Arsenal Synergy

How pitches play together beyond their individual grades

Contents
1 The Mix Bonus 2 Velocity Separation 3 Tunnel Contrast 4 Why Linear, Not XGBoost? 5 What Synergy Explains 6 Positive vs Negative Synergy
Arsenal Synergy v2.1 at a Glance
RidgeCV
Model type
26
Arsenal features
0.147
Test R²
~500
Samples/year

Synergy operates at the pitcher-season level, not per-pitch. It measures the residual CSW (called strikes + swinging strikes) after removing what individual pitch grades already predict. The leftover signal is the mix effect — how pitches interact.

1. The Mix Bonus

Two pitchers can have identical individual pitch grades yet produce very different results. The reason: their pitches either complement or duplicate each other. Arsenal Synergy captures this interaction effect.

Pitcher A — Complementary Arsenal
Pitch Movement Profile Horizontal Break (inches) vs Induced Vertical Break (inches) 0" HB +16" HB -16" HB +20" IVB 0" -20" IVB FF 95 mph SL 82 mph 14" HB gap 13 mph gap Synergy: +3 Velocity gap 13 mph HB separation 14 in VB separation 10 in Tunnel similarity High Pitches look the same out of the hand, then diverge dramatically. Hitters can't adjust.
Pitcher B — Redundant Arsenal
Pitch Movement Profile Horizontal Break (inches) vs Induced Vertical Break (inches) 0" HB +16" HB -16" HB +20" IVB 0" -20" IVB FF 92 mph FC 88 mph 4" HB gap 4 mph gap Synergy: -2 Velocity gap 4 mph HB separation 4 in VB separation 3 in Tunnel similarity Moderate Pitches look similar AND end up in similar spots. Hitters see one "pitch" in two slight variations. Easy to sit on.
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Analogy: Imagine a band where every instrument plays in the same register. Technically competent, but no contrast, no dynamics. A great band has bass, midrange, and treble — instruments that are individually good and occupy different sonic space. Synergy measures the arrangement, not the musicians.

2. Velocity Separation

The speed gap between a pitcher's fastest and slowest offerings is one of the strongest synergy signals. Large velocity spreads force hitters to cover a wider timing window, making each pitch harder to square up.

Velocity Spectrum
70 76 82 88 94 100 CU 76 CH 81 SL 86 FF 97 21 mph Four distinct speed clusters. Hitters must cover huge timing window.
70 76 82 88 94 100 SI 91 FC 89 FF 93 4 mph Everything in 89-93 band. Batter grooves one timing, hits all three.

3. Tunnel Contrast

Tunneling is the art of making different pitches look identical to the batter for as long as possible. Two pitches that share the same tunnel window — the path from release to about 20 feet from the plate — then diverge to different locations, create maximum deception.

The Tunnel Window
REL Release point TUNNEL ZONE Both pitches look identical to the batter here DECISION POINT ~170ms to react FF High zone SL Low/away 16" divergence STRIKE ZONE Identical trajectory (~250ms) Diverging (~170ms to react)

The longer two pitches share a tunnel, the less time the batter has to recognize the difference. Great synergy arsenals maximize the shared distance while maximizing the final separation. It's not enough to tunnel well — the pitches must also end up in very different spots.

Feature Categories

The 26 arsenal-level features capture four dimensions of pitch mix quality. Hover over each tag to see what it measures.

Mix Balance
pitch_type_countNumber of distinct pitch types thrown usage_entropyHow evenly pitches are distributed (high = balanced) max_usage_shareUsage % of the most thrown pitch secondary_usage_sumCombined usage of non-primary pitches
Velocity Separation
velo_rangeGap between fastest and slowest pitch (mph) velo_spread_stdStandard deviation of pitch velocities fb_off_velo_gapSpeed difference between fastball and offspeed velo_cluster_countNumber of distinct speed clusters
Movement Spread
hb_rangeHorizontal break range across arsenal ivb_rangeInduced vertical break range across arsenal movement_hull_areaArea of the convex hull in movement space max_movement_distMaximum pairwise movement distance between any two pitches avg_movement_distAverage pairwise movement distance
Tunnel Contrast
tunnel_similarityHow similar pitches look in the first 20 feet of flight late_divergenceHow much pitches separate in the final 20 feet tunnel_ratioRatio of shared tunnel to final divergence (higher = more deceptive) release_consistencyHow tightly release points cluster across pitch types

4. Why Linear, Not XGBoost?

Stuff+, Location+, and Pitching+ all use XGBoost — a powerful tree-based model that thrives on millions of rows. So why does Arsenal Synergy use a simple RidgeCV (regularized linear regression)?

