["BayesicFitting"]

Global	Documentation
Home	Manual
Readme	Glossary
Notes	Design
Examples	Classes
	Trouble
	Style

class FootballModel( NonLinearModel )	Source

More or less complex model for the outcome of football marches.

The input values are a (nteams,2) list of integers. They represent teams that play a match, the first at home the other away.

For each team the complexity lists parameters

name	complexity	limits	default	comment
Attack	1	0<a	n/a	trials on the goal
Defensive strength	2	0<b<1	0	fraction of trials stopped
Midfield strength	3	0<c<2	1	relative strength of the team
Home advantage	4	0<d<2	1	advantage of playing at home
Strategy	5	0<e<2	1	defensive <-> offensive

Note: Computational runtime errors/warnings occur when (some of) the parameters are at their limits.

The default values are chosen such that they dont have effect on the results. I.e. a model with complexity=5 and all parameters at the defaults except for "trials", has the same result as a model with complexity 1 with the same "trials" value.

For information what is calculated at each level of complexity, see info at the methods goals1(), goals2(), ... goals5(), below.

Note This is about the game that most of the world calls football.

Examples

fm = FootballModel( 18 ) 
print( fm.npars )
90

Author : Do Kester

Attributes

nteams : int
number of teams
complexity : int
degree of complexity, default = 5.

Attributes from Model

npchain, parameters, stdevs, xUnit, yUnit

Attributes from FixedModel

npmax, fixed, parlist, mlist

Attributes from BaseModel

npbase, ndim, priors, posIndex, nonZero, tiny, deltaP, parNames

FootballModel( nteams, complexity=5, copy=None, **kwargs )

Calculate the score of football matches

The number of parameters is ( nteams * complexity )

Parameters

nteams : int
number of teams
complexity : 1 <= int <= 5
of the model
copy : FootballModel
model to copy
fixed : None or dictionary of {int:float|Model}
     int index of parameter to fix permanently.
     float|Model values for the fixed parameters.
     Attribute fixed can only be set in the constructor.
     See: FixedModel

copy( )

Copy method.

getPrior( k )

Return the prior of the parameter, indicated by k modulo the complexity

Parameters

k : int
parameter number.

goals1( xdata, par )

Consider attack (a) only.

S1 = a1
S2 = a2

Parameters

xdata : array of int
list of matches team 1 vs team 2
par : array_like
attack values

goals2( xdata, par )

Consider attack (a) and defense (d).

S1 = a1 * ( 1 - d2 )
S2 = a2 * ( 1 - d1 )

Parameters

xdata : array of int
list of matches team 1 vs team 2
par : array_like
team values

goals3( xdata, par )

Consider attack (a), defense (d) and midfield (m).

The ratio of the midfield strength modifies attack and defense

S1 = a1 * √(m1/m2) * ( 1 - d2 (m2/m1) )
S2 = a2 * √(m2/m1) * ( 1 - d1 (m1/m2) )

Parameters

xdata : array of int
list of matches team 1 vs team 2
par : array_like
team values

goals4( xdata, par )

Consider attack (a), defense (d), midfield (m) and home advantage (h).

The strategy modifies the midfield strangth of the home team.

mh = m1 * h1
S1 = a1 * √(mh/m2) * ( 1 - d2 (m2/mh) )
S2 = a2 * √(m2/mh) * ( 1 - d1 (mh/m2) )

Parameters

xdata : array of int
list of matches team 1 vs team 2
par : array_like
team values

goals5( xdata, par )

Consider attack (a), defense (d), midfield (m), home advantage (h), and strategy (s)

A offensive strategy (s>1) strenghtens the attach and weakens the defense.
A defensive strategy (s<1) strenghtens the defense and weakens the attack.

mh = m1 * h1
S1 = a1 * √(s1 * mh/m2) * ( 1 - d2 (s2 * m2/mh) )
S2 = a2 * √(s2 * m2/mh) * ( 1 - d1 (s1 * mh/m2) )

Parameters

xdata : array of int
list of matches team 1 vs team 2
par : array_like
team values

baseResult( xdata, params )

Returns the partials at the input value.

The partials are the powers of x ( xdata ) from 0 to degree.

Parameters

xdata : array_like [2:nteams]
list of team ids playing against each other.
params : array_like
parameters for the model

basePartial( xdata, params, parlist=None )

Returns the partials at the input value.

The partials are the powers of x ( xdata ) from 0 to degree.

Parameters

xdata : array_like
values at which to calculate the partials
params : array_like
parameters for the model (ignored for LinearModels).
parlist : array_like
list of indices of active parameters

part1( xdata, par )