# A Hierarchical Bayesian Model of Pitch Framing

## TL;DR

This paper presents a Bayesian hierarchical model to quantify and evaluate catchers' pitch framing ability in baseball, accounting for umpire, pitch, and contextual factors, and translating effects into runs saved.

## Contribution

It introduces a novel Bayesian hierarchical approach to estimate and assess pitch framing effects, providing a more accurate and interpretable metric for evaluating catchers.

## Key findings

- Estimated umpire strike call probabilities adjusted for context
- Quantified catchers' framing effects in terms of runs saved
- Proposed a new metric for framing impact assessment

## Abstract

Since the advent of high-resolution pitch tracking data (PITCHf/x), many in the sabermetrics community have attempted to quantify a Major League Baseball catcher's ability to "frame" a pitch (i.e. increase the chance that a pitch is called as a strike). Especially in the last three years, there has been an explosion of interest in the "art of pitch framing" in the popular press as well as signs that teams are considering framing when making roster decisions. We introduce a Bayesian hierarchical model to estimate each umpire's probability of calling a strike, adjusting for pitch participants, pitch location, and contextual information like the count. Using our model, we can estimate each catcher's effect on an umpire's chance of calling a strike.We are then able to translate these estimated effects into average runs saved across a season. We also introduce a new metric, analogous to Jensen, Shirley, and Wyner's Spatially Aggregate Fielding Evaluation metric, which provides a more honest assessment of the impact of framing.