Figure 3
From: Space evaluation in football games via field weighting based on tracking data
(a) Scatter plot of \( z_{1}(\vec {x}_{\text{e}}, t_{\text{o}}) \) and \( z_{2}(\vec {x}_{\text{e}}, t_{\text{o}}) \) for 34,189 passes obtained from 45 football games. Plots for failed and successful passes almost distribute in \( z_{1} < 0 \) and \( z_{1} > 0 \) domains, respectively. (b) Probability distributions of \( z_{1}(\vec {x}_{\text{e}}, t_{\text{o}}) \) for successful and failed passes. The dotted curves are the fitted normal distribution curves. (c) Success probability of passes as a function of \( z_{1}(\vec {x}_{\text{e}}, t_{\text{o}}) \). The success probabilities are calculated by averaging the value of q over each \( z_{1} \). The dotted curve is the fitted sigmoid function given by Eq. (5), indicating that \( z_{1}(\vec {x}, t) \) signifies the degree of safety for a pass made to \( \vec {x} \) at time t.
