Duckworth-Lewis Method

Description

This repository contains the implementation and analysis of the Duckworth-Lewis Method for ODI cricket matches using data from 1999 to 2011. The objective is to model the run production function using a mathematical formulation and optimize parameters for the model to predict runs scored based on overs remaining and wickets in hand.

The repository includes:

• Data cleaning and preprocessing.
• Implementation of the Duckworth-Lewis Method.
• Parameter optimization using custom loss functions.
• Visualization of the run production functions.

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Dataset

The dataset contains detailed information about ODI cricket matches played between 1999 and 2011, including:

• Match ID
• Innings details
• Wickets in hand
• Runs required to win
• Overs left to play

Cleaned Dataset

After preprocessing, the dataset focuses on:

1. First innings data only.
2. Key metrics:
   • Wickets in hand
   • Runs to score
   • Overs left

Data cleaning ensures:

• Proper date formatting.
• Removal of invalid or erroneous data points.
• Calculation of derived metrics such as Runs to score and Overs left.

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Model Overview

The Duckworth-Lewis run production model is defined as:

Where:

• ( Z(u, w) ): Predicted runs for ( u ) overs remaining and ( w ) wickets in hand.
• ( Z_0(w) ): Initial run-scoring potential with ( w ) wickets in hand.
• ( L(w) ): Rate of scoring potential decay.

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Implementation Details

Data Cleaning

• The clean_data function processes the raw dataset to produce a cleaned and usable format for analysis.
• Key steps:
  1. Properly format date fields.
  2. Filter for first-innings data.
  3. Remove errors and anomalies.
  4. Compute derived metrics.

Run Production Model

• The run_production_model function implements the mathematical formulation to predict runs based on ( u ), ( Z_0(w) ), and ( L(w) ).

Loss Function

• A custom loss function is used to optimize the model parameters:

Where ( y' ) is the predicted score, and ( y ) is the actual score.

Parameter Optimization

1. Preliminary Optimization:
   • Parameters ( Z_0(w) ) and ( L(w) ) are optimized for each wicket category.
2. Weighted Average Slope:
   • A common slope ( L ) is calculated as the weighted average of ( L(w) ).
3. Final Optimization:
   • Refitting ( Z_0(w) ) using the common slope ( L ).

Visualization

• Plots are generated to visualize the preliminary and final run production functions for all wicket categories.

Results

Preliminary Parameters

• ( Z_0(w) ): Initial scoring potential per wicket.
• ( L(w) ): Slope indicating scoring potential decay.
• Normalized loss: 6.18

Final Parameters

• ( Z_0(w) ): Refined scoring potential per wicket.
• Common slope ( L ): 10.63
• Normalized loss: 6.19

Plots

1. Preliminary Run Production Functions (Figure 1): Shows ( Z(u, w) ) based on preliminary ( Z_0(w) ) and ( L(w) ).

2. Final Run Production Functions (Figure 2): Updated ( Z(u, w) ) using refined parameters.

Dependencies

• Python 3.x
• Required libraries: numpy, pandas, matplotlib, scipy

Contact

If you have any questions or suggestions, please feel free to reach out to me at nvarjunmani07@gmail.com.