A Machine Learning Framework for Off Ball Defensive Role and Performance Evaluation in Football

TL;DR

A covariate-dependent Hidden Markov Model (CDHMM) tailored to corner kicks, a highly structured aspect of football games, is introduced and it is shown how these contributions provide a interpretable evaluation of defensive contributions against context-aware baselines.

Abstract

Evaluating off-ball defensive performance in football is challenging, as traditional metrics do not capture the nuanced coordinated movements that limit opponent action selection and success probabilities. Although widely used possession value models excel at appraising on-ball actions, their application to defense remains limited. Existing counterfactual methods, such as ghosting models, help extend these analyses but often rely on simulating "average" behavior that lacks tactical context. To address this, we introduce a covariate-dependent Hidden Markov Model (CDHMM) tailored to corner kicks, a highly structured aspect of football games. Our label-free model infers time-resolved man-marking and zonal assignments directly from player tracking data. We leverage these assignments to propose a novel framework for defensive credit attribution and a role-conditioned ghosting method for counterfactual analysis of off-ball defensive performance. We show how these contributions provide a interpretable evaluation of defensive contributions against context-aware baselines.

Figures (16)

• Figure 1: A visualization of a team defending an inswinging corner. Blue circles represent defenders assigned to man-marking roles, with dashed black lines connecting them to their assigned attacker (red circles). Blue triangles indicate defenders in zonal marking roles, positioned in a compact structure near the goalmouth.
• Figure 2: This figure illustrates the estimated zonal states for a team from the 2023/24 Premier League season when defending against inswinging and outswinging corner deliveries. Each sub-figure presents 10 zonal emission distributions, marked by a red circle indicating the mean position and encircled by a 66% confidence interval. The colour of each ellipse denotes the average fraction of the corner sequence duration that a defender spends in that zonal state before transitioning to a man-marking state. Pitch markings are shown in black; goalposts are represented by black squares and the penalty spot by a black circle.
• Figure 3: A comparison of league-average man-marking factors, $\gamma_o$, across the pitch for inswinging (left) and outswinging (right) corner deliveries. The heatmaps reveal differences in defensive behaviour, outswinging corners are associated with slightly tighter man-marking across a broader area, particularly beyond the near-post zone. In both cases, the average offset between defenders and their assigned attackers decreases as the attacker nears the goal.
• Figure 4: Distribution of learned transition model parameters for different defensive behaviours during all 2023/24 season corner kicks. Each column corresponds to a transition type: $\beta_m$ for continuing to man-mark the same attacker, $\beta_z$ for continuing to zonally defend a designated zone, and $\beta_s$ for switching from zonal or one man-marking state to another man-marking assignment. The top two rows show the distribution of parameter weights across all teams for inswinging and outswinging deliveries, respectively. The bottom row illustrates within-team differences between inswinging and outswinging deliveries, highlighting delivery-specific tactical adaptations. These parameters are estimated from team and delivery specific Hidden Markov Models.
• Figure 5: Each subplot shows how the probability of continuing to man-mark a specific attacker ($p_m$) varies spatially under different defender velocities for an individual team in the 2023/24 season during inswinging corners. The attacker is fixed at the origin $(0, 0)$ and moves rightward with velocity $(2.0, 0.0)$, with height $1.85\,\text{m}$ and weight $82\,\text{kg}$. In all panels, the defender moves in the same direction (rightward), with speed increasing from left to right. Red arrows indicate the attacker's velocity vector; green arrows in the top-right corner of each plot indicate the defender’s velocity. We plot three iso-probability contours at $p_m = 0.25$, $0.5$, and $0.75$ to highlight decision boundaries. As defender speed increases, the model assigns lower $p_m$ values to trailing positions and higher values to regions more aligned with the attacker's trajectory, reflecting the influence of velocity alignment on predicted marking persistence. Note that since data is sampled at 25 frames per second, the one-second transition probability of maintaining a man-marking assignment is given by $p_m^{25}$.