PROPRIETARY & CONFIDENTIAL

SmartSwing AI Technical Documentation

Complete reference for the SmartSwing AI biomechanics analysis engine — covering every formula, correlation, analysis workflow, scoring model, grip inference algorithm, and architectural decision that powers the platform. This document serves as the "central brain" backup of the proprietary analyzer.

Last updated: April 8, 2026 | Engine version: 2.0 | Author: SmartSwing AI Engineering

Technical Architecture

SmartSwing AI is a multi-page static web application with serverless backend functions, designed for real-time biomechanical analysis in the browser.

Stack Components

Layer	Technology	Purpose
Frontend	HTML + CSS + Vanilla JS	Zero-framework, maximum compatibility
Pose Detection	MoveNet / MediaPipe (17-keypoint)	Real-time body landmark tracking
Biomechanics	advanced-biomechanics-engine.js	Joint angles, kinematics, scoring
Grip Analysis	grip-analysis-engine.js	Grip inference from body kinematics
State	app-data.js (SmartSwingStore)	Client-side store + Supabase sync
Hosting	Vercel	Static hosting + serverless functions
Database	Supabase (PostgreSQL)	Auth, profiles, assessments, reports
Payments	Stripe	Hosted checkout + webhook sync
AI Coach	Claude API (Anthropic)	Personalized coaching narratives

Data Flow Pipeline

Analysis Pipeline (End-to-End)

Video Input (upload / YouTube URL / webcam)
    |
    v
Pose Detection (MoveNet Thunder / MediaPipe)
    |  Outputs: 17 keypoints × N frames
    |  Each keypoint: { x, y, score }
    v
Frame Processing (per-frame metrics)
    |  Joint angles, velocities, rotations
    |  Head stability, balance, COM tracking
    v
Contact Frame Detection (peak wrist speed)
    v
Grip Analysis Engine (5 indicators → Gaussian classifier)
    |  Output: detected_grip, confidence, distribution
    v
Sequence Analysis (kinematic chain, power, efficiency)
    v
Session Aggregation (means, stdDevs, ranges)
    v
Scoring Pipeline (component → weighted → overall)
    |  Level-adjusted benchmarks, grade, percentile
    v
AI Coach Narrative (Claude API call)
    v
Report Generation (HTML template assembly)
    v
Persistence (localStorage + Supabase cloud sync)

Keypoint Model (MoveNet 17-Point)

SmartSwing uses the MoveNet Thunder model (or MediaPipe equivalent) that produces 17 body keypoints per frame. Each keypoint provides (x, y, confidence_score).

Index	Keypoint	Body Part	Usage
0	NOSE	Head	Head stability tracking
1	LEFT_EYE	Head	Head orientation
2	RIGHT_EYE	Head	Head orientation
3	LEFT_EAR	Head	Head rotation proxy
4	RIGHT_EAR	Head	Head rotation proxy
5	LEFT_SHOULDER	Upper body	Shoulder rotation, joint angles
6	RIGHT_SHOULDER	Upper body	Shoulder rotation, joint angles
7	LEFT_ELBOW	Arm	Elbow angle, kinematic chain
8	RIGHT_ELBOW	Arm	Elbow angle, kinematic chain
9	LEFT_WRIST	Arm	Racquet speed proxy, grip analysis
10	RIGHT_WRIST	Arm	Racquet speed proxy, grip analysis
11	LEFT_HIP	Core	Hip rotation, COM, balance
12	RIGHT_HIP	Core	Hip rotation, COM, balance
13	LEFT_KNEE	Lower body	Knee bend, power generation
14	RIGHT_KNEE	Lower body	Knee bend, power generation
15	LEFT_ANKLE	Lower body	Footwork, base width, balance
16	RIGHT_ANKLE	Lower body	Footwork, base width, balance

Dominant side is auto-detected by comparing confidence score sums for left vs right arm keypoints. Minimum keypoint confidence threshold: 0.3.

