Background
The Marcel projection system is a simple but effective player performance forecasting method created by Tom Tango. It uses a weighted average of the last 3 seasons plus regression to the mean.
I've been using these default parameters in npb-prediction (blog post), but they were originally calibrated for MLB data:
Are these optimal for NPB (Nippon Professional Baseball)? I ran a comprehensive grid search to find out.
Study Design
Grid Search
Evaluation
Results: Hitters
OPS MAE — Top 5 (with 2020)
Previous (5/4/3, REG_PA=1200): .06227 — ranked 224th out of 720
Improvement: .06227 → .06142 = 1.37% MAE reduction
Optimal Weights Differ by Metric
AVG favors the oldest season (stability), while SLG minimizes it (recency). The optimal parameters align with each metric's characteristics.
Results: Pitchers
ERA MAE — Top 5 (with 2020)
Previous (5/4/3, REG_IP=600): .69105 — ranked 75th out of 600
Improvement over previous: 1.35% (with 2020) / 1.53% (without 2020)
Bootstrap Validation
300 bootstrap resamples to test if the improvement is statistically significant.
Hitter OPS (optimal 8/4/3 reg=2000 vs previous 5/4/3 reg=1200):
The lower bound of the 95% CI is above zero — statistically significant (p
Key Findings: NPB vs MLB
Hitters: More Recency Bias + Stronger Regression
The simultaneous increase in both w0 and REG_PA seems contradictory but is actually coherent:
NPB has higher roster turnover and larger year-to-year variance, making this "trust trends but don't trust extremes" approach optimal.
Pitchers: Last Year's Performance is Most Predictive
The most striking finding: w1 (1-year-ago) is larger than w0 (most recent). This contradicts the conventional assumption that the most recent season is always most important.
NPB pitchers show larger year-to-year ERA variance, and incorporating the prior year helps smooth out temporary fluctuations.
Recommended Parameters
These parameters will be applied to npb-prediction.
Reproducibility
Run via GitHub Actions:
gh workflow run "Optimize Marcel Weights" \
--repo yasumorishima/npb-marcel-weight-study \
-f memo="weight optimization"
All result CSVs are saved in results/.
Summary
Marcel is simple, but there's room for improvement when you calibrate parameters to your league.
Data sources: baseball-data.com / npb.jp
GitHub: https://github.com/yasumorishima/npb...l-weight-study
More...
The Marcel projection system is a simple but effective player performance forecasting method created by Tom Tango. It uses a weighted average of the last 3 seasons plus regression to the mean.
I've been using these default parameters in npb-prediction (blog post), but they were originally calibrated for MLB data:
| w0 / w1 / w2 | Weights for last 3 years | 5 / 4 / 3 |
| REG_PA | Regression strength (hitters) | 1200 |
| REG_IP | Regression strength (pitchers) | 600 |
Are these optimal for NPB (Nippon Professional Baseball)? I ran a comprehensive grid search to find out.
Study Design
Grid Search
| Hitters | w0(3-8) × w1(1-5) × w2(1-4) × REG_PA(6 values) | 720 |
| Pitchers | w0(3-8) × w1(1-5) × w2(1-4) × REG_IP(5 values) | 600 |
Evaluation
- Cross-validation: 2019–2025 (7 years)
- Two scenarios: with 2020 (COVID-shortened season) / without 2020
- Metric: MAE (Mean Absolute Error)
- Data: 3,780 hitter rows / 3,773 pitcher rows (2015–2025)
- Runtime: ~4.5 hours on GitHub Actions
Results: Hitters
OPS MAE — Top 5 (with 2020)
| 8/4/3 | 2000 | .06142 |
| 7/3/3 | 2000 | .06142 |
| 7/5/1 | 2000 | .06143 |
| 8/5/1 | 2000 | .06145 |
| 4/3/1 | 1200 | .06146 |
Previous (5/4/3, REG_PA=1200): .06227 — ranked 224th out of 720
Improvement: .06227 → .06142 = 1.37% MAE reduction
Optimal Weights Differ by Metric
| AVG | 3/2/4 | 1500 | .02160 |
| OBP | 7/3/3 | 1500 | .02449 |
| SLG | 4/3/1 | 1000 | .04200 |
| OPS | 8/4/3 | 2000 | .06142 |
AVG favors the oldest season (stability), while SLG minimizes it (recency). The optimal parameters align with each metric's characteristics.
Results: Pitchers
ERA MAE — Top 5 (with 2020)
| 4/5/2 | 800 | .68171 | .13065 |
| 3/4/1 | 800 | .68172 | .13103 |
| 3/4/1 | 600 | .68228 | .13068 |
| 3/4/2 | 800 | .68304 | .13099 |
| 3/3/2 | 800 | .68312 | .13118 |
Previous (5/4/3, REG_IP=600): .69105 — ranked 75th out of 600
Improvement over previous: 1.35% (with 2020) / 1.53% (without 2020)
Bootstrap Validation
300 bootstrap resamples to test if the improvement is statistically significant.
Hitter OPS (optimal 8/4/3 reg=2000 vs previous 5/4/3 reg=1200):
| Mean improvement | 0.00084 |
| 95% CI | [0.00022, 0.00147] |
| best > default | 99.7% |
| p-value | 0.003 |
The lower bound of the 95% CI is above zero — statistically significant (p
Key Findings: NPB vs MLB
Hitters: More Recency Bias + Stronger Regression
| Recent year weight | 5 | 8 |
| 2-years-ago weight | 3 | 1–3 |
| Regression (REG_PA) | 1200 | 2000 |
The simultaneous increase in both w0 and REG_PA seems contradictory but is actually coherent:
- w0=8: Emphasize recent trends in the weighted average
- REG_PA=2000: Pull extreme performances back to the mean more aggressively
NPB has higher roster turnover and larger year-to-year variance, making this "trust trends but don't trust extremes" approach optimal.
Pitchers: Last Year's Performance is Most Predictive
| Recent year weight | 5 | 3–4 |
| 1-year-ago weight | 4 | 4–5 |
| 2-years-ago weight | 3 | 1–2 |
| Regression (REG_IP) | 600 | 800 |
The most striking finding: w1 (1-year-ago) is larger than w0 (most recent). This contradicts the conventional assumption that the most recent season is always most important.
NPB pitchers show larger year-to-year ERA variance, and incorporating the prior year helps smooth out temporary fluctuations.
Recommended Parameters
| Hitters | 8/4/3 | REG_PA=2000 | Bootstrap p=0.003 |
| Pitchers | 4/5/2 | REG_IP=800 | Optimal for both ERA and WHIP across scenarios |
These parameters will be applied to npb-prediction.
Reproducibility
Run via GitHub Actions:
gh workflow run "Optimize Marcel Weights" \
--repo yasumorishima/npb-marcel-weight-study \
-f memo="weight optimization"
All result CSVs are saved in results/.
Summary
- The conventional Marcel weights (5/4/3) are not optimal for NPB
- Hitters: stronger recency (w0=8) + stronger regression (REG_PA=2000)
- Pitchers: the prior year is more predictive than the most recent year
- Bootstrap test confirms significance at p=0.003
Marcel is simple, but there's room for improvement when you calibrate parameters to your league.
Data sources: baseball-data.com / npb.jp
GitHub: https://github.com/yasumorishima/npb...l-weight-study
More...