How the playing styles are built

Playing styles in the Swiss Super League are described by two independent axes: an offensive build-up axis (possession -> direct) and a defensive pressing-height axis (low block -> high press). Each axis is reduced from a small set of style indicators with PCA and clustered into three archetypes with k-means. The cross-product yields 3 × 3 = 9 transparent playing styles — each named directly by the combination of its two parts, e.g..

The training set contains 104 team-season observations from 16 clubs across the ten seasons 2015/16 to 2024/25, provided by Wyscout. The current 2025/26 season is held out as an out-of-sample observation (the FC Thun promotion). Season-level aggregation smooths match-specific noise from opponent strength, home/away effects and game state, and captures the recurring patterns that define a playing style (Hewitt et al. 2016, Fernández-Navarro et al. 2016).

Volume KPIs such as passes_per90, shots_per90 or xg_per90 strongly correlate with team strength and would dominate PC1. Instead the feature set is built from ratios (forward-pass share), shares (possession %) and indices (recovery height index, loss height index). Set-piece, cross and long-ball indicators are intentionally excluded — they signal a tactical accent rather than a main style and would otherwise bias PC1.

Wyscout records ~100 columns per match. The 14 features that drive the playing-style model are either taken directly from Wyscout's published columns or computed deterministically at season level from Wyscout sums. Below is the full provenance table — for each feature its source, what it measures, and (where applicable) the exact formula. A convention worth stating upfront: shares and ratios are built from season-summed numerators and denominators (e.g. season-total forward_passes ÷ season-total passes), not as means of per-match quotients. This keeps the ratios numerically stable when individual matches have very small denominators.

Both feature sets are standardised (mean 0, SD 1) and transformed into independent principal components. The number of retained components is set by the cumulative-variance rule (≥ 70 %). The first principal component is sign-fixed: PC1+ is "direct" for the offensive set (forward_pass_share loads positively) and "high press" for the defensive set (recovery_height_index loads positively). This produces an asymmetric dimensionality that mirrors the underlying tactical reality: the offensive style space is genuinely two-dimensional, the defensive style space is essentially one-dimensional (pressing height). The feature design passes the three standard PCA suitability tests — KMO sampling adequacy, Bartlett's sphericity test and per-feature VIF — and a feature-leave-out sensitivity analysis (defensive cluster solution Adjusted Rand Index ≥ 0.85) confirms the result is robust against the choice of indicators.

k-means with n_init = 200 is applied on the principal-component scores. The cluster count k = 3 is fixed a priori by theory (Plakias et al. 2024: direct / pragmatic / possession for offensive play; Bauer & Anzer 2021: high press / mid press / low block for defensive play). The empirical validation rests on a consensus of three independent indicators across k = 2 … 7: 1. Inertia (elbow method) — diminishing returns in within-cluster sum of squares. 2. Silhouette score — geometric separation of clusters. 3. Bootstrap-ARI (200 resamples) — reproducibility of cluster assignments. A pure silhouette argmax would prefer k = 2 (a well-known mathematical bias toward small k; Halkidi 2001, Plakias 2023). Only the consensus across theory + elbow + stability justifies the choice of k = 3 — and would also forfeit the theoretically grounded *pragmatic* middle category.

Cluster naming is heuristic and reproducible from the z-profile of each cluster. Offensive thresholds: forward_pass_share > 0.5 SD and avg_passes_per_possession < −0.3 SD → "Direct Vertical Play"; avg_passes_per_possession > 0.5 SD and pass_acc_pct > 0.3 SD → "Possession-Oriented"; otherwise "Pragmatic Style". Defensive thresholds: recovery_height_index > 0.7 SD → "High Press", < −0.7 SD → "Low Block", otherwise "Mid Press". The final style name of a team-season is then simply the cross-product of its two axes: "{offensive} × {defensive}". This keeps the model entirely transparent — every label can be derived directly from the cluster assignment.

For a held-out season such as Thun 2025/26 the model re-uses the trained transformations. The features are standardised with the trained scaler, projected into the PCA space, and assigned to the nearest k-means centroid by Euclidean distance. This keeps the style space stable: results from the current season are directly comparable to historical ones, and the same composite style name (e.g. "Direct Vertical Play × High Press") follows immediately.

Every chart on the analysis page uses the same visual vocabulary so a team-season's full composite style can be read from a single marker — without consulting a legend.

104 team-seasons is a small sample. Season-level aggregation smooths match-specific noise but also erases within-season variation and the influence of opponent strength, home/away effects and game state. Wyscout's event coding is not perfectly consistent (e.g. the definition of "possession" has changed over time) and some features are more affected by noise than others (e.g. avg_passes_per_possession is more volatile than possession_pct). The model captures broad style patterns but cannot explain every nuance of a team's tactical identity and should be complemented with qualitative analysis for a full picture.