Calibration (Pixel-to-Metric Conversion)

Auto-Calibration (Player Height)

Calibration Formula

heightPixels = |shoulder.y - ankle.y|
estimatedTorsoHeight = 0.9 m
pixelsToMeters = 0.9 / heightPixels

Manual Calibration (Court Lines)

Manual Override

pixelsToMeters = realWorldDistance / pixelDistance

Core Geometry Formulas

Euclidean Distance

distance(A, B)

d = sqrt( (B.x - A.x)^2 + (B.y - A.y)^2 )

3-Point Angle

angle3Points(A, B, C) — angle at vertex B

u = B → A = (A.x - B.x, A.y - B.y)
v = B → C = (C.x - B.x, C.y - B.y)
cos(angle) = dot(u, v) / (|u| × |v|)
angle = acos( clamp(cos, -1, 1) ) × (180 / pi)

Signed Angle (Rotation)

signedAngle(u, v)

cross = u.x × v.y - u.y × v.x
angle = atan2(cross, dot(u, v)) × (180 / pi)

Velocity Calculation

Keypoint Velocity (m/s → mph)

distPixels = distance(wrist[t-1], wrist[t])
distMeters = distPixels × pixelsToMeters
speedMS = distMeters / timeDelta // timeDelta default = 1/30 s
speedMPH = speedMS × 2.237
speedKPH = speedMS × 3.6

Joint Angle Calculations

All joint angles use the 3-point angle formula with the joint as vertex B:

Joint	Point A	Vertex B	Point C	Optimal Range
Elbow	Shoulder	Elbow	Wrist	140-170 deg
Shoulder	Hip	Shoulder	Elbow	80-120 deg
Hip	Shoulder	Hip	Knee	150-175 deg
Knee	Hip	Knee	Ankle	145-165 deg

Angular velocity is calculated between consecutive frames:

Angular Velocity

angularVelocity = (angle[t] - angle[t-1]) / timeDelta // deg/s

Rotations & X-Factor

Hip Rotation

Hip line angle vs horizontal

hipLine = leftHip → rightHip
hipRotation = signedAngle(hipLine, horizontalAxis)

Shoulder Rotation

Shoulder line angle vs horizontal

shoulderLine = leftShoulder → rightShoulder
shoulderRotation = signedAngle(shoulderLine, horizontalAxis)

X-Factor (Hip-Shoulder Separation)

Key Power Indicator

separation = |shoulderRotation - hipRotation|
xFactor = abs( wrapAngle(separation) )
Optimal range: 30-50 degrees

The X-Factor measures the rotational separation between hips and shoulders during the swing. Greater separation stores elastic energy in the trunk musculature, enabling more powerful rotation through the kinetic chain. Professional players typically achieve 40-55 degrees of X-Factor at peak loading.

Trunk Tilt

Lateral Body Tilt

hipMid = midpoint(leftHip, rightHip)
shoulderMid = midpoint(leftShoulder, rightShoulder)
verticalRef = (hipMid.x, hipMid.y - 100)
trunkTilt = angle3Points(verticalRef, hipMid, shoulderMid)

Stability & Balance

Center of Mass (COM)

Weighted COM Approximation

shoulderMid = midpoint(leftShoulder, rightShoulder)
hipMid = midpoint(leftHip, rightHip)
COM.x = 0.4 × shoulderMid.x + 0.6 × hipMid.x
COM.y = 0.4 × shoulderMid.y + 0.6 × hipMid.y
// Hips weighted 60%, shoulders 40%

Head Stability (Rolling Window = 10 frames)

Stability Score

variance = sum(pixelOffset^2) / historyLength
stability = max(0, 100 - variance)
displacement = sqrt(variance) × pixelsToMeters × 100 // in cm

Balance Score

COM vs Base of Support

baseWidth = |rightAnkle.x - leftAnkle.x|
anklesMidX = (rightAnkle.x + leftAnkle.x) / 2
comOffset = |COM.x - anklesMidX|
balanceRatio = 1 - (comOffset / (baseWidth / 2))
balanceScore = max(0, min(100, balanceRatio × 100))

Kinematic Chain Sequencing

The kinetic chain principle states that efficient power transfer requires proximal-to-distal activation: hips first, then shoulders, then elbow, then wrist. SmartSwing detects peak velocity timing for each segment.

Peak Velocity Detection

For each segment (hip, shoulder, elbow, wrist):
  peakIdx = argmax(velocity[segment]) across all frames

Delays:
  hipToShoulder = peakShoulder - peakHip
  shoulderToElbow = peakElbow - peakShoulder
  elbowToWrist = peakWrist - peakElbow

Proper sequence: ALL delays > 0
efficiency = 100 if proper, else 50

Contact Point Quality

Contact Position (Dominant Hand)

inFront = wrist.x > hip.x // for right-handed; flipped for left
distance = |wrist.x - hip.x| × pixelsToMeters × 100 // cm

Optimal range: 25-45 cm in front
quality = 100 if optimal
quality = max(0, 100 - |distance - 35| × 2) if outside

Power Generation Score

Composite score from three weighted factors:

