Formula Weight Comparison - Before vs After

The Problem

Original Formula over-weighted volume (total assists) and under-weighted rate stats:

# OLD - Volume Dominant
raw_score = (
    (assist_rate * 30) +           # Weak: 0.86 pts for elite 2.87% rate
    (throwout_rate * 5) +          # Moderate
    (home_throws * 2) +            # DOMINANT: 16 pts for 8 home throws
    (batter_extra_outs * 1.5) +    # Moderate
    (total_assists * 0.5)          # Strong: 4 pts for 8 assists
)
# Result: Volume (20 pts) overwhelmed rate (0.86 pts) by 23x

Old Formula Results

Rank	Player	Score	Assist Rate	Home Throws	Total Assists
1	Lieberthal	25.86	2.87% ❌	8 ✓	8 ✓
2	Matthews	23.30	2.66% ❌	7 ✓	7 ✓
3	gathj001	21.00	6.67% ✓	4	6
4	Taguchi	20.88	8.64% ✓✓	3	7

Problem: So Taguchi has 3x better assist rate but ranks last because of low volume!

The Solution

New Formula prioritizes rate stats while giving credit for quality:

# NEW - Rate Dominant (Simplified)
raw_score = (
    (assist_rate * 300) +          # DOMINANT: 25.9 pts for elite 8.64% rate
    (home_throws * 1.0) +          # Quality bonus: 8 pts for 8 home throws
    (batter_extra_outs * 1.0) +    # Quality bonus
    (total_assists * 0.1)          # Minimal volume: 0.8 pts for 8 assists
)
# Result: Rate (25.9 pts) dominates, quality/volume are tiebreakers
# Note: Removed throwout_rate - redundant since assists = outs

New Formula Results

Rank	Player	Score	Assist Rate	Home Throws	Total Assists	Why?
1	Taguchi	26.52	8.64% ✓✓	3	7	Elite rate rewarded!
2	gathj001	24.61	6.67% ✓	4	6	Good rate
3	Lieberthal	21.11	2.87%	8 ✓	8	Volume can't overcome low rate
4	Matthews	19.69	2.66%	7 ✓	7	Lowest rate = lowest score

Solution: Players ranked by assist rate quality first, volume second!

Weight Changes Breakdown

Component	Old Weight	New Weight	Change	Impact
Assist Rate	30	300	+900%	Dominant driver
Throwout Rate	5	REMOVED	-100%	Redundant (assists = outs)
Home Throws	2.0	1.0	-50%	Minor quality indicator
Batter Extra Outs	1.5	1.0	-33%	Minor quality indicator
Volume (Total Assists)	0.5	0.1	-80%	Minimal bonus only

Component Contribution Examples

Elite Rate Player (8.64% rate, 3 home throws, 7 assists)

Example High Assist Rate Player

Component	Old Formula	New Formula (Simplified)
Assist Rate (8.64%)	2.59 pts	25.92 pts ✓
Throwout Rate (86%)	4.29 pts	REMOVED
Home Throws (3)	6.0 pts	3.0 pts
Batter Extra (3)	4.5 pts	3.0 pts
Volume (7)	3.5 pts	0.7 pts
TOTAL	20.88	32.62 ✓

High Volume Player (2.87% rate, 8 home throws, 8 assists)

Example Volume-Based Player

Component	Old Formula	New Formula (Simplified)
Assist Rate (2.87%)	0.86 pts	8.61 pts
Throwout Rate (100%)	5.0 pts	REMOVED
Home Throws (8)	16.0 pts ❌	8.0 pts ✓
Batter Extra (0)	0.0 pts	0.0 pts
Volume (8)	4.0 pts	0.8 pts ✓
TOTAL	25.86 ❌	17.41 ✓

Key Difference:

Old: Volume (20 pts) >> Rate (0.86 pts) - Wrong priority!
New: Rate (8.61 pts) dominates, quality/volume are minor bonuses
Removed: Throwout rate (redundant with assists)

Design Philosophy

Simplified Rate-First Approach

Assist Rate (300x) - How often do they throw out runners per opportunity?
- Elite (8%+): 24+ points
- Average (3%): ~9 points
- Poor (1%): ~3 points
Quality Indicators (1.0x each) - What types of plays do they make?
- Home throws: 1 point each (minor bonus)
- Batter extra outs: 1 point each (minor bonus)
Volume Bonus (0.1x) - Minimal credit for total assists
- Only used as tiebreaker
- 10 assists = 1 point
Throwout Rate - REMOVED (redundant)
- Assists are already outs by definition
- No need to measure "efficiency" of assists

Expected Behavior

High rate, low volume (platoon player with cannon arm): Ranks high ✓
High rate, high volume (everyday elite arm): Ranks highest ✓
Low rate, high volume (lucky positioning): Ranks lower ✓
Low rate, low volume (weak arm): Ranks lowest ✓

Validation Questions

Run python test_retrosheet_arms.py and check:

✓ Are players with 8%+ assist rates in the top tier?
✓ Are players with <2% assist rates in the bottom tier?
✓ Do home throws provide meaningful but not dominant bonuses?
✓ Is the distribution still normal (-6 to +5)?
✓ Do known strong arms (Ichiro, Guerrero) rank appropriately?

Updated: 2025-11-15 Status: Rate-dominant formula implemented Next Step: Run validation script to confirm distribution

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