The Global Player Index (GPI) is a standardized player rating system that evaluates footballers based on their team strength, opponent strength, match performances, and availability. Inspired by the Elo rating system, it ensures that player ratings reflect actual competitive environments rather than arbitrary baselines.
The GPI system consists of two key components:
- Initial GPI Calculation: Determines a player's starting rating based on their league and team.
- GPI Updates: Adjusts a player's rating after each match based on performance, opponent strength, and playing time.
Step 1: Initializing GPI
A player's initial GPI is assigned based on their league’s Elo rating and their team’s Elo rating, ensuring that players start with a rating reflective of the competitive level of their playing environment. This methodology aligns with Elo-based ranking principles, where a player’s initial value is determined relative to competition rather than an arbitrary baseline.
This ensures that:
- Players debuting in higher-ranked leagues begin with a higher initial GPI than those in lower-ranked leagues.
- Players in stronger teams within a league receive a higher starting GPI than those in weaker teams.
- The system does not assume a player’s quality but situates them within the competitive landscape they enter.
While the initial GPI reflects competition strength, it does not determine a player’s long-term trajectory. Match-by-match performance dictates how GPI evolves, ensuring that overestimated or underestimated initial values are quickly corrected. For players transferring between leagues, their GPI remains unchanged upon transfer, as their ability is not inherently affected by switching competitions. Instead, their GPI naturally adjusts through performance updates in the new league.
Step 2: Updating GPI After Each Match
Once a player has an initial GPI, it is dynamically adjusted after each match based on performance, opponent strength, and match outcome. The update process follows a point-based system similar to Elo ratings:
- Exceeding expectations → GPI gains.
- Underperformance → GPI losses.
Scaling Factor (K = 15)
The extent to which a single match influences GPI is controlled by a scaling factor (K = 15), chosen because it:
- Keeps consistency with league and team Elo calculations.
- Prevents excessive volatility.
- Balances stability and adaptability.
Adjusted Expectation
The expectation component moderates how much performance impacts GPI:
- Good performance → Rewards increase when expectations are harder to exceed.
- Bad performance → Penalties are stronger when expectations are higher.
Minutes Played
A minutes adjustment factor ensures longer performances have greater influence on GPI changes:
- Short appearances → Smaller effect.
- Full matches → Full impact.
- Logarithmic scaling prevents small differences (e.g., 85 vs. 90 minutes) from being exaggerated.
Handling Players Who Do Not Play
If a player does not participate (0 minutes), their GPI gradually declines to reflect inactivity. This is modeled with a logarithmic penalty based on consecutive games missed:
- Missing 1–2 games → Small penalty.
- Missing a full season → Substantial but not catastrophic drop.
- Logarithmic decay avoids overly harsh punishment for long-term injuries.
