Using the Viterbi Algorithm for Baseball Betting: A Case Study on Nippon Professional Baseball

Introduction

The field of sports betting has evolved significantly with the rise of data analytics and machine learning. Among the various algorithms leveraged for predictive modeling, the Viterbi algorithm—originally developed for signal decoding in digital communication—has emerged as a potent tool for analyzing sequential data. This article explores the workings of the Viterbi algorithm and demonstrates how it can be applied to sports betting, particularly in forecasting outcomes in Nippon Professional Baseball (NPB), Japan’s top-tier baseball league.

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What is the Viterbi Algorithm?

The Viterbi algorithm is a dynamic programming algorithm used to find the most probable sequence of hidden states—called the Viterbi path—that result in a sequence of observed events. It is commonly associated with Hidden Markov Models (HMMs), where a system is modeled as a Markov process with unobservable (hidden) states.

Key Concepts:

1. Hidden Markov Model (HMM):

   • A statistical model where the system being modeled is assumed to follow a Markov process with unobservable states.

   • Components:

     • States (S): Hidden states the model transitions between (e.g., team "form" or "momentum").

     • Observations (O): Visible outputs (e.g., match results).

     • Transition Probabilities (A): Probability of moving from one state to another.

     • Emission Probabilities (B): Probability of observing a certain output from a state.

     • Initial Probabilities (π): Probabilities of starting in a particular state.

2. Viterbi Algorithm Goal:

   • Given a sequence of observations, determine the most likely sequence of hidden states.

Algorithm Steps:

1. Initialization: Set up probabilities for the first observation using initial probabilities.

2. Recursion: For each time step, calculate the highest probability path to each state.

3. Termination: Find the path with the maximum overall probability.

4. Backtracking: Retrieve the sequence of hidden states.

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Relevance to Sports Betting

Sports games, like those in Nippon Professional Baseball, often exhibit patterns and momentum shifts that are not directly visible. For instance, a team may go on a winning streak not purely due to luck but because of strategic form or player dynamics—hidden factors that influence outcomes. The Viterbi algorithm helps uncover these latent patterns by analyzing observable data (e.g., win/loss sequences) and inferring the hidden states (e.g., “in-form” vs. “out-of-form”).

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Nippon Professional Baseball: A Primer

Nippon Professional Baseball (NPB) is the highest level of baseball in Japan, consisting of two leagues:

• Central League (CL)

• Pacific League (PL)

Each league contains 6 teams, and the season consists of 143 games per team, providing a rich dataset for modeling.

Unique Features of NPB Relevant to Modeling:

• Frequent rematches and tight travel schedules.

• Pitcher rotations and rest days significantly impact outcomes.

• High importance of “form” and team chemistry in shorter playoff series.

• Cultural tendencies toward tactical play and low-scoring games.

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Applying the Viterbi Algorithm to NPB Betting

Step 1: Define States and Observations

• Hidden States: "High Form", "Medium Form", "Low Form"

• Observations: Game outcomes (e.g., Win, Loss), runs scored, runs allowed

These categories simplify modeling while capturing team momentum.

Step 2: Build the Hidden Markov Model

Data Required:

• Historical game results (date, opponent, result)

• Pitcher performance metrics

• Team-level stats (batting average, ERA, etc.)

Estimating Probabilities:

• Transition Matrix (A): Derived from historical sequences—e.g., frequency of transitioning from "High Form" to "Low Form" after a loss.

• Emission Matrix (B): Probability of a team winning given a hidden state.

• Initial Probabilities (π): Based on pre-season power rankings or early season results.

Step 3: Sequence Prediction Using the Viterbi Algorithm

Using observed sequences (e.g., W, L, W, W, L), apply the Viterbi algorithm to infer the most likely form sequence of a team. This hidden state sequence allows bettors to estimate future performance.

Example:

Suppose we observe the following game results for the Hanshin Tigers:

W, W, L, L, W

Using the trained HMM:

• The Viterbi algorithm determines the sequence:

  High, High, Medium, Low, Medium
  

From here, we may infer that despite the last win, the team is still in "Medium" form and is less likely to win the next game against a top-tier opponent.

Step 4: Integrate into Betting Strategy

With the hidden states estimated:

• Compute win probabilities for upcoming games.

• Identify value bets where bookmaker odds underestimate a team in “High Form”.

• Avoid betting on teams in “Low Form” regardless of historical performance.

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Enhancing the Model with Advanced Features

Incorporate Pitching Matchups:

• Treat starting pitcher as a contextual variable modifying emission probabilities.

Temporal Weighting:

• More recent games can be given higher importance in calculating state transitions.

Home/Away Modifiers:

• Adjust emission probabilities for home field advantage, especially relevant in NPB where some stadiums significantly favor pitchers or batters.

Betting Odds Calibration:

• Compare model-generated win probabilities to bookmaker odds.

• Calculate expected value (EV) of bets:

  $$\text{EV} = (\text{Probability of Win}) \times (\text{Payout}) - (1 - \text{Probability of Win}) \times (\text{Stake})$$

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Case Study: Viterbi in Action

Let’s walk through a hypothetical use-case.

Scenario:

• Team: Tokyo Yakult Swallows

• Last 7 games: W, L, W, W, L, L, L

Observation:

• The Viterbi path suggests a form decline: High → Medium → Low

Next Opponent: Fukuoka SoftBank Hawks (top-tier team)

Model Estimate:

• Probability of Yakult winning: 34%

• Bookmaker odds: 2.70 (implied probability ≈ 37%)

EV Calculation:

$$\text{EV} = 0.34 \times 1.70 - 0.66 \times 1 = 0.578 - 0.66 = -0.082$$

Conclusion: Negative expected value → Avoid bet.

Now, suppose the odds were 3.10:

$$\text{EV} = 0.34 \times 2.10 - 0.66 = 0.714 - 0.66 = +0.054$$

Conclusion: Positive EV → Consider betting.

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Challenges and Considerations

1. Data Quality:

Accurate game logs, player data, and timely updates are critical.

2. Overfitting:

Using too many states or features can lead to models that fit historical data well but perform poorly in prediction.

3. Market Efficiency:

Betting markets may already price in some of the “form” dynamics, reducing edge.

4. Dynamic Changes:

Team strategies, injuries, or roster changes may alter transition/emission dynamics, necessitating frequent model updates.

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Conclusion

The Viterbi algorithm offers a robust framework for uncovering hidden dynamics in sports outcomes. When applied to Nippon Professional Baseball Predictions, it can reveal valuable insights into team form and help bettors make informed decisions. While no model guarantees profits, using HMMs and the Viterbi algorithm provides a disciplined, data-driven approach that enhances the long-term viability of sports betting strategies.

As the sports betting industry grows and becomes increasingly competitive, those who can model and interpret hidden patterns—like those inferred through the Viterbi algorithm—will have a significant edge.