Factor 1: X-Factor Score

Optimal: 30-50 degrees
xScore = 100 if in range
xScore = max(0, 100 - |xFactor - 40| × 2) if outside

Factor 2: Knee Angle Score

Optimal: 145-165 degrees
kneeScore = 100 if in range
kneeScore = max(0, 100 - |kneeAngle - 155|) if outside

Factor 3: Racquet Speed Score

Baseline: 85 mph
speedScore = min(100, (maxRacquetSpeed / 85) × 100)

Final Power Score

powerScore = average(xScore, kneeScore, speedScore)

Efficiency Score

Deduction-Based Scoring

baseScore = 100

Deductions:
  Poor kinematic sequence: -20
  Low balance (< 70): -(70 - balance) × 0.5
  High head displacement (> 5 cm): -displacement

efficiencyScore = max(0, min(100, baseScore - deductions))

Overall Score Calculation

Component Weighting (Default)

Raw Score Formula

rawScore = biomechanics × 0.62
         + timing × 0.14
         + footwork × 0.08
         + positioning × 0.08
         + readiness × 0.08

Level Adjustment

Floor + Boost

Minimum floors: Beginner = 30, Intermediate = 40, Advanced = 50
Profile boost: Beginner = 1.0x, Intermediate = 1.05x, Advanced = 1.10x

adjustedScore = max(floor, rawScore × boost)
progressBonus = min(5, improvement_delta) // up to +5 pts
overallScore = min(100, adjustedScore + progressBonus)

Component Scores

Component	Weight	Inputs
Biomechanics	62%	Racquet speed, acceleration, wrist lag, knee bend, shoulder/hip rotation
Timing	14%	Contact timing consistency vs optimal swing phase
Footwork	8%	Stride length, base width, movement smoothness
Positioning	8%	Distance from baseline, angle to ball, recovery position
Readiness	8%	Preparation time, racket position pre-contact, stance

Each component uses scoreMetricAgainstBenchmark() with three deviation windows:

Soft (within 20%): Score 80-100
Good (within 15%): Score 60-80
Fair (within 10%): Score 40-60

Shot-Type Scoring Models

Each shot type uses custom component weights (via SHOT_SCORING_MODELS):

Shot Type	Biomechanics	Timing	Positioning	Footwork	Readiness
Forehand	70%	10%	10%	5%	5%
Backhand	65%	12%	12%	6%	5%
Serve	75%	15%	5%	3%	2%
Volley	60%	20%	10%	5%	5%
Slice	68%	12%	10%	5%	5%
Drop Shot	55%	20%	15%	5%	5%
Lob	58%	15%	18%	5%	4%

Grading & Percentiles

Letter Grade Thresholds

Grade	Score Range	Meaning
A+	95-100	Elite execution
A	90-94	Excellent
B+	85-89	Very good
B	80-84	Good
C+	75-79	Above average
C	70-74	Average
D	60-69	Below average
F	<40	Needs significant work

Percentile Calculation

Hyperbolic Tangent Z-Score Transform

z = (playerScore - levelMean) / levelStdDev
percentile = 50 × (1 + tanh(z / 1.7))

Level shifts: Beginner +5%, Intermediate 0%, Advanced -5%

The 1.7 divisor compresses the distribution to match typical tournament bell curves, ensuring meaningful differentiation across the 0-100 percentile range.

Benchmark System

Level-Specific Tolerance Multipliers

Level	Tolerance	Effect
Beginner	1.5x	More forgiving — wider acceptable range
Intermediate	1.0x	Standard benchmark expectations
Advanced	0.7x	Stricter — narrow acceptable range

Additional adjustment factors:

AGE_ADJUSTMENTS: Modifies benchmark expectations by age bracket
GENDER_ADJUSTMENTS: Adjusts power-related benchmarks by gender

KPI Calculations

KPI	Calculation	Interpretation
Timing Consistency	StdDev of contact timing (ms) within benchmark window	Lower = more consistent
Footwork Efficiency	Stride length variance + base width consistency	Lower variance = better
Positioning Score	Avg distance from ideal court position, normalized 0-100	Higher = better positioning
Contact Height	Consistency of strike height above court surface	Lower variance = better
Speed Consistency	Racquet velocity StdDev as % of benchmark mean	Lower = more repeatable

Grip Analysis Engine

The grip analysis engine infers the player's grip type from body-only kinematic signals at the contact frame. Since MoveNet provides only body landmarks (no finger or hand detail), the engine uses five proxy indicators that correlate strongly with grip type according to biomechanics literature.

