openskill.models.weng_lin.common

Common functions for the Weng-Lin models.

Module Contents

Functions

_ladder_pairs(teams)

Returns a list of pairs of ranks that are adjacent in the ladder.

_unwind(tenet, objects)

Retain the stochastic tenet of a sort to revert original sort order.

phi_major(x)

Normal cumulative distribution function.

phi_major_inverse(x)

Normal inverse cumulative distribution function.

phi_minor(x)

Normal probability density function.

v(x, t)

The function \(V\) as defined in Weng and Lin [2011]

vt(x, t)

The function \(\tilde{V}\) as defined in Weng and Lin [2011]

w(x, t)

The function \(W\) as defined in Weng and Lin [2011]

wt(x, t)

The function \(\tilde{W}\) as defined in Weng and Lin [2011]
openskill.models.weng_lin.common._ladder_pairs(teams)[source]

Returns a list of pairs of ranks that are adjacent in the ladder.

Parameters:

teams (List[Any]) – A list of teams.

Returns:

A list of pairs of teams that are adjacent in the ladder.

Return type:

List[List[Any]]

openskill.models.weng_lin.common._unwind(tenet, objects)[source]

Retain the stochastic tenet of a sort to revert original sort order.

Parameters:

  • tenet (List[float]) – A list of tenets for each object in the list.

  • objects (List[Any]) – A list of teams to sort.

Returns:

Ordered objects and their tenets.

Return type:

Tuple[List[Any], List[float]]

openskill.models.weng_lin.common.phi_major(x)[source]

Normal cumulative distribution function.

Parameters:

x (float) – A number.

Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.phi_major_inverse(x)[source]

Normal inverse cumulative distribution function.

Parameters:

x (float) – A number.

Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.phi_minor(x)[source]

Normal probability density function.

Parameters:

x (float) – A number.

Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.v(x, t)[source]

The function \(V\) as defined in Weng and Lin [2011]

Parameters:
Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.vt(x, t)[source]

The function \(\tilde{V}\) as defined in Weng and Lin [2011]

Parameters:
Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.w(x, t)[source]

The function \(W\) as defined in Weng and Lin [2011]

Parameters:
Returns:

A number.

Return type:

float

openskill.models.weng_lin.common.wt(x, t)[source]

The function \(\tilde{W}\) as defined in Weng and Lin [2011]

Parameters:
Returns:

A number.

Return type:

float