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Dr Ian Plummer

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Technical
Why Minus Players win Handicap Games

In handicap tournaments minus players do win, in general, more often than expected.  David Maugham, currently ranked World #1 (9.iv.6), gives his opinion. This followed a tournament at the Pendle Club. An appendix gives the results of handicap games played at Cheltenham Easter Tournaments.

OK, I suppose I ought to comment, since I was actually there...

The Conditions

Firstly, specific to this tournament, I had a massive advantage because the lawns were very difficult to play on. There was an issue with a contractor putting twice as much sand on as was required last year, which, combined with the poor weather early in the season, meant that there had been very little grass growth this year. This meant that the lawns were very tufty and bobbly. Combined with the fact that we were using Barlow GTs (where any poor contact significantly reduces the amount of momentum transferred to the object ball), this made rushing very difficult, and gentle strokes a bit of a lottery. On top of this, the lawns were slow (although not outrageously so) and as a consequence, the ability to play big agricultural full rolls and half rolls was significantly more useful than it is normally.

Bisque Usage

In actual play, most people tried to use their bisques correctly (go to peg with the first), although there were several times where they could have been more efficient using them. I got the first ball round on 3 or 4 occasions, and only in one was I pegged out. Most of the other games I got in after the opponent had got to peg and 3-back or so, after all the bisques had run out. I think about three quarters of the games were Riggalled1. Only one of my games was +1 (where the opponent did try to peg out off a half bisque), but there were probably half a dozen more which were in single figures, and none were over +17.

Tactical and Physical Ability

Secondly, on a more general note, I believe that, notwithstanding Dave Kibble’s experience, minus players have an advantage in handicap play. Even in "normal" conditions I would expect to win ~75% of my handicap games, and probably should have a handicap 2-3 steps lower in order to have a 50% chance in a handicap game.

Addressing Dave's specific point (about players going round with their bisques in two turns) this is a holdover from the days when we had people changing handicaps, and they needed an objective standard upon which to base peoples ability. It was kept by Bill Lamb to create the hypothetical conceptual scratch player (CSP), who, with no bisques, would go round without making a mistake. The bottom end was then pegged at -2 because if you give a CSP two bisques, he can set a break up from anywhere and will then go round not making any mistakes. Unfortunately this was complete bollocks in reality.

The Automatic Handicapping System (AHS) is a feedback system which should allow everyone to achieve a position where they will win 50% of their games (im/deprovement notwithstanding), this ignores all concept of a CSP and takes into account tactical as well as physical ability, and will have non-transitive effects as well. For example, some players (typically newcomers) will have physical ability which will be of a higher level than their tactical ability (because it is easy to practice 4-ball breaks, and not so easy to practice all the funny possible situations that croquet games can get into: 3-ball games, Aunt Emma, timed games, etc.) as a consequence these players will deal easily with minus players (because they have lots of bisques) but will deal poorly with players of their own level because they can't dig breaks out, and don't have the tactics to deal with the players who have been around for a few years and have a fairly consistent handicap. Minus players, on the whole, will lose more than 50% of their games to the first group, but will win more than 50% against the second group (because the minus player has both tactical and physical ability (and often a psychological advantage too). And since there are a lot more players in the second group (usually because the first group don't maintain their handicap for very long), the minus players will win more than 50% of their games overall. At least, that's my theory.

I did a piece of analysis a few years ago, based on about 6 years worth of data from the Easter weekend at Cheltenham, which clearly showed that minus players have an advantage. It might be an idea for the Handicap Committee to try and get data on all the handicap games played by minus players to see whether this is a general problem. The solution is easy, if there is a problem, which is just to change the trigger points for handicap changes, as this will not affect the points change in advanced games, (well, it would be slightly smoother, but that's about it) since there are still 10 steps between 2100 and 2600 regardless of the actual handicap assigned to those points. For example:

HCap

Current Trigger Index

Proposed Trigger Index

Linear Trigger Index

0

2000

2000

2000

-0.5

2100

2050

2050

-1

2250

2100

2100

-1.5

2400

2200

2150

-2

2600

2300

2200

-2.5

2800

2400

2250

-3

3050

2550

2300

-3.5

 

2700

2350

-4

 

2850

2400

-4.5

 

3000

2450

An advanced game, between a 2700 index player and a 2100, it would still be a 18/2 game regardless of their handicaps, but in a handicap game, the 2100 would receive an extra half or whole bisque (-3.5 versus -1, as opposed to -2/-2.5 versus -0.5). It's even conceivable that the scale should remain linear below 2000 (i.e. 50 points per handicap step) which would make 2800 a -8!

Dave

Appendix

Winning Probabilities in Handicap Games

David Maugham writes: I did a small analysis a few years ago based on a few years worth of data from one handicap tournament (the Easter weekend at Cheltenham).

I originally posted this in April '99, from the number of games I'd guess this was 3 or 4 years worth of data.

The graph is a record of the number of games played between players in various bands. Reading horizontally gives wins and vertically is losses.

Games

Losses

2 - (-½)

0 - 2½

3 - 6

7 - 12

12 above

Total

Wins

2 - (-½)

3

22

49

31

31

136

0 - 2½

17

14

45

42

27

145

3 - 6

24

49

66

65

61

265

7 - 12

23

42

71

46

38

220

12 above

14

22

33

36

30

135

Total

81

149

264

220

187

901

Converting into % of games won from the above table yields:

% Wins

2 - (-½)

0 - 2½

3 - 6

7 - 12

12 above

2 - (-½)

 
56%
67%
57%
69%

0 - 2½

 
 
48%
50%
55%

3 - 6

   
 
48%
63%

7 - 12

     
 
51%

Hence people in the 3-6 band won 48% of their games against people in the 7-12 band.

As you can see, the minus players win over 50% of their games and, a fact I had forgotten, the 12s+ tend to lose more than 50% to all of the other groups. The groups in the middle were fairly good with respect to each other. I realise that this is a fairly small sample, and is subject to potential anomalies (i.e. being very early season may skew the results) and does not have the full benefit of the AHS, but it implies to me that, on the whole, minus players should give away more bisques and high handicappers should receive more too.

Subjectively, there has been a downward drift in handicaps because of the AHS, so it may be that the high handicaps *are* getting more bisques. However the minus players have not been getting more minus (at least not appreciably) so I don't know whether the other point is being addressed. It may be that there are more "worse" minus players now than there were 5-10 years ago (or, to put it a different way, the ability of a modern -1 is lower than the ability of a -1 from 10 years age), so it's possible that that would have the same effect. Of course, it means that a "good" minus player will still win more than 50% of his games.

Dave

1To 'Riggall' someone is to peg them out (named after Leslie Riggall, a late South African who wrote on the disadvantages of "pegging out" one ball when its partner ball has not yet finished the course of hoops, thus causing the "pegged out" ball to be removed from the game). Or "to Riggall one off" is to peg out ones own ball.

Author: David Maugham
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Updated 28.i.16
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