# Outfield Arm Rating Improvement Proposal

## Executive Summary

This document proposes an improved method for calculating outfield arm ratings using Retrosheet play-by-play event data. The current method relies solely on Baseball Reference's `bis_runs_outfield` statistic, which is not available for historical seasons. The proposed method uses multiple metrics from detailed play-by-play data to create a more nuanced and historically-available arm rating system.

## Current Implementation

**Location:** `defenders/calcs_defense.py:382-406`

**Current Method:**
- Uses `bis_runs_outfield` from Baseball Reference defensive stats
- Takes the **maximum** value across all OF positions played (LF/CF/RF)
- Maps to a -6 to +2 scale based on fixed thresholds
- Thresholds calibrated to 2005 data (top value: 23 for Jim Edmonds)

**Limitations:**
1. `bis_runs_outfield` not available for all historical seasons
2. Single-metric approach doesn't capture nuance of arm strength
3. Doesn't differentiate between "strong arm with poor positioning" vs "weak arm with good positioning"
4. No adjustment for position-specific expectations (RF arms typically stronger than LF)

## Available Retrosheet Data

The `retrosheets_events_2005.csv` file contains detailed play-by-play data with these arm-relevant fields:

### Direct Arm Indicators
- **`a7`, `a8`, `a9`**: Assists by LF, CF, RF (when OF throws result in outs)
- **`po7`, `po8`, `po9`**: Putouts by LF, CF, RF (catches/fields)
- **`brout_b`, `brout1`, `brout2`, `brout3`**: Which baserunners were thrown out (identifies who got the out)

### Context Fields
- **`br1_pre/post`, `br2_pre/post`, `br3_pre/post`**: Runner positions before/after play
- **`event`**: Play description (e.g., "S7/G5.BX2(74)" = single to LF, batter out at 2nd by LF→2B)
- **`loc`**: Hit location (e.g., "7LS+" = LF line drive short)
- **`hittype`**: L (line drive), F (fly ball), G (ground ball)

## 2005 Season Analysis Results

### League-Wide Statistics

| Position | Total Assists | Thrown Out Home | Batter Extra Base Outs | Avg Assist Rate | Avg Throwout Rate |
|----------|--------------|-----------------|----------------------|----------------|-------------------|
| LF       | 294          | 184             | 102                  | 3.01%          | 86.71%            |
| CF       | 247          | 167             | 63                   | 2.04%          | 81.23%            |
| RF       | 288          | 170             | 93                   | 2.77%          | 79.52%            |

### Top Performers (by Total Assists)

**Left Field:**
1. tagus001 (7 assists, 8.64% rate, 3 home throws)
2. evera001, piera001 (6 assists each, 100% throwout rate)

**Center Field:**
1. liebm001 (8 assists, 2.87% rate, 8 home throws)
2. mathm001 (7 assists, 2.66% rate, 7 home throws)

**Right Field:**
1. kenna001, canor001, gathj001 (6 assists each)

### Key Insights
- Average assist rate varies by position (LF: 3.01%, CF: 2.04%, RF: 2.77%)
- High throwout rates (79-87%) suggest most assists occur on "sure outs"
- Home plate throws are rare but high-value (strongest arm indicator)
- Batter extra-base outs (preventing runners from stretching singles to doubles) common

## Proposed Arm Rating Formula

### Multi-Metric Composite Score

```python
arm_score = (
    (assist_rate * 300) +                   # PRIMARY: Assist rate (dominant)
    (home_throws * 1.0) +                   # Quality: home plate throws
    (batter_extra_outs * 1.0) +            # Quality: preventing extra bases
    (total_assists * 0.1)                   # Minimal volume bonus
)
```

**Design Philosophy:**
- **Assist rate dominates** - Only rate stat needed (assists are already outs)
- **Quality bonuses** - Home throws and batter extra outs add minimal context
- **No throwout rate** - Redundant since assists = outs by definition
- **Volume minimized** - Raw assist count provides minor bonus only
- **Example:** 8.64% assist rate = 25.9 points vs 2.87% rate = 8.6 points

