2023 Monaco Grand Prix

Dynamic Rating System (DRS)

DRS is an ELO-inspired rating engine for motorsports racing. It measures how far a driver exceeds or falls short of expectations in every race — not just who wins, but how much better (or worse) they did than their car, form, and rivals suggest they should have.

1. Expected Performance

For every driver in the race, we calculate their expected win probability against every other driver using the classic ELO formula:

Expected = 1 / (1 + 10(OpponentElo - MyElo)/400)

Then average all those expected scores → this is what the driver “should” have achieved based purely on current skill rating.

2. Actual Performance

Turns finishing position into a 0–1 score:

• Normalized = (total drivers - position) / (total - 1) → P1 = 1.0, last = 0.0
• Score = Normalized^1.2 (slightly rewards higher finishes more)
• Points bonus: P1–P10 get up to +0.3 extra
• Teammate beat: +0.10 (backmarker teams get +0.05 extra)
• Finish multiplier: ×1.05 for finishing
• DNF: 0.1 + (laps completed / 60) × 0.3 × team reliability factor

3. Performance Difference

Diff = Actual Score – Expected Score

Positive = outperformed expectations. Negative = underperformed.

4. Dynamic K-Factor (Learning Rate)

Base = 28. Then adjusted:

• High Elo (>1900) → ×0.7 (slow learning)
• Low Elo (<1400) → ×1.4 (fast learning)
• Podium → ×1.4 | P4–P10 → ×1.2 | Back of grid → ×1.1
• Smaller field → lower K | Tighter competition → higher K

Final K clamped between 15 and 45.

5. Modifiers

• Race Weight (1.0–1.5): Bigger fields, closer Elo spread, more top drivers → more important race → bigger Elo swings.
• Reliability Factor: DNF → ~0.7–0.9 (less penalty if car is unreliable or many laps done). Finish → ×1.03.
• Team Expectation: Did you beat your team’s average? Sigmoid curve gives 0.6–1.4× boost/penalty.

6. Intelligent Capping

• Standard: ±25 Elo
• Backmarker upside → up to +30, downside only -15
• DNF → no positive gain
• Exceptional: (e.g. backmarker in P4) → up to +40
• Catastrophic: (e.g. 1950 Elo driver P17) → down to -30

Full Calculation Flow (per driver)

1. Build team strength (current + 60% historical)
2. Expected = average win-probability vs all others
3. Actual = position → score + bonuses
4. Diff = Actual – Expected
5. Raw Change = K × Diff
6. Apply: Race Weight × Reliability × Team Expectation
7. Cap intelligently → Final Elo change

Examples

The Idea: Reward drivers for punching above their weight. Penalize underperformance — but fairly, with context. The system learns and self-corrects over time.