Key Innovation

Traditional grip detection requires high-resolution hand imaging. SmartSwing's approach uses inferential kinematics — the body's configuration at contact frame strongly constrains which grip the player must be using. For example, a Western forehand grip forces high wrist extension, elevated contact point, and steep swing plane — detectable from shoulder/elbow/wrist positions alone.

Contact Frame Detection

Peak Wrist Speed Method

For i = 1 to frames.length:
speed[i] = distance(wrist[i-1], wrist[i]) / timeDelta[i]
contactIdx = argmax(speed)

timeDelta = (frames[i].timestamp - frames[i-1].timestamp) || (1/30)
Minimum: 3 frames required, wrist confidence >= 0.3

Five Kinematic Indicators

1. Wrist Extension Angle (degrees)

Forearm vs Hand Velocity Direction

forearm = elbow → wrist
handDir = avg wrist displacement over ±2 frames around contact
angle = |atan2(cross2(forearm, handDir), dot(forearm, handDir))|
If angle > 90: fold to (180 - angle)

Continental: 0-15 deg | Eastern: 15-25 deg | Semi-Western: 25-40 deg | Western: 40-60 deg

2. Contact Height Ratio (normalized)

Wrist Position Relative to Torso

heightRatio = (hip_y - wrist_y) / (hip_y - shoulder_y)

0 = wrist at hip level | 1 = wrist at shoulder | >1 = above shoulder
Continental → low contact | Western → high contact

3. Swing Plane Angle (degrees above horizontal)

6-Frame Lookback Trajectory

wristPath = wrist[contactIdx-6] → wrist[contactIdx]
swingPlane = atan2(deltaY_upward, |deltaX|)

Continental: ~5-15 deg | Western: ~40-55 deg

4. Elbow Angle at Contact (degrees, 0-180)

Standard 3-Point Angle

u = shoulder → elbow, v = elbow → wrist
elbowAngle = acos(clamp(dot(u,v) / (|u| × |v|), -1, 1))

Extended arm → larger angle (serve/volley) | Bent → smaller (Western forehand)

5. Forearm Pronation Proxy (normalized 0-1)

Forearm vs Trunk Angle

Gaussian Classifier

Each grip type is modeled as a diagonal-covariance Gaussian in 5D indicator space. Classification scores are computed as the product of per-indicator Gaussian likelihoods:

Per-Indicator Gaussian Score

z = (observedValue - center) / sigma
gScore = exp(-(z^2) / 2)
Floor: max(0.01, gScore) // prevents single-indicator zero-killing

Per-Grip Total Score

gripScore = product( gScore(indicator[i]) ) for all valid indicators
Minimum 2 valid indicators required

Probability Distribution

distribution[grip] = gripScore[grip] / sum(all gripScores)
confidence = max(distribution) // rounded to 3 decimal places

Grip Parameter Tables

Each cell shows [center, sigma] for the Gaussian classifier.

Forehand Grips

Grip	Wrist Ext	Height	Swing Plane	Elbow	Pronation
Continental	[10, 8]	[0.45, 0.20]	[10, 10]	[165, 12]	[0.20, 0.20]
Eastern	[20, 8]	[0.75, 0.15]	[20, 10]	[158, 12]	[0.40, 0.20]
Semi-Western	[33, 10]	[0.95, 0.15]	[32, 10]	[148, 12]	[0.60, 0.20]
Western	[50, 12]	[1.15, 0.20]	[48, 12]	[140, 12]	[0.80, 0.20]

Backhand Grips

Grip	Wrist Ext	Height	Swing Plane	Elbow	Pronation
Continental	[12, 8]	[0.55, 0.20]	[12, 10]	[165, 12]	[0.25, 0.20]
Eastern BH	[22, 10]	[0.85, 0.18]	[22, 10]	[155, 14]	[0.45, 0.20]
Two-Handed BH	[18, 10]	[0.85, 0.20]	[24, 12]	[150, 15]	[0.50, 0.25]

Serve Grips

Grip	Wrist Ext	Height	Swing Plane	Elbow	Pronation
Continental	[15, 10]	[1.35, 0.30]	[30, 20]	[155, 15]	[0.30, 0.25]
Eastern	[25, 12]	[1.30, 0.30]	[28, 20]	[155, 15]	[0.45, 0.25]
Semi-Western	[35, 14]	[1.25, 0.30]	[26, 20]	[150, 15]	[0.60, 0.25]

