# Outfield Arm Rating Scale - Quick Reference

## Normal Distribution (-6 to +5)

```
                     NORMAL DISTRIBUTION CURVE

    Elite                                              Very Weak
    -6                          0                          +5
    |                           |                           |
    |  -5  -4  -3  -2  -1   |   0   |   +1  +2  +3  +4  +5 |
    |                       |       |                       |
    |<--- Above Average --->|Average|<--- Below Average --->|
    |      (Top 50%)        |       |     (Bottom 50%)      |

    0.6% 2.3% 6.7% 16% 31% 50% | 50% 31% 16% 6.7% 2.3% 0.6%
         Players at each percentile
```

## Rating Breakdown

### Elite Arms (Negative Ratings = Better)

| Rating | Description        | Z-Score  | Approx %   | Frequency  |
|--------|-------------------|----------|------------|------------|
| **-6** | Elite Cannon      | > 2.5    | ~1%        | Very Rare  |
| **-5** | Outstanding       | 2.0-2.5  | ~2%        | Rare       |
| **-4** | Excellent         | 1.5-2.0  | ~3%        | Uncommon   |
| **-3** | Very Good         | 1.0-1.5  | ~5%        | Above Avg  |
| **-2** | Above Average     | 0.5-1.0  | ~15%       | Common     |
| **-1** | Slightly Above    | 0.0-0.5  | ~30%       | Common     |

### Average Arms

| Rating | Description        | Z-Score  | Approx %   | Frequency  |
|--------|-------------------|----------|------------|------------|
| **0**  | Average           | -0.5-0.0 | ~40%       | Very Common|

### Weak Arms (Positive Ratings = Worse)

| Rating | Description        | Z-Score  | Approx %   | Frequency  |
|--------|-------------------|----------|------------|------------|
| **+1** | Slightly Below    | -0.8--0.5| ~20%       | Common     |
| **+2** | Below Average     | -1.2--0.8| ~10%       | Above Avg  |
| **+3** | Poor              | -1.5--1.2| ~5%        | Uncommon   |
| **+4** | Very Poor         | -1.8--1.5| ~2%        | Rare       |
| **+5** | Very Weak         | < -1.8   | ~1%        | Very Rare  |

**Note:** Thresholds calibrated to actual data after 300x assist_rate weight compressed z-score distribution.

## Expected Distribution (162 Players)

Based on normal distribution, in a typical season with ~162 qualified outfielders:

| Rating Range | Count | Description |
|-------------|-------|-------------|
| -6 to -4    | ~10   | Elite/Excellent arms (top tier) |
| -3 to -1    | ~62   | Above average to very good |
| 0           | ~18   | Average (largest single group) |
| +1 to +3    | ~62   | Below average to poor |
| +4 to +5    | ~10   | Very poor/weak arms (bottom tier) |

## Comparison to Previous Scale

**Old Scale:** -6 to +2 (9 levels)
- Skewed toward negative (better arms)
- Limited granularity for weak arms (only 3 levels: 0, +1, +2)
- Not symmetric

**New Scale:** -6 to +5 (12 levels)
- Symmetric distribution around 0 (average)
- Equal granularity for elite and weak arms
- Follows normal distribution percentiles
- More meaningful differentiation at extremes

## Practical Guidelines

### For Elite Arms (-4 to -6)
- Strong deterrent effect on baserunners
- Frequently throw out runners attempting to advance
- High home plate assist count
- Can turn singles into outs on aggressive baserunning

### For Average Arms (-1 to +1)
- Typical MLB outfielder arm strength
- Will get assists but not at elite rate
- Runners will test them opportunistically
- Positioning and reads matter more than raw strength

### For Weak Arms (+3 to +5)
- Runners take extra bases frequently
- Low assist totals relative to opportunities
- May be limited defensively to certain positions
- Often DHs or older players playing outfield occasionally

## Integration Notes

When implementing, ensure:
- Minimum 50 balls fielded for qualification
- Position-specific baselines (LF/CF/RF different)
- Z-score calculation accounts for position
- Players below sample size get 0 (average) rating

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**Reference:** `/docs/of_arm_rating_improvement_proposal.md` for full methodology