License: Motion capture data from Driveline OpenBiomechanics Project under CC BY-NC-SA 4.0 (non-commercial, share-alike).
Citation: Wasserberger KW, Brady AC, Besky DM, Jones BR, Boddy KJ. The OpenBiomechanics Project: The open source initiative for anonymized, elite-level athletic motion capture data. (2022).
License: https://creativecommons.org/licenses/by-nc-sa/4.0/
Derivative works (graphs, GIFs) in this article follow the same license. Commercial use by professional sports organization employees is restricted.
The Finding
Pitchers with nearly identical arm speed (24–26 m/s) can differ by up to 13 mph in pitch velocity.
Arm strength alone doesn't explain this gap. So what does?
I analyzed 61 pro pitchers using Driveline OpenBiomechanics C3D motion capture data and found 5 body mechanics factors that explain the difference.
→ GitHub: https://github.com/yasumorishima/baseball-cv
The Data
Driveline OpenBiomechanics Project (OBP)
- 61 pitchers, C3D motion capture files
- 45 markers (shoulder, elbow, wrist, pelvis, knee, heel, etc.)
- 360 Hz sampling rate
- Pitch speed range: 71.3–93.1 mph
I used ezc3d to read the C3D files (I contributed a bug fix to this library, which is what started this project).
Defining "Body Efficiency"
Arm speed and pitch velocity are strongly correlated (r=0.67). That's expected.
The key insight: compute the residual after regressing pitch speed on arm speed:
lm = LinearRegression().fit(df[['peak_wrist_linear_speed']], df['pitch_speed_mph'])
df['body_efficiency'] = df['pitch_speed_mph'] - lm.predict(df[['peak_wrist_linear_speed']])
Positive = "throws faster than arm speed predicts" → efficient body use
Negative = "arm is fast but doesn't translate" → arm-reliant
I split pitchers into quintiles Q1 (least efficient) through Q5 (most efficient).
Graph 1: The Big Picture
Three panels:
Left (scatter): Arm speed (x) vs pitch velocity (y). Notice vertical spread — same arm speed, very different outcomes.
Center (R² steps): Each bar shows how much predictive power is added by each factor. Taller = more explained.
Right (Q1 vs Q5): Each bar shows how far each group deviates from the overall average (positive = favorable direction for pitch speed, negative = unfavorable).
The 5 Factors
| Factor | R² | Physical meaning |
|---|---|---|
| Arm speed + Height | 0.473 | Baseline |
| + Stride (translation) | 0.477 | How far the lead foot travels |
| + Leg lift (elastic) | 0.522 | Knee height before stride |
| + Arm chain (whip) | 0.562 | Whether the body drives the elbow |
| + Knee smoothness | 0.648 | Smoothness of lead leg trajectory |
R²=0.648 means these 5 factors explain ~65% of pitch speed variance. Arm speed alone explained ~47% — an 18-point improvement.
What each factor means
Stride: How far the lead foot advances before landing. Longer stride = more translational energy transferred to the arm.
Leg lift: Knee height during windup. Higher knee = more elastic energy stored in the hip, released during the stride.
Arm chain (whip): Ratio of elbow speed to wrist speed. Lower = body is pulling the elbow (body-driven). Higher = arm working independently.
Knee smoothness: How smoothly the lead knee moves through its 3D trajectory. Measured by the irregularity of the knee's path — lower = smoother, more controlled movement.
Why Does Knee Smoothness Matter?
This is the most counterintuitive finding:
- Looking at all pitchers: r=+0.12 (faster pitchers move their whole body more intensely, so knee irregularity tends to be higher too)
- After controlling for arm speed: r=−0.45*** (among pitchers with the same arm speed, smoother knees = faster pitches)
The effect only appears after removing arm speed's influence — meaning the raw data masks the true relationship. Once you account for arm speed, smoother knees consistently predict faster pitches.
Proposed mechanism: smooth knee → more efficient pelvis rotation → higher pelvis/arm speed ratio (+17%) → the body "whips" the arm through the kinematic chain
Graph 2: Q1 vs Q5 Head-to-Head
| Metric | Q1 (inefficient) | Q5 (efficient) |
|---|---|---|
| Arm speed | 24.73 m/s | 24.69 m/s |
| Pitch speed | 79.1 mph | 89.3 mph |
| Gap | — | +10.2 mph |
Arm speed difference: 0.04 m/s. Pitch speed difference: 10.2 mph (~16 km/h).
Skeleton GIF: Same Arm Speed, 10 mph Apart
Left (Q1): Arm 26.56 m/s → 80.8 mph (stride 0.30m)
Right (Q5): Arm 24.96 m/s → 91.8 mph (stride 0.89m)
Red = lead leg. Orange star = foot landing position. Both are synchronized at foot strike.
The difference in stride length is immediately visible. Q5 drives the entire body forward while Q1 stays more upright.
Root Cause: Why Is Q1's Stride Short?
I traced the cause to ankle braking — how much the lead foot decelerates on landing.
- Q1: ankle braking ≈ 0.06 m/s² (nearly none)
- Q5: ankle braking ≈ 3.58 m/s² (strong brake)
ankle_braking → stride correlation: r=+0.55*
Lead knee lift also differed:
- Q1: max knee flexion 85.4° (shallow lift)
- Q5: max knee flexion 76.0° (deep lift)
The causal chain:
Shallow knee lift → short stride
Weak ankle brake → short stride
↓
Less body translation
↓
Weaker kinematic chain → lower pitch speed
Summary
- Among pitchers with the same arm speed, pitch velocity can vary by 13 mph
- A "body efficiency" residual metric exposes this gap
- 5 body mechanics factors explain 64.8% of pitch speed variance (R²=0.648)
- Knee smoothness contributes most (+0.087 R²); its effect only becomes visible after controlling for arm speed
- Root cause: ankle braking and knee lift → stride → kinematic chain
The data suggests that "how the body is sequenced" matters as much as raw arm speed — consistent with established biomechanics literature on the kinematic chain.
→ GitHub: https://github.com/yasumorishima/baseball-cv
Data: Driveline OpenBiomechanics Project (CC BY-NC-SA 4.0, non-commercial)
ezc3d: pyomeca/ezc3d (MIT License)
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