**Why No Throwout Rate:**
- In baseball statistics, an assist is ALREADY an out by definition
- "Throwout rate" was measuring relay throws vs direct outs
- This created redundancy with assist_rate
- Simplified formula focuses on pure assist rate + quality indicators

### Position-Adjusted Z-Score
- Calculate league-average and standard deviation by position (LF/CF/RF)
- Convert raw score to z-score: `(player_score - position_avg) / position_stddev`
- Map z-score to -6 to +2 rating scale

### Minimum Sample Size
- Require 50+ balls fielded (putouts + assists) to qualify
- Players below threshold get league-average rating (0)

## Proposed Rating Scale

Distribution calibrated to actual data after formula adjustments:

| Z-Score Range | Arm Rating | Description | Approx % | Examples (2005) |
|--------------|------------|-------------|----------|-----------------|
| > 2.5        | -6         | Elite cannon | ~1% | Elite assist rates |
| 2.0 to 2.5   | -5         | Outstanding | ~2% | Outstanding assist rates |
| 1.5 to 2.0   | -4         | Excellent   | ~3% | Excellent assist rates |
| 1.0 to 1.5   | -3         | Very Good   | ~5% | Very good assist rates |
| 0.5 to 1.0   | -2         | Above Average | ~15% | Above average assist rates |
| 0.0 to 0.5   | -1         | Slightly Above | ~30% | Slightly above average |
| -0.5 to 0.0  | 0          | Average     | ~40% | Average assist rates |
| -0.8 to -0.5 | 1          | Slightly Below | ~20% | Slightly below average |
| -1.2 to -0.8 | 2          | Below Average | ~10% | Below average assist rates |
| -1.5 to -1.2 | 3          | Poor        | ~5% | Poor assist rates |
| -1.8 to -1.5 | 4          | Very Poor   | ~2% | Very poor assist rates |
| < -1.8       | 5          | Very Weak   | ~1% | 0 assists / very weak arms |

**Distribution Notes:**
- **Adjusted for formula**: 300x weight on assist_rate compressed z-score spread
- **Thresholds calibrated**: Based on actual 2005 data distribution
- **Full range used**: Ensures -6 to +5 scale is fully utilized
- **Worst arms**: Players with 0 assists (z ≈ -1.82) receive +5 rating
- **Average centered**: Rating 0 represents middle ~40% of qualified OFs

