openskill.models.weng_lin.common module

Common functions for the Weng-Lin models.

openskill.models.weng_lin.common._ladder_pairs(teams: List[Any]) → List[List[Any]][source]

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

Parameters:

teams – A list of teams.

Returns:

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

openskill.models.weng_lin.common._unwind(tenet: List[float], objects: List[Any]) → Tuple[List[Any], List[float]][source]

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

Parameters:

  • tenet – A list of tenets for each object in the list.

  • objects – A list of teams to sort.

Returns:

Ordered objects and their tenets.

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

Normal cumulative distribution function.

Parameters:

x – A number.

Returns:

A number.

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

Normal inverse cumulative distribution function.

Parameters:

x – A number.

Returns:

A number.

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

Normal probability density function.

Parameters:

x – A number.

Returns:

A number.

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

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

Parameters:

  • x – A number.

  • t – A number.

Returns:

A number.

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

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

Parameters:

  • x – A number.

  • t – A number.

Returns:

A number.

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

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

Parameters:

  • x – A number.

  • t – A number.

Returns:

A number.

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

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

Parameters:

  • x – A number.

  • t – A number.

Returns:

A number.