Statistics of Snooker Variables

by Martin Los

Dutch flag

The statistical analysis of the mean and the error of the mean for snooker variables.


Legenda
-------
F             : sum of fouls of a player in one frame
T             : total of a player in one frame
LH            : low handicap of a player in one frame
HH            : high handicap of a player in one frame
PK            : potting power of a player in one frame
_a            : a variable for player A
_b            : a variable for player B
x(i)          : value of variable x for frame number i
<x>           : (approximation of) the mean of variable x
s(x)          : (approximation of) the variance of variable x
^             : raise to the power
SQRT(x)       : square root of expression x
Som(i=1,N)(x) : the sum over i=1 to N of (an i dependent) expression x


We have the following formulae:

LH_a = T_a - (F_a + F_b)    
HH_a = T_a - F_b            
PK_a = T_a - F_a      

For player B, the above formulae are the same, just replace _a's with _b's and vice versa.      

Per frame T_a, T_b, F_a and F_b are calculated, which yields the handicaps and potting 
power of both players.

I assume the values LH, HH and PK are EXACTLY the same within one frame.
The statistical approach here only deals with means and variances of the means of
LH, HH and PK over N frames.

<LH> = 1/N Som(i=1,N)(LH(i))  (likewise for HH and PK)

s(LH) = SQRT(1/(N(N-1)) Som(i=1,N)( LH(i)-<LH>) )  

The standard presentation for LH is usally written as:

<LH> +- s(LH)  (mean +- one standaard deviation)

Round <LH> to s(LH)/(2 SQRT(N)) 
Round s(LH) to s(LH)/(2N SQRT(N)).

E.g. 29.576576 round to 0.3 = round to 0.1 = 29.6
      43.115 round to 0.07 = round to 0.01 = 43.12

If you, for example, calculate a new <LH> each week over the last 25 frames,
take as LH(1) the <LH> of the previous week and the LH(2) to LH(25) of the latest 24 frames.
This implies that the mean score of k weeks back is weighted with a factor N^(-k).

(PD) Public Domain 1995-2005, written by Martin Los. All parts of the above text may be copied, distributed, stored in a retrieval system or translated without permission of the author. However, I do appreciate it very much if you mention me as the original author. Thanks to Cor van Dusschoten for explaining the snooker scoring.
Translated to English, July 3, 2005.

Back