# socceraction.vaep.formula#

Implements the formula of the VAEP framework.

socceraction.vaep.formula.defensive_value(actions, scores, concedes)#

Compute the defensive value of each action.

VAEP defines the defensive value of an action as the change in conceding probability.

$\Delta P_{concede}(a_{i}, t) = P^{k}_{concede}(S_i, t) - P^{k}_{concede}(S_{i-1}, t)$

where $$P_{concede}(S_i, t)$$ is the probability that team $$t$$ which possesses the ball in state $$S_i$$ will concede in the next 10 actions.

Parameters
• actions (pd.DataFrame) – SPADL action.

• scores (pd.Series) – The probability of scoring from each corresponding game state.

• concedes (pd.Series) – The probability of conceding from each corresponding game state.

Returns

The defensive value of each action.

Return type

pd.Series

socceraction.vaep.formula.offensive_value(actions, scores, concedes)#

Compute the offensive value of each action.

VAEP defines the offensive value of an action as the change in scoring probability before and after the action.

$\Delta P_{score}(a_{i}, t) = P^{k}_{score}(S_i, t) - P^{k}_{score}(S_{i-1}, t)$

where $$P_{score}(S_i, t)$$ is the probability that team $$t$$ which possesses the ball in state $$S_i$$ will score in the next 10 actions.

Parameters
• actions (pd.DataFrame) – SPADL action.

• scores (pd.Series) – The probability of scoring from each corresponding game state.

• concedes (pd.Series) – The probability of conceding from each corresponding game state.

Returns

The offensive value of each action.

Return type

pd.Series

socceraction.vaep.formula.value(actions, Pscores, Pconcedes)#

Compute the offensive, defensive and VAEP value of each action.

The total VAEP value of an action is the difference between that action’s offensive value and defensive value.

$V_{VAEP}(a_i) = \Delta P_{score}(a_{i}, t) - \Delta P_{concede}(a_{i}, t)$
Parameters
• actions (pd.DataFrame) – SPADL action.

• Pscores (pd.Series) – The probability of scoring from each corresponding game state.

• Pconcedes (pd.Series) – The probability of conceding from each corresponding game state.

Returns

The ‘offensive_value’, ‘defensive_value’ and ‘vaep_value’ of each action.

Return type

pd.DataFrame

offensive_value()
defensive_value()