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YMori
YMori

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Adding Bayesian Ensemble + Monte Carlo to an NPB Prediction App

#baseball #python #bayesian #datascience

Introduction

I've been running a personal NPB (Japanese pro baseball) prediction app:

It used Marcel projections (3-year weighted average) and ML (XGBoost/LightGBM). Decent, but I wanted better accuracy. After adding Bayesian corrections, the predicted standings changed significantly.

Terms

Term Meaning
Marcel Predict next year from weighted average of past 3 years
Bayesian Combine prior knowledge with data. Gives uncertainty estimates
CI Credible interval — range where the true value falls with 80%/95% probability
OPS On-base + Slugging. Overall batting metric
ERA Earned Run Average. Runs allowed per 9 innings
MAE Mean Absolute Error. Average prediction miss. Lower = better

Problems with the Previous Approach

Problem 1: All Foreign Players Treated as "Average"

Marcel needs 3 years of NPB data. First-year foreign players have none, so all 24 of them were treated as league-average. Dalbec (Giants, .355 wOBA in MLB) and Hummel (BayStars, .240 wOBA) were calculated identically.

Problem 2: Skill Metrics Ignored

Marcel averages past results directly. Two players with OPS .800 might have very different K% and BB% profiles, which affects how stable their performance will be next year.

Problem 3: No Uncertainty

"Maki's OPS: .812" gives no sense of how much it might vary. The difference between .750-.870 and .790-.830 matters a lot for team projections.

What Changed with Bayesian Integration

Foreign Players: Average → Individual Predictions

Built a model to convert MLB/KBO stats to NPB projections. For example, a .350 wOBA MLB hitter maps to approximately .350 × 1.235 = .432 NPB-equivalent wOBA.

All 24 players' names and prior-league stats were individually web-verified (guessing English names from katakana is surprisingly error-prone).

Foreign hitter examples:

Player Team Prior wOBA NPB Pred OPS 80% CI
Sano Dragons .370 .760 .632–.889
Seymour Buffaloes .365 .735 .607–.863
Dalbec Giants .355 .725 .577–.884
Hummel BayStars .240 .694 .530–.849

Foreign pitcher examples:

Player Team Prior ERA NPB Pred ERA 80% CI
Quijada Swallows 3.26 2.76 1.28–4.24
Hjelle Buffaloes 3.90 3.34 1.05–5.59
Cox BayStars 8.86 3.36 1.82–4.85

Players with poor prior-league stats get pulled toward league average (Bayesian regression effect), but with wider CIs = lower confidence.

Japanese Players: K%/BB%/BABIP Corrections

Three models combined into a final prediction:

Model Weight Notes
Marcel 35% Strong baseline, especially for pitcher ERA
Bayesian correction 40% K%/BB%/BABIP/age adjustment on top of Marcel
ML 25% XGBoost/LightGBM

Did Accuracy Improve?

8-year backtest (2018–2025, predict each year and compare to actual):

Metric Marcel MAE Bayesian MAE Improvement prob.
Hitter wOBA 0.05023 0.04980 97.1%
Pitcher ERA 1.23008 1.22241 97.1%

Small improvement, but consistent — 97% probability of beating Marcel across 8 years.

Historical Marcel Accuracy for Context

Overall (8 years × 12 teams = 96 team-years):

Metric Value
Wins MAE 6.4 wins
Avg rank error 1.42 positions
Exact rank rate 18%
Within 1 rank 65%

Recent examples of Marcel misses:

Year Team Actual Predicted Miss
2025 Swallows (CL) 57W (6th) 72W (4th) +15
2024 SoftBank (PL) 91W (1st) 75W (2nd) -16
2024 Buffaloes (PL) 63W (5th) 78W (1st) +15

Patterns:

  • Overestimates bottom teams, underestimates top teams (regression to mean)
  • Can't predict collapses (2024 Buffaloes: defending champions → 5th place)
  • Foreign player impact not captured when all treated as average

How Did the 2026 Standings Change?

Central League — Tigers Runaway Disappears, 4-Team Deadlock

Team Marcel Bayesian Diff P(Pennant)
Tigers 80.1W (1st) 71.5W (1st) -8.6 26.0%
Giants 70.7W (3rd) 71.1W (2nd) +0.4 20.2%
Dragons 68.8W (5th) 71.0W (3rd) +2.2 21.2%
BayStars 71.3W (2nd) 70.7W (4th) -0.6 20.2%
Carp 70.4W (4th) 69.1W (5th) -1.3 12.3%
Swallows 64.3W (6th) 61.2W (6th) -3.1 0.1%

Tigers dropped from 80.1W to 71.5W (-8.6). Skill corrections pulled them down. Giants at 71.1W even after losing Okamoto to MLB. Four teams within 0.8 wins — Tigers 26%, Dragons 21%, Giants 20%, BayStars 20%. Swallows at 61.2W (78% last place) after Murakami's MLB departure.

Pacific League — Lions Surge

Team Marcel Bayesian Diff P(Pennant)
Hawks 80.5W (1st) 81.3W (1st) +0.8 47.9%
Fighters 76.8W (2nd) 79.1W (2nd) +2.3 27.2%
Buffaloes 73.8W (3rd) 77.5W (3rd) +3.7 17.6%
Lions 68.6W (4th) 74.9W (4th) +6.3 7.1%
Eagles 65.5W (5th) 66.7W (5th) +1.2 0.1%
Marines 67.1W (6th) 64.9W (6th) -2.2 0.1%

Lions +6.3 wins — foreign player projections offsetting Imai's MLB departure.

Summary

Problem Before After
Foreign players All league-average 24 individual projections from prior-league stats
Skill metrics Not used K%/BB%/BABIP corrections on Marcel
Uncertainty None (point estimates) 80%/95% credible intervals on every prediction
Team standings Single number 10,000 Monte Carlo sims with pennant probabilities
Accuracy Marcel MAE 0.050 0.0498 (97% probability of improvement)

The accuracy gain is modest, but "foreign players are no longer invisible," "MLB departures are reflected," and "every prediction comes with uncertainty" meaningfully changed the standings picture. The CL went from "Tigers runaway" to a four-team deadlock.

Caveat: Data Limitations

During this work, I discovered that players who moved to MLB (Murakami, Okamoto) were still included in the team simulation — the roster filter only existed in the Streamlit display layer, not in the CSV generation pipeline. Fixed and regenerated, but there may be other oversights I haven't caught.

This is a personal project without professional-grade QA. The data is best treated as automated model output, not authoritative predictions.

Data Sources

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