1. Introduction

This document summarizes the methodology and findings related to predicting the Pickleball Ball Coefficient of Restitution (PBCOR) for pickleball paddles. Leveraging established correlations between key paddle characteristics and their proxies, a linear regression model has been developed to provide a simplified and effective prediction tool for Coretek Pickleball LLC.

2. Proxy Relationships

Based on previous experiments, strong correlations have been identified betwieen fundamental paddle properties and more commonly measurable proxies:

• The paddle's Coefficient of Restitution (COR) correlates over 90% with **Static Deflection**. For modeling purposes, **Absolute Deflection Force (ADF_lb)** under a standard USAP verification load is utilized as the direct proxy for static deflection.
• The paddle's Moment of Inertia (MOI) correlates over 90% with **Swingweight**. For modeling purposes, **MOI_oz_in^2** (Moment of Inertia in ounce-inches squared) is utilized as the direct proxy for Swingweight.

These high correlations enable the use of more accessible measurements to predict complex performance metrics.

3. PBCOR Linear Regression Model

A linear regression model has been established to predict PBCOR ($PBCOR_p$) using the identified proxies. The formula is as follows:

The specific constants derived from the linear regression analysis are:

4. Interpretation of USAP PBCOR Rule

Based on the coefficients in the linear regression model, the USAP's approach to PBCOR can be interpreted as a balanced metric where both paddle flexibility and moment of inertia play a role:

• Deflection (via $ADF_{lb}$): The negative coefficient for $ADF_{lb}$ ($-0.002152$) indicates that a *higher Absolute Deflection Force* (i.e., a stiffer paddle) results in a *lower predicted PBCOR*. Conversely, a paddle that requires less force to deflect (more flexible) will contribute to a higher PBCOR. This suggests that the USAP rule favors paddles with a certain degree of flexibility for ball rebound.
• Moment of Inertia (via $MOI_{oz\_in^2}$): The positive coefficient for $MOI_{oz\_in^2}$ ($0.000007351$) indicates that a *higher Moment of Inertia* (or swingweight) contributes *positively* to the predicted PBCOR. This aligns with the understanding that higher MOI can enhance a paddle's stability and power transfer upon impact, leading to a more consistent and potentially higher rebound.

Thus, the model suggests a nuanced interplay where both characteristics contribute to the overall PBCOR, with flexibility inversely related and MOI directly related to the final value.

5. Simplification of COR Measurement

Given the high correlation (over 90%) between COR and static deflection, the measurement of COR can be significantly simplified. Instead of direct, dynamic COR measurements (e.g., ball drop tests), the focus can shift to accurately measuring **Absolute Deflection Force (ADF_lb)**. A separate predictive relationship can then be established to estimate COR directly from ADF_lb, streamlining the testing process. This approach offers advantages in terms of reduced complexity, potential cost-effectiveness, increased measurement speed, and improved consistency compared to traditional COR testing methods.