Shot-Grip Appropriateness Mapping

Shot Type	Expected Grips	Mismatches & Severity
Forehand	Eastern, Semi-Western, Western	Continental = medium
Serve	Continental	Eastern = high, Semi-W = critical, Western = critical
Volley	Continental	Eastern = medium, Semi-W/Western = high
Slice	Continental	Eastern = medium, Semi-W/Western = high
Drop Shot	Continental	Eastern = medium, Semi-W/Western = high
Backhand	Continental, Eastern BH, Two-Handed	Eastern = medium, Semi-W = medium, Western = high
Lob / Return	All grips accepted	No mismatches

Permissive coaching mode: Grip mismatches generate coaching callouts but do NOT penalize the overall score. This ensures players receive actionable guidance without being unfairly scored.

Coaching Recommendations

The engine generates structured recommendations based on detected grip vs shot type:

Critical Mismatch Rules

Trigger	Recommendation	Drills
Serve + non-Continental	Switch to Continental — unlocks forearm pronation for slice/kick serves	grip-bevel-check-continental, shadow-serve-pronation-snap
Volley/Slice/Drop + non-Continental	Use Continental — only grip for both FH+BH punch volleys	grip-bevel-check-continental, punch-volley-no-switch
Forehand + Continental	Move to Eastern or Semi-Western — caps topspin ceiling	grip-bevel-check-eastern, low-to-high-shadow-swing
Forehand + Western (beginner)	Consider Semi-Western — Western is difficult for low balls	—

Report Structure

The analysis report is generated as an HTML template assembled from session data:

Session Header — Date, duration, shot count by type, overall grade
Score Breakdown — Biomechanics, timing, footwork, positioning, readiness (bar charts)
Grade Details — Per-shot-type grades with percentile rankings
Grip Analysis — Detected grip, confidence, distribution bars, severity badge, coaching notes
Benchmark Comparison — Player metrics vs profile-adjusted benchmarks
Progress Context — Personal best tracking, session-over-session delta, streaks
Milestone Achievements — Level-specific unlocked badges based on score thresholds
KPI Summary — Timing consistency, footwork efficiency, positioning, contact height
AI Coaching Narrative — Swing Story, Analogy, Feel This, Your Potential
Tailored Drills — Shot-type-specific drills based on weakest component scores
Tactical Suggestions — Pattern-based playing recommendations
Consistency Analysis — Standard deviation visualization across metrics

AI Coach Narrative

SmartSwing uses Claude (Anthropic) to generate personalized coaching insights. The prompt includes session data, shot type, score, and player profile. The response follows a strict four-section format:

Narrative Format

Swing Story — 2-3 sentences describing what happened in plain English

The Analogy — One clear metaphor or everyday comparison (max 2 sentences)

Feel This — Specific physical sensation/cue for next practice (2-3 sentences)

Your Potential — One sentence about what's achievable in 2-4 weeks

Rules: Calibrate language to player level (beginner = simple analogies, pro = technical precision). Be honest but encouraging. Never use generic filler. Total: 150-220 words.

Stack & Hosting

Service	Provider	Purpose
Hosting	Vercel	Static files + serverless /api/*.js
Database	Supabase (PostgreSQL)	Auth, profiles, assessments, reports
Storage	Supabase Storage	Buckets: tennis-videos, analysis-reports
Payments	Stripe	Checkout sessions + webhook sync
AI	Anthropic (Claude)	Coaching narratives
CI/CD	GitHub Actions	Auto-deploy to Vercel on push

Database Schema (Supabase)

Core Tables

Table	Purpose
`profiles`	User profiles, subscription_tier, stripe IDs, player settings
`assessments`	Saved analysis results — scores, angles, metrics, grip_assessment (JSONB)
`coach_sessions`	Booked coaching sessions
`contact_messages`	Contact form submissions
`player_goals`	Player-set improvement targets
`progress_events`	Timeline entries (milestones, achievements)
`drill_assignments`	Auto-generated drill plans from assessments
`analysis_reports`	Full report HTML/data
`shot_benchmarks`	Reference benchmarks by level/age/gender
`drill_library`	Curated drill database
`tactic_library`	Tactical pattern database
`customer_subscriptions`	Stripe subscription state mirror
`report_usage_monthly`	Server-authoritative free report quota

Grip Assessment Column

The assessments.grip_assessment column (JSONB) stores:

{
  "detected_grip": "semi-western",
  "confidence": 0.847,
  "distribution": { "continental": 0.02, "eastern": 0.11, ... },
  "indicators": { "wrist_extension": 31.4, "contact_height": 0.92, ... },
  "shot_match": { "expected": ["eastern","semi-western","western"], "severity": null },
  "recommendations": [{ "action": "maintain", "title": "...", "why": "...", "how_steps": [] }],
  "drill_ids": [],
  "contact_frame_index": 42,
  "handedness": "right",
  "notes": []
}

Auth & Billing Flow

Authentication

Supabase Auth handles email/password + Google/Apple OAuth. Flow: signup.html → auth-callback.html → welcome.html → dashboard.html. Local browser fallback (demo mode) activates when Supabase config is missing.

