The Outlier

Overview

• Player z-scores: Two z-scores are calculated. Individual z-scores compare a player's performance to their OWN average of a stat, while League z-scores compare a player's performance to the LEAGUE's average of that stat.
  
  Individual z-scores are combined with league z-scores using a weighted approach, where individual z-scores have a higher impact on outlier score and league z-scores have a slightly lower impact on outlier score. Since rookie players have no previous season's averages to reference, their stats are scored solely in comparison to the league average.


• Team z-scores: Team-level stats are evaluated only against that team’s own season averages—no league hybrid is used for team metrics.


• Noise control: Players who play under 10 minutes in a game are excluded, and percentages require minimum attempts (e.g., for FG%, 3P%, FT%) to avoid misleading extremes.

Scoring formula

Each player stat is measured as a z-score relative to both the player’s own season averages and the league’s averages. The final hybrid score blends these components:

// compute player z-score and league z-score
player_z = (actual - player_mean) / player_std
league_z = (actual - league_mean) / league_std

// combine using configured weights
combined_z = player_weight * player_z + league_weight * league_z

// apply stat weight for final score
weighted_score = combined_z * stat_weight

• player_weight and league_weight multipliers are set to 0.6 and 0.4 respectively.
• Team scores always compare against team season averages only.

Stat Weights

Not all stats influence game outcomes equally. To reflect their impact, each stat is multiplied by a stat weight in the scoring formula. Higher-weighted stats contribute more heavily to outlier ranking.

• High-impact examples: PTS, TS%, eFG%, and TOV often receive higher weights because they directly correlate with winning margins and overall game efficiency.
• Medium-impact examples: REB, AST, and STL may carry moderate weights since they affect possession control and ball movement but are more context-dependent.
• Low-impact or volatile stats: BLK, PF, or niche efficiency metrics typically have lower weights to reduce noise and outlier inflation.

Why this method

The hybrid model balances two important perspectives: individual consistency and league-wide rarity. A performance might be ordinary for one player but extraordinary in the league context—or vice versa. Weighting both helps highlight the most meaningful statistical outliers without overreacting to small-sample noise.

Example

If a player who averages 8 points (std 4) scores 24 in a game, their player_z = (24−8)/4 = 4.0. With player_weight = 0.7, league_weight = 0.3, and a stat weight of 1.2, that game becomes a significant positive outlier that rises to the top of the rankings.

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