If the seven teams are G , Xe, Xa, K, Z , V , and N and they have each
played four times with the following results :
G vs N = 3-1 such that G gains 3 point and N gains 0 points
G vs Z = 2-0 " " G " 3 " " Z " 0 "
G vs Xa = 2-0 " " G " 3 " " Xa " 0 "
G vs K = 1-1 " " G " 1 " " K " 1 "
Xe vs N = 2-0 " " Xe " 3 " " N " 0 "
Xe vs K= 2-1 " " Xe " 3 " " K " 0 "
Xe vs V = 3-1 " " Xe " 3 " " V " 0 "
Xe vs Z = 1-2 " " Xe " 0 " " Z " 3 "
Xa vs K = 1-1 " " Xa " 1 " " K " 1 "
Xa vs V = 2-0 " " Xa " 3 " " V " 0 "
Xa vs N = 2-1 " " Xa " 3 " " N " 0 "
K vs Z = 3-1 " " K " 3 " " Z " 0 "
Z vs V = 2-2 " " Z " 1 " " V " 1 "
V vs N = 2-2 " " V " 1 " " N " 1 "
then the classification for the seven teams is as follows :
team gamesp~d won tied lost points
G 4 3 1 0 10
Xe 4 3 0 1 9
Xa 4 2 1 1 7
K 4 1 2 1 5
Z 4 1 1 2 4
V 4 0 2 2 2
N 4 0 1 3 1
What I am wondering is whether it is possible to write some program such
that from the observed gamesplayed and points
you could determine the games won and/or tied and/or lost , ie whether you
could reveal the third and fourth and fifth columns of information, the
won-tied-lost columns .
As a matter of fact , the points held by G , which is 10 , given that it has
played four games has to be a construct of 3*3 + 1*1 .The 9 held by Xe is
also coming from 3 wins and 1 loss .The 7 points held by Xa is also clear
that it must be coming from 2 wins and 1 tie and the other is a loss . The 5
points held by K have to come from 1 win and 2 ties and 1 loss .
The 4 points held by Z might be vague in that it could be 1 win 1 tie and 2
lost OR 0 win 4 ties and 0 lost .The derivation of the points held by V
and N is also clear as crystal .
Obviously , the more games played , and the more teams competing, the more
difficult it gets to derive the teams' won-tied-lost distribution.It would
be quite interesting if this could be resolved by some program .
----- Original Message -----
From: McKenna, Timothy <[email protected]>
To: <[email protected]>
Sent: Friday, November 05, 2004 10:36 PM
Subject: st: RE: Re: program
> No matter what you program/language you are working in, you still won't be
able to differentiate if a team does:
>
> observed: 6 points, 6 games played
>
> The possible actual game results are:
> 0 wins, 6 ties
> 1 win, 3 ties
> 2 wins, 4 losses
>
> If you have the results for all seven teams in the league you might be
able to determine that there is only one combination of results that could
generate the observed league wide standings. Is this the question you are
asking?
>
> -----Original Message-----
> From: victor michael zammit [mailto:[email protected]]
> Sent: Friday, November 05, 2004 4:27 PM
> To: [email protected]
> Subject: st: Re: program
>
>
> Dear Statalist,
> given a soccer (football) league,with seven teams and each team plays once
> against the other six teams to complete one round ; the three possible
> outcomes for any game is a win, a tie or a loss, ie three points , one
point
> or zero point ,respectively.Is it possible to write a program that could
> give you the number of games the given team has won and /or tied and/or
> lost , given that you know the number of games it has played and the
number
> of points that it received ?
> Victor M. Zammit
>
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