A Win-Expectancy Framework for Contextualizing Runs Batted In: Introducing ARBI and CRBI

TL;DR

This paper introduces ARBI and CRBI, two context-aware metrics for evaluating batting performance by incorporating Win Expectancy, providing a more accurate measure of a player's offensive contribution in baseball.

Contribution

The paper develops ARBI and CRBI, novel RBI metrics that account for game context and leverage, improving upon traditional RBI's limitations.

Findings

ARBI and CRBI better reflect true offensive value.

These metrics improve player evaluation and forecasting.

They offer a more nuanced understanding of run production impact.

Abstract

Runs Batted IN (RBI) records the number of runs a hitter directly drives in during their plate appearances and reflects a batter's ability to convert opportunities into scoring. Because producing runs determines game outcomes, RBI has long served as a central statistic in evaluating offensive performance. However, traditional RBI treats all batted-in runs equally and ignores th game context in which they occur, such as leverage, score state, and the actual impact of a run on a team's chance of winning. In this paper, we introduce two new context-aware metrics-Adjusted RBI (ARBI) and Contextual RBI (CRBI)-that address the fundamental limitations of RBI by incorporating Win Expectancy (WE). ARBI rescales each RBI according to the change in WE before and after the scoring event, assigning more value to runs that meaningfully shift the likelihood of winning and less to runs scored in low-leverage situations. We then extend this framework to CRBI, which further differentiates RBIs with the same WE change by accounting for the terminal WE at the end of the event. This refinement captures the idea that an RBI increasing WE from, for example, 0.45 to 0.65 has a larger competitive impact than one increasing WE from 0.05 to 0.25, even though both represent a 20% increase. Together, ARBI and CRBI provide calibrated, context-sensitive measures of offensive contribution that more accurately reflect the true value of run production. These metrics modernize the interpretation of RBI and have broad applications in player evaluation, forecasting, contract evaluation, and decision-making in baseball analytics.