📊 Why Robust Z-Score Matters - A standardization method designed to reduce the impact of skewed distributions and outliers - It can be seen as a middle ground between Percentile and Z-Score 🧵Thread.

Role Ranking - Ball-Playing Centre-Back - Last 365 Days - Top 5 Leagues U-21 CB - 900+ mins played Jacobo Ramón and Jérémy Jacquet stand out. Personally, I'm expecting Vitor Reis to raise his performance even further as the team recovers its form.

*Correction: U-23 → All Age

Shots (Head) vs Aerial Success % - T5 U-23 CB - 900+ mins (L365) Charlie Cresswell's Shot (Head) per 90min is the 2nd highest in the sample. His Bayesian win rate (adjusted for number of attempts) is also high, indicating he can contribute in aerial duels both IP / OOP.

- All Ages Many of South America's top goalkeepers are in their 30s, limiting the pool of players who could potentially move to Europe in the future.

PSxG - GA % vs Crosses Stopped % - Next 6 Leagues U-23 GK - 900+ mins (L365) In this category, there appear to be few step-up options following Roefs, Lammens, and Trafford. Among the few candidates, Antwerp's Taishi Brandon Nozawa is posting impressive numbers.

🇧🇷 Souza (19) Club: Santos Position: LB MV: 5M € Hard to extract detailed traits from this viz alone, but high npxG, Interceptions, Touch-Verticality (min(Def3rdT, Att3rdT)/Touches), and Prog-P Received vs positional peers suggest solid work rate and off-ball movement.

🇵🇹 Pablo Felipe (22) Club: Gil Vicente → West Ham Position: CF Fee: 23M € npxG (PAdj) is average, but npPSxG-npxG per npxG is excellent. For this season at least, his shooting efficiency really stands out.

🏴󠁧󠁢󠁥󠁮󠁧󠁿 Max Alleyne (20) True to his City academy roots (like Harwood-Bellis and Callum Doyle), a CB who contributes to ball progression. High tackle volume with few fouls conceded. Unproven in T5 leagues, but at this level shows no clear weaknesses in the metrics.

Using data from @fbref, I created a SCORE to assign to players in the top 5 european leagues, evaluating separately their performances in ground duels and aerial duels. The metrics considered for each category are: ◦ Number of duels won per 90 minutes (p90) ◦ Success

🇧🇷 Alysson (19) Club: Grêmio Position: RW MV: 8M € A teenage left-footer who aggressively attempts Take-Ons. Still raw, but compared to similar profiles he records a high number of Defensive Actions, indicating potential to adapt to roles that require hard work OOP.

📊 Why Robust Z-Score Matters - A standardization method designed to reduce the impact of skewed distributions and outliers - It can be seen as a middle ground between Percentile and Z-Score 🧵Thread.

References - Modified Z-Score | Oracle Help Center https://t.co/6gt5uSfEpl - ロバストzスコア：中央値と四分位数で，非正規分布，外れ値を含む標準化 | Laboratory of Biology, Okaya, Nagano, Japan https://t.co/eUQHWGQuYw - 統計解析(z-スコアの算出について） | Japan Biotechnology

Conclusion Robust Z-Score sits squarely between Percentiles and Z-Scores. It retains magnitude while staying robust to skewness and outliers. I rarely see football analysts using this method. If this thread adds Robust Z-Score to your analytical toolkit, I'll be thrilled.

Limitations of Robust Z-Score Robust Z-Score isn't perfect. It fails when Q3 = Q1 (IQR = 0), causing division by zero. This happens with "zero-inflated" stats where most players have 0 (e.g., set-piece metrics when including non-takers). However, I don’t see this as a major

Example 2 Now let’s look at xA (PAdj). Among midfielders, xA tends to split players into clear high and low groups. In this sample, the Z-Score median drops to 37.7—an even more skewed distribution. A Z-Score of 50 corresponds to xA(PAdj) = 0.084, while a Percentile or Robust

Example 1 Next, I compare Percentile, Z-Score, and Robust Z-Score for Progressive Passes (PAdj). Because Percentile ignore distance, their distribution looks almost uniform. Z-Score and Robust Z-Score, on the other hand, reflect the wider spread in the top half of the data.

Example (Setup) Let's examine real data (n=251) using violin and box plots. - Last 365 Days - T5 leagues, DM & CM - 1,350+ mins played I first plotted Progressive Passes (PAdj) by league with violin and box plots. In football, a small number of elite players often produce

What Is Robust Z-Score? Robust Z-Score addresses Z-Score's main weaknesses by using the median and the normalized IQR (NIQR) instead of the mean and standard deviation. Steps: 1. Calculate IQR: IQR = Q3 − Q1 (75th percentile - 25th percentile) 2. Normalize IQR: NIQR = IQR /

Pros and Cons of Traditional Methods Both Percentile and Z-Score come with clear pros and cons. Percentile + Intuitive、robust to outliers - Loses distance information (90th vs 91st percentile might represent vastly different actual performance gaps) Z-Score + Preserves

Conventional Standardization Methods When comparing player stats, two standardization methods are most commonly used. - Percentile Shows where a player’s value ranks within the sample, scaled from 0 to 100. It’s intuitive and does not depend on the shape of the distribution. -