Case Study 1: Evaluating Premier League Midfielders — A Multi-Dimensional Approach

Background

A mid-table Premier League club is looking to strengthen their central midfield during the January transfer window. The coaching staff wants a box-to-box midfielder who can contribute both defensively and offensively. The analytics department has been asked to produce a shortlist of the top 5 candidates from within the Premier League, supported by data.

This case study walks through the complete analytical process from data preparation to final recommendation.

Objectives

1. Define a position-specific metric set for central midfielders
2. Filter and normalize the data using per-90 rates and minimum-minute thresholds
3. Standardize metrics using z-scores within the central midfielder peer group
4. Build radar chart profiles for top candidates
5. Construct a composite performance index with role-appropriate weights
6. Present findings in a format that bridges analytics and coaching

The Data

We work with a simulated dataset based on realistic statistical distributions drawn from the 2023-24 Premier League season. The dataset contains 65 central midfielders (including central midfielders, defensive midfielders, and box-to-box types) who played at least 900 minutes.

Key fields include: player name, age, team, minutes played, and 15 per-90 statistical categories.

Step 1: Metric Selection

For a box-to-box midfielder, we select eight metrics spanning four dimensions:

Offensive contribution: - Non-penalty expected goals (npxG) per 90 - Expected assists (xA) per 90

Ball progression: - Progressive passes per 90 - Progressive carries per 90

Defensive contribution: - Tackles won per 90 - Interceptions per 90

Possession quality: - Pass completion percentage - Pressure success rate (%)

These eight metrics capture the dual-ended nature of the box-to-box role: a player who both disrupts opposition build-up and drives their own team's attacks.

Step 2: Data Preparation and Normalization

All raw counts are converted to per-90 rates. We apply a minimum threshold of 900 minutes (approximately 10 full matches) to exclude players with unreliable small-sample rates.

# Filter: central midfielders with at least 900 minutes
cm_data = df[
    (df["position"].isin(["CM", "DM", "CM/DM"])) &
    (df["minutes"] >= 900)
].copy()

Step 3: Z-Score Standardization

Each metric is converted to a z-score relative to the central midfielder peer group:

$$ z_{ij} = \frac{x_{ij} - \bar{x}_j}{\sigma_j} $$

This allows us to compare metrics measured on different scales. A z-score of +1.0 means the player is one standard deviation above the group average for that metric.

Step 4: Composite Index Construction

We construct a Box-to-Box Composite Index (B2B-CI) using weights that reflect the balanced nature of the role:

$$ \text{B2B-CI}_i = \sum_{j=1}^{8} w_j \cdot z_{ij} $$

Step 5: Results

The composite index produces a ranking. The top 5 candidates in our simulated data set are:

Step 6: Radar Chart Analysis

Radar charts for the top 3 candidates reveal distinct profiles:

• Player Alpha shows a well-rounded profile with particular spikes in progressive passes (+1.8 SD) and progressive carries (+1.6 SD). Their defensive numbers are solid (+0.8 SD for tackles, +0.7 SD for interceptions). This is the archetypal box-to-box profile.

• Player Beta is the most defensively oriented of the top 3. Tackles (+1.9 SD) and interceptions (+1.5 SD) are exceptional, but offensive numbers are closer to average. At age 23, there is development upside.

• Player Gamma is the most technically polished, with elite pass completion (+1.7 SD) and pressure success rate (+1.4 SD), but with more modest progression and defensive numbers.

Step 7: Age Curve Consideration

Incorporating age curves adds a forward-looking dimension:

• Player Beta (age 23) is likely still improving. Based on typical age curves for box-to-box midfielders (peak at 26-29), they have 3-6 years of improvement ahead.
• Player Alpha (age 25) is approaching peak years, offering immediately high performance.
• Player Gamma (age 27) is at peak, offering the highest current level but less future improvement.

The choice between these candidates depends on the club's time horizon: immediate impact (Alpha or Gamma) vs. long-term investment (Beta).

Discussion Questions

1. Weight sensitivity: How would the ranking change if defensive metrics received double the weight? Use the code provided in code/case-study-code.py to experiment.

2. Transfer feasibility: The composite index ranks players by statistical profile, but ignores contract situation, transfer fee, wages, and willingness to move. How should these non-statistical factors be integrated into the shortlisting process?

3. System fit: Player Alpha's progressive carrying numbers are exceptional, but the buying club plays a conservative, possession-recirculation style. How might system fit override raw metric quality?

4. Validation: What additional evidence (video, tracking data, interview) would you want before making a final recommendation?

Key Takeaways

• Multi-dimensional evaluation prevents the trap of evaluating midfielders solely on goals and assists
• Z-score standardization enables fair cross-metric comparison
• Composite indices are useful for initial screening but must be supplemented with profile-level (radar chart) analysis
• Age curves add a temporal dimension that is critical for transfer decisions
• Statistical shortlists are the beginning, not the end, of the recruitment process

Code Reference

The complete code for this case study is in code/case-study-code.py, Section 1. It includes data generation, metric computation, z-score standardization, composite index construction, and radar chart visualization.