## Implementation Pseudocode

```python
def calculate_retrosheet_arm_rating(df_events, player_bbref_id, season_pct=1.0):
    """
    Calculate OF arm rating from Retrosheet play-by-play events

    Args:
        df_events: DataFrame of retrosheet events for the season
        player_bbref_id: Player's baseball-reference ID (key_bbref)
        season_pct: Percentage of season completed (for proration)

    Returns:
        int: Arm rating from -6 to +2
    """

    # Find all positions this player played
    arm_ratings_by_pos = []

    for of_pos, a_col, po_col, fielder_col in [
        ('LF', 'a7', 'po7', 'l7'),
        ('CF', 'a8', 'po8', 'l8'),
        ('RF', 'a9', 'po9', 'l9')
    ]:
        # Get all plays at this position for this player
        player_plays = df_events[df_events[fielder_col] == player_bbref_id]

        if len(player_plays) == 0:
            continue

        # Calculate component metrics
        balls_fielded = player_plays[(player_plays[po_col] > 0) | (player_plays[a_col] > 0)].shape[0]

        if balls_fielded < 50 * season_pct:  # Minimum sample size
            continue

        total_assists = player_plays[player_plays[a_col] > 0].shape[0]

        throwouts = player_plays[
            (player_plays[a_col] > 0) &
            ((player_plays['brout1'] == int(a_col[-1])) |
             (player_plays['brout2'] == int(a_col[-1])) |
             (player_plays['brout3'] == int(a_col[-1])) |
             (player_plays['brout_b'] == int(a_col[-1])))
        ].shape[0]

        home_throws = player_plays[
            (player_plays[a_col] > 0) &
            ((player_plays['brout1'] == int(a_col[-1])) |
             (player_plays['brout2'] == int(a_col[-1])) |
             (player_plays['brout3'] == int(a_col[-1])))
        ].shape[0]

        batter_extra_outs = player_plays[
            (player_plays[a_col] > 0) &
            (player_plays['brout_b'] == int(a_col[-1]))
        ].shape[0]

        # Calculate rates
        assist_rate = total_assists / balls_fielded if balls_fielded > 0 else 0
        throwout_rate = throwouts / total_assists if total_assists > 0 else 0

        # Composite score
        raw_score = (
            (assist_rate * 30) +
            (throwout_rate * 5) +
            (home_throws * 2) +
            (batter_extra_outs * 1.5) +
            (total_assists * 0.5)
        )

        # Get league stats for this position (pre-calculated)
        position_avg = get_position_average(of_pos, season_pct)
        position_std = get_position_stddev(of_pos, season_pct)

        # Calculate z-score
        z_score = (raw_score - position_avg) / position_std if position_std > 0 else 0

        arm_ratings_by_pos.append(z_score)

    if not arm_ratings_by_pos:
        return 0  # Default average rating

    # Use maximum z-score across positions (best arm showing)
    max_z = max(arm_ratings_by_pos)

    # Map to -6 to +5 scale (normal distribution)
    if max_z > 2.5:
        return -6    # Elite (top 0.6%)
    elif max_z > 2.0:
        return -5    # Outstanding (top 2.3%)
    elif max_z > 1.5:
        return -4    # Excellent (top 6.7%)
    elif max_z > 1.0:
        return -3    # Very Good (top 16%)
    elif max_z > 0.5:
        return -2    # Above Average (top 31%)
    elif max_z > 0.0:
        return -1    # Slightly Above (top 50%)
    elif max_z > -0.5:
        return 0     # Average (middle 38%)
    elif max_z > -1.0:
        return 1     # Slightly Below (bottom 31%)
    elif max_z > -1.5:
        return 2     # Below Average (bottom 16%)
    elif max_z > -2.0:
        return 3     # Poor (bottom 6.7%)
    elif max_z > -2.5:
        return 4     # Very Poor (bottom 2.3%)
    else:
        return 5     # Very Weak (bottom 0.6%)
```

## Advantages of Proposed Method

1. **Historical Availability**: Retrosheet data available from 1921-present
2. **Multi-Dimensional**: Captures different aspects of arm strength
3. **Context-Aware**: Accounts for position-specific expectations
4. **Nuanced**: Distinguishes between volume and quality of throws
5. **Transparent**: Clear formula allows for tuning/debugging

## Disadvantages

1. **Data Processing**: Requires parsing large play-by-play files
2. **Complexity**: More complex than single-stat lookup
3. **Sample Size**: Platoon players may not have enough opportunities
4. **Indirect Measurement**: Measures outcomes, not true arm strength

## Integration with Current System

### Option 1: Hybrid Approach (Recommended)
- Use Baseball Reference `bis_runs_outfield` when available (2003+)
- Fall back to Retrosheet calculation for historical seasons
- Calibrate both scales to produce equivalent ratings

### Option 2: Full Replacement
- Always use Retrosheet calculation for consistency
- Remove dependency on Baseball Reference defensive stats
- Requires one-time validation against known strong/weak arms

## Next Steps

1. **Validate against known data**: Compare 2005 Retrosheet ratings vs Baseball Reference
2. **Tune weights**: Adjust formula weights based on correlation with existing ratings
3. **Calculate league baselines**: Pre-compute position averages/stddev for all seasons
4. **Performance optimization**: Cache calculations, optimize dataframe operations
5. **Integration testing**: Run full season card generation with new method

## Sample Players for Validation

Test the formula against these known arm strengths from 2005:

**Strong Arms (Should get -4 to -6):**
- Jim Edmonds (CF) - Gold Glove, known cannon
- Ichiro Suzuki (RF) - Multiple award winner
- Carl Crawford (LF) - Defensive specialist

**Average Arms (Should get -1 to 0):**
- Most regular outfielders

**Weak Arms (Should get +1 to +2):**
- DHs playing OF occasionally
- Aging veterans with diminished tools

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**Created:** 2025-11-15
**Author:** Claude (Jarvis)
**Status:** Proposal / Awaiting Review