The answer is data. Synergy operates at the pitcher-season level. Each row is one pitcher's entire season, not one pitch. That means ~500 samples per year, not ~5 million.

The Bias-Variance Tradeoff
Model Complexity Simple Complex Prediction Error Bias Variance Total Error RidgeCV Sweet spot at ~500 rows XGBoost Overfits at ~500 rows With limited data, complexity hurts. Simple model + regularization = best out-of-sample predictions.
RidgeCV (What We Use)

Linear model with built-in regularization

  • Cross-validates to pick regularization strength
  • Each feature gets one coefficient — fully interpretable
  • Can't overfit with only 26 features and regularization
  • Test R² = 0.147 — stable and reliable
XGBoost (Tested, Rejected)

Powerful but data-hungry

  • Needs thousands of rows to learn stable splits
  • With 500 rows, trees memorize individual pitchers
  • Train R² looks great (~0.4+), test R² collapses
  • Predictions don't generalize year-over-year
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The math is simple: With 5 million pitches, XGBoost can find subtle nonlinear interactions in the data. With 500 pitcher-seasons, even moderate complexity leads to overfitting. RidgeCV's regularization shrinks unimportant coefficients toward zero, keeping only the features that consistently matter across years.

5. What Synergy Explains

Synergy captures the gap between how a pitcher should perform (based on individual pitch grades) and how they actually perform. Here are the two archetypes.

The Overperformer
Stuff+ 94 Loc+ 97 Pitch+ 96 Individual grades: mediocre Synergy: +3 Actual results: top 20% Great mix makes mediocre stuff play up

This pitcher throws a diverse arsenal with excellent tunneling. Each individual pitch is average, but hitters struggle because they can never lock into one timing or movement pattern. The whole is greater than the sum of its parts.

The Underperformer
Stuff+ 112 Loc+ 108 Pitch+ 110 Individual grades: elite Synergy: -3 Actual results: just above avg Redundant mix lets hitters adjust

Each pitch individually has nasty stuff. But the cutter and fastball look the same, and the slider and sweeper overlap in movement. Hitters face fewer "different looks" than the pitch count suggests. Individually great, collectively redundant.

What the R² = 0.147 Means

An R² of 0.147 means synergy explains about 15% of the CSW variance that individual grades don't. That's a modest but meaningful signal — enough to move a pitcher 2-3 points on a 100-scale. It won't turn a bad pitcher good, but it separates otherwise similar pitchers.

14.7%
of residual CSW variance explained by arsenal composition alone

6. Positive vs Negative Synergy

Synergy is reported on a centered scale where 0 means no mix effect. Positive values mean the arsenal plays up beyond what the individual grades predict. Negative values mean the arsenal plays down despite individual quality.

The Synergy Scale
-5 Severe penalty -3 Redundant mix 0 No mix effect +3 Great mix bonus +5 Elite synergy B FF/FC overlap Arsenal plays down -2 synergy points C A FF/SL contrast Arsenal plays up +3 synergy points
NEGATIVE SYNERGY
Arsenal plays down
Pitches overlap in velocity, movement, or both. Hitters can sit on one speed/shape and cover multiple offerings. Even great individual stuff can't overcome a predictable mix.
POSITIVE SYNERGY
Arsenal plays up
Pitches create diverse looks: wide velocity spread, different movement profiles, good tunneling. Hitters can never settle into a plan. Average stuff becomes effective through deception.
Bottom Line

Arsenal Synergy answers a question that individual pitch grades can't: does this pitcher's mix make sense?

It won't add 10 points to anyone's grade. But when two pitchers have similar Stuff+ and Location+, synergy is often what separates the one who gets results from the one who puzzles scouts. It's the arrangement of the orchestra, not the skill of the musicians.

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