# Pickleball Rating System v2.0 - Quick Reference

## Match Outcome Calculation

### Singles Match
```
Outcome = Points Scored by Player / Total Points in Match
```

**Example:** Player scores 11 points, opponent scores 9 points
- Total = 20 points
- Outcome = 11 / 20 = 0.55

### Doubles Match: Effective Opponent

```
Effective Opponent Rating = Opponent 1 Rating + Opponent 2 Rating - Teammate Rating
```

**Example:**
- Opponents: 1500, 1500
- Teammate: 1500
- Effective: 1500 + 1500 - 1500 = 1500 (neutral)

**With strong teammate:**
- Opponents: 1500, 1500
- Teammate: 1600
- Effective: 1500 + 1500 - 1600 = 1400 (weaker-seeming opponent)

**With weak teammate:**
- Opponents: 1500, 1500
- Teammate: 1400
- Effective: 1500 + 1500 - 1400 = 1600 (stronger-seeming opponent)

## Rating Update Distribution (Doubles Only)

After computing the team's rating change (via Glicko-2), distribute to each partner:

```
Change for Player 1 = Team Change × (RD₁² / (RD₁² + RD₂²))
Change for Player 2 = Team Change × (RD₂² / (RD₁² + RD₂²))
```

**Example:** Team gains +30 points
- Alice: RD = 100 (established)
- Bob: RD = 150 (newer)

```
Total Weight = 100² + 150² = 10,000 + 22,500 = 32,500

Change for Alice = +30 × (10,000 / 32,500) ≈ +9.2
Change for Bob   = +30 × (22,500 / 32,500) ≈ +20.8
```

Bob gets more despite the team's shared success because his rating is less certain.

## Expected Point Win Probability

For a player rated R_player vs opponent rated R_opponent:

```
P(win point) = 1 / (1 + 10^((R_opponent - R_player) / 400))
```

**Examples:**

| Player | Opponent | Difference | P(Win Point) |
|--------|----------|-----------|--------------|
| 1500 | 1500 | 0 | 0.500 (50%) |
| 1600 | 1500 | -100 | 0.640 (64%) |
| 1400 | 1500 | +100 | 0.360 (36%) |
| 1700 | 1500 | -200 | 0.759 (76%) |

## Glicko-2 Parameter Meanings

| Parameter | Symbol | Range | Meaning |
|-----------|--------|-------|---------|
| **Rating** | r | 400–2400 | Skill estimate. 1500 = average |
| **Rating Deviation** | d | 30–350 | Uncertainty. Lower = more confident |
| **Volatility** | σ | 0.03–0.30 | Consistency. Higher = more erratic |

### Initial Values for New Players
- Rating: 1500
- RD: 350 (very uncertain)
- Volatility: 0.06

### After ~30 Matches (Established)
- Rating: varies (1300–1700 typical)
- RD: 50–100 (fairly confident)
- Volatility: 0.04–0.08

## V2 Changes Summary

### What Changed from V1

| Aspect | v1.0 | v2.0 |
|--------|------|------|
| **Match Outcome** | Arbitrary tanh(margin) formula | Performance ratio (points/total) |
| **Expected Difficulty** | Ignored | Accounted for (point-based Elo) |
| **Team Rating** | Simple average | Not used directly |
| **Effective Opponent** | Not personalized | R_opp1 + R_opp2 - R_teammate |
| **RD Distribution** | weight = 1/d² | weight = d² (FIXED) |
| **Effect of high RD** | Slower updates (wrong) | Faster updates (correct) |
| **Ratings** | Separate singles/doubles | Prepared for unified rating |

### Why This Matters

1. **More Fair to Uncertain Ratings** — New/returning players now update faster, converging to their true skill more quickly.

2. **Accounts for Teammate Strength** — In doubles, carrying a weak partner is rewarded; being carried by a strong partner is appropriately devalued.

3. **Performance Measured vs Expectations** — A 1500-rated player barely beating a 1400-rated player is underperformance; the system now reflects that.

4. **Theoretically Grounded** — Every formula has a clear mathematical justification, not just "this seemed reasonable."

## Common Questions

### Q: Why does my doubles rating change seem weird?

A: In v2.0, your effective opponent depends on your teammate's rating. Winning with a strong teammate is less impressive than winning with a weak teammate (even if the score is identical).

### Q: Should I play more singles or more doubles?

A: In v1.0, they were separate. In v2.0 (coming), they'll be consolidated into one rating. Either way contributes equally to your skill estimate.

### Q: What if my rating is really high/low?

A: The system works at any rating. The formulas scale appropriately. You might face extreme "effective opponents" in doubles with huge rating imbalances, but that's realistic.

### Q: How long until my rating stabilizes?

A: Roughly 30–50 matches to reach RD ~100. After that, rating changes slow down (you're confident in the estimate) but still respond to actual performance.

### Q: Can I lose rating by winning?

A: Only in the (rare) case where you dramatically underperform expectations. For example, a 1600-rated player barely beating a 1300-rated player might lose 1–2 points because they underperformed what a 1600-rated player should do against a 1300-rated player.

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**See `rating-system-v2.tex` for the complete technical report with derivations and detailed examples.**
