2.8 2.9 3 3.1 3.3 3.4 3.5 3.6 3.8 4 4.3 4.5 4.8 5 5.3 5.5 6 6.5 7 7.5
11 2.3 2.4 2.5 2.6 2.8 2.9 3 3.1 3.3 3.4 3.5 3.6 3.8 3.9 4 4.3 4.5 4.8 5 5.3 5.5 5.8 6.3 6.8 7.3 7.8
12 2.5 2.6 2.8 2.9 3 3.1 3.3 3.4 3.5 3.6 3.8 3.9 4 4.1 4.3 4.5 4.8 5 5.3 5.5 5.8 6 6.5 7 7.5 8
14 3 3.1 3.3 3.4 3.5 3.6 3.8 3.9 4 4.1 4.3 4.4 4.5 4.6 4.8 5 5.3 5.5 5.8 6 6.3 6.5 7 7.5 8 8.5
16 3.5 3.6 3.8 3.9 4 4.1 4.3 4.4 4.5 4.6 4.8 4.9 5 5.1 5.3 5.5 5.8 6 6.3 6.5 6.8 7 7.5 8 8.5 9
18 4 4.1 4.3 4.4 4.5 4.6 4.8 4.9 5 5.1 5.3 5.4 5.5 5.6 5.8 6 6.3 6.5 6.8 7 7.3 7.5 8 8.5 9 9.5
20 4.5 4.6 4.8 4.9 5 5.1 5.3 5.4 5.5 5.6 5.8 5.9 6 6.1 6.3 6.5 6.8 7 7.3 7.5 7.8 8 8.5 9 9.5 10

There is a potential confusion for minus players (the orange section); -2 vs -2 yields a base of -1 . "We're -2s, the base is -1 hence we have a bisque each". However, number of bisques received = Handicap minus base; -2 - (-1) = -1, a minus bisque . Perhaps I give you my minus bisque and you give me yours :-)

For a comparison the same display is used to show a conventional base-6 event: e.g. the base is active in the blue region. The values in the cells here show the bisque difference which would be given to the weaker player.

  -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 11 12 14 16 18 20
-2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 8 9 10 11 12 13 14 16 18 20 22
-1.5 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 15.5 17.5 19.5 21.5
-1 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 7 8 9 10 11 12 13 15 17 19 21
-0.5 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 14.5 16.5 18.5 20.5
0 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 11 12 14 16 18 20
0.5 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 13.5 15.5 17.5 19.5
1 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 5 6 7 8 9 10 11 13 15 17 19
3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 12.5 14.5 16.5 18.5
4 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3 4 5 6 7 8 9 10 12 14 16 18
4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 11.5 13.5 15.5 17.5
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2 3 4 5 6 7 8 9 11 13 15 17
5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 10.5 12.5 14.5 16.5
6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1 2 3 4 5 6 7 8 10 12 14 16
6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 9.5 11.5 13.5 15.5
7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 9 11 13 15
8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0 1 2 3 4 5 6 8 10 12 14
9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1                    
10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2                    
11 10.5 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3                    
12 11.5 11 10.5 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4                    
13 12.5 12 11.5 11 10.5 10 9.5 9 8.5 8 7.5 7 6.5 6 5                    
14 13.5 13 12.5 12 11.5 11 10.5 10 9.5 9 8.5 8 7.5 7 6                    
16 15.5 15 14.5 14 13.5 13 12.5 12 11.5 11 10.5 10 9.5 9 8                    
18 17.5 17 16.5 16 15.5 15 14.5 14 13.5 13 12.5 12 11.5 11 10                    
20 19.5 19 18.5 18 17.5 17 16.5 16 15.5 15 14.5 14 13.5 13 12                    
22 21.5 21 20.5 20 19.5 19 18.5 18 17.5 17 16.5 16 15.5 15 14                    

What is the Effect of the Divisor?

The variable method suggests dividing the sum of the handicaps by 4; what is the effect of dividing by another number? The smaller the divisor the higher the base and hence the fewer bisques there are in the game. Consequently the game will take, on average, longer.

Dividing by 3: (HA + HB)/3, the orange area shows where the variable base is applied

effect of dividing by 3 - area plot

Divide by 4: (HA+HB)/4, the green area shows where the variable base is applied

effect of dividing by 4 - area plot

Divide by 5: (HA+HB)/5, the violet area shows where the variable base is applied. The divisor is large hence the base is correspondingly low. This increases the number of bisques in the game. This should lead to a faster game.

effect of dividing by 5 - area plot

Comment

Clearly from the displays above the variable base affects more game pairs and if playing to a base reduces the time for a game then it would be expected to speed the whole tournament.

The question which requires more thought however is; "is it balanced and fair?"

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Updated 28.i.16
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