Structure of Pitch-Pattern Motifs in Major League Baseball

TL;DR

The paper tackles how sequential pitch usage in MLB is organized beyond single-pitch metrics by analyzing motifs of lengths $L \in \{1,2,3,4,5\}$ from ~12.4 million Statcast pitches (2008–2025). It combines macro-level diversity measures ($H_L$, $D_L$) with micro-level motif-outcome analysis, and reveals language-like scaling (Zipf's law and Heaps' law) in pitch sequencing, yet finds no strong link between motif diversity and traditional performance indicators such as ERA or wins. The key contributions include demonstrating a non-random, grammar-like structure in pitch usage and identifying dominant motif groups ($G_0$, $G_1$, $G_3$) that underpin sequences, while also highlighting the limits of motif-based approaches for predicting outcomes without richer contextual information. The study provides a foundation for integrating pitch grammar-inspired features with context-rich models (e.g., velocity, location, count leverage, batter responses) to improve understanding and potential forecasting of pitching performance.

Abstract

Baseball consists of two teams alternating between batting and fielding while competing to score runs through sequential pitching events. Recent advances in tracking technology have enabled all Major League Baseball (MLB) clubs to record every pitch with high resolution, yet most quantitative studies have primarily emphasized single-pitch metrics, leaving the role of sequential structure less explored. Here, we examine pitch-pattern motifs of multiple lengths using approximately 12.4 million Statcast pitch recordings from the 2008-2025 MLB regular seasons at two complementary scales. At the macroscale, we quantify pitch-sequence diversity using the Shannon entropy and inverse Simpson index and examine their relationships with earned run average and win totals. At the microscale, we compare hit and out frequencies across pitch-pattern motifs. Rather than identifying outcome-determining sequences, we find that motif usage exhibits stable, non-random organization, as reflected in Zipf s and Heaps' laws, while showing limited association with conventional performance measures. While language-like scaling (Zipf's and Heaps' laws) clearly reveals an underlying 'grammar' of MLB pitch sequences, that grammar alone is insufficient to account for performance indicators such as ERA or wins. These results suggest that sequence-based analyses clarify the structural organization of pitch usage, while also delineating the limits of motif-based approaches for explaining performance without richer contextual information.

Figures (13)

• Figure 1: Pitch-speed distribution over the season. In the MLB dataset, pitch types are classified into 18 categories (see Table \ref{['table:pitch_type']}). We show the seasonal trends in pitch release speed, observed from the 2008 to 2025 seasons, excluding pitch types that account for less than 1% of all pitches: (a) fastball, (b) sinker, (c) cutter, (d) changeup, (e) split-finger, (f) forkball, (g) screwball, (h) curveball, and (i) knuckle curve. In each panel, we visualize the annual distribution of release speed using smooth density shapes for each year, and indicate the seasonal average with the black line. Overall, most pitch types exhibit a gradual increase in release speed across seasons. All statistics use the filtered dataset containing 12,322,641 pitches.
• Figure 2: Total number of pitches across seasons. The combined height of the blue and orange bars indicates the total number of pitches per season, while the orange bars alone represent the number of pitches thrown by qualified pitchers. Except for the shortened 2020 season due to the COVID-19, the total pitch count remains around 700,000 per year. Notably, despite the relatively stable overall pitch volume, the proportion contributed by qualified pitchers has steadily declined in recent years.
• Figure 3: The number of pitches across individual teams. The MLB consists of two leagues (the National League and the American League), each divided into three divisions (East, Central, and West) with five teams per division, for a total of 30 teams (see Table \ref{['table:mlb_team']}). The proportions of pitches thrown by pitchers who recorded at least 162 innings in a given season are shown: (a) the total number of pitches $N_{\rm pitch}$ and (b) the corresponding proportion. In both panels, the combined height of the blue and orange bars indicates the total number of pitches per team, while the orange bars represent the number of pitches thrown by qualified pitchers. From 2008 to 2025, teams averaged approximately 400,000 pitches per season, with about 30% contributed by pitchers meeting the qualification threshold.
• Figure 4: Schematic illustration of pitch-pattern motif construction. The pitch-pattern motif is constructed as follows: (i) the 20 Statcast pitch sequence are remapped into the six groups listed in Table \ref{['table:pitch_type']} to simplify the analysis; (ii) each pitch sequence is swept with a sliding window of length $L$ (panels (a--c) illustrate examples for $L=1,~2,~5$) to enumerate all contiguous $L$-pitch strings; and (iii) the resulting unique strings are treated as pattern motifs that form the basis of the information-theoretic analysis of pitch usage.
• Figure 5: Pattern motif information across motif length. (a-e) the Shannon entropy, $H_L$, of pattern usage for motif lengths $L=1\dots5$, (f–j) the inverse Simpson diversity index, $D_L$, for the same lengths. Panel pairs share a length: (a, f) $L=1$ ($G_i$ frequencies), (b, g) $L=2$, (c, h) $L=3$, (d, i) $L=4$, and (e, j) $L=5$. Each point indicates one of the 393 pitchers who meet the qualified threshold (at least 162 innings pitched), a requirement that keeps the sequences long enough for dependable diversity estimates. ERA sets the x-axis and win totals set the color scale; ERA and wins rise together, yet neither $H_L$ nor $D_L$ shows a clear link to those statistics.