| """Implements the formula of the Atomic-VAEP framework."""
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| import pandas as pd
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| from pandera.typing import DataFrame, Series
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| from socceraction.atomic.spadl import AtomicSPADLSchema
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| def _prev(x: pd.Series) -> pd.Series:
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| prev_x = x.shift(1)
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| prev_x[:1] = x.values[0]
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| return prev_x
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| def offensive_value(
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| actions: DataFrame[AtomicSPADLSchema], scores: Series[float], concedes: Series[float]
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| ) -> Series[float]:
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| r"""Compute the offensive value of each action.
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| VAEP defines the *offensive value* of an action as the change in scoring
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| probability before and after the action.
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| .. math::
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| \Delta P_{score}(a_{i}, t) = P^{k}_{score}(S_i, t) - P^{k}_{score}(S_{i-1}, t)
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| where :math:`P_{score}(S_i, t)` is the probability that team :math:`t`
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| which possesses the ball in state :math:`S_i` will score in the next 10
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| actions.
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| Parameters
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| ----------
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| actions : pd.DataFrame
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| SPADL action.
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| scores : pd.Series
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| The probability of scoring from each corresponding game state.
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| concedes : pd.Series
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| The probability of conceding from each corresponding game state.
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| Returns
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| -------
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| pd.Series
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| he ffensive value of each action.
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| """
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| sameteam = _prev(actions.team_id) == actions.team_id
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| prev_scores = _prev(scores) * sameteam + _prev(concedes) * (~sameteam)
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| prevgoal_idx = _prev(actions.type_name).isin(["goal", "owngoal"])
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| prev_scores[prevgoal_idx] = 0
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| return scores - prev_scores
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| def defensive_value(
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| actions: DataFrame[AtomicSPADLSchema], scores: Series[float], concedes: Series[float]
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| ) -> Series[float]:
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| r"""Compute the defensive value of each action.
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| VAEP defines the *defensive value* of an action as the change in conceding
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| probability.
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| .. math::
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| \Delta P_{concede}(a_{i}, t) = P^{k}_{concede}(S_i, t) - P^{k}_{concede}(S_{i-1}, t)
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| where :math:`P_{concede}(S_i, t)` is the probability that team :math:`t`
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| which possesses the ball in state :math:`S_i` will concede in the next 10
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| actions.
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| Parameters
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| ----------
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| actions : pd.DataFrame
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| SPADL action.
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| scores : pd.Series
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| The probability of scoring from each corresponding game state.
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| concedes : pd.Series
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| The probability of conceding from each corresponding game state.
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| Returns
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| -------
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| pd.Series
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| The defensive value of each action.
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| """
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| sameteam = _prev(actions.team_id) == actions.team_id
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| prev_concedes = _prev(concedes) * sameteam + _prev(scores) * (~sameteam)
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| prevgoal_idx = _prev(actions.type_name).isin(["goal", "owngoal"])
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| prev_concedes[prevgoal_idx] = 0
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| return -(concedes - prev_concedes)
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| def value(
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| actions: DataFrame[AtomicSPADLSchema], Pscores: Series[float], Pconcedes: Series[float]
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| ) -> pd.DataFrame:
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| r"""Compute the offensive, defensive and VAEP value of each action.
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| The total VAEP value of an action is the difference between that action's
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| offensive value and defensive value.
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| .. math::
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| V_{VAEP}(a_i) = \Delta P_{score}(a_{i}, t) - \Delta P_{concede}(a_{i}, t)
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| Parameters
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| ----------
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| actions : pd.DataFrame
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| SPADL action.
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| Pscores : pd.Series
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| The probability of scoring from each corresponding game state.
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| Pconcedes : pd.Series
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| The probability of conceding from each corresponding game state.
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| Returns
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| -------
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| pd.DataFrame
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| The 'offensive_value', 'defensive_value' and 'vaep_value' of each action.
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| See Also
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| --------
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| :func:`~socceraction.vaep.formula.offensive_value`: The offensive value
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| :func:`~socceraction.vaep.formula.defensive_value`: The defensive value
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| """
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| v = pd.DataFrame()
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| v["offensive_value"] = offensive_value(actions, Pscores, Pconcedes)
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| v["defensive_value"] = defensive_value(actions, Pscores, Pconcedes)
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| v["vaep_value"] = v["offensive_value"] + v["defensive_value"]
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| return v
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|