Billing

Stripe Checkout sessions created via api/create-checkout-session.js. Webhook (api/stripe-webhook.js) updates Supabase profiles.subscription_tier. Client syncs via restoreSupabaseSession() on dashboard load.

Plan Definitions

Plan	Reports	Drills	Coaching
Free	3 lifetime	Basic	None
Starter	10/month	Full library	AI coach
Pro	Unlimited	Full + custom	AI + human
Elite	Unlimited	Full + custom	Priority 1-on-1

Academic References & Studies

The SmartSwing AI engine draws from established sports biomechanics research:

Pose Estimation & Motion Analysis

Cao, Z. et al. (2019) — "OpenPose: Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields." IEEE TPAMI. Foundation for real-time multi-keypoint body tracking.
Google Research (2021) — "MoveNet: Ultra fast and accurate pose detection model." TensorFlow Hub. The primary pose model used by SmartSwing for 17-keypoint detection.
Bazarevsky, V. et al. (2020) — "BlazePose: On-device Real-time Body Pose tracking." CVPR Workshop. Alternative MediaPipe pose model for cross-platform fallback.

Tennis Biomechanics

Elliott, B. (2006) — "Biomechanics and Tennis." British Journal of Sports Medicine, 40(5). Comprehensive review of tennis stroke mechanics, kinetic chain principles, and injury prevention. Key source for joint angle benchmarks and optimal ranges.
Reid, M., Elliott, B., & Crespo, M. (2013) — "Mechanics and Learning Practices Associated with the Tennis Forehand: A Review." Journal of Sports Science & Medicine, 12(2). Source for forehand grip-specific mechanics and wrist extension patterns.
Knudson, D. & Blackwell, J. (2005) — "Upper Extremity Angular Kinematics of the One-Handed Backhand Drive in Tennis Players With and Without Tennis Elbow." International Journal of Sports Medicine. Elbow angle and wrist lag benchmarks for backhand analysis.
Abrams, G. et al. (2011) — "Biomechanics of the Tennis Serve." Sports Health, 3(6). Serve kinematic chain timing, shoulder rotation, and pronation mechanics. Foundation for serve-specific scoring weights and Continental grip enforcement.
Landlinger, J. et al. (2010) — "Key Performance Indicators for Tennis." Journal of Sports Science & Medicine, 9. Source for KPI definitions and benchmark calibration across skill levels.

Grip Biomechanics

Groppel, J.L. (1992) — "High Tech Tennis." Leisure Press. Foundational reference on grip mechanics and their effect on ball contact, spin production, and shot selection.
Brody, H. (2002) — "The Physics and Technology of Tennis." Racquet Tech Publishing. Physics of grip pressure, wrist action, and contact geometry. Source for grip-contact height correlations.
Vergauwen, L. et al. (1998) — "Wrist and Forearm Muscle Activity in Tennis." British Journal of Sports Medicine, 32. EMG studies of forearm pronation across grip types. Foundation for the pronation proxy indicator.

Kinetic Chain & Power Transfer

Kibler, W.B. (1995) — "Biomechanical Analysis of the Shoulder During Tennis Activities." Clinics in Sports Medicine, 14(1). Hip-shoulder separation (X-Factor) research and proximal-to-distal sequencing principles.
Fleisig, G. et al. (2003) — "Kinematic and Kinetic Comparison Between Baseball Pitching and Football Passing." Journal of Applied Biomechanics. Cross-sport validation of kinetic chain principles applied to tennis serve mechanics.
Putnam, C.A. (1993) — "Sequential Motions of Body Segments in Striking and Throwing Skills." Journal of Biomechanics, 26. Theoretical foundation for proximal-to-distal activation sequencing used in kinematic chain scoring.

Scoring & Performance Assessment

Hughes, M. & Franks, I. (2004) — "Notational Analysis of Sport." Routledge. Framework for performance quantification and statistical analysis in racquet sports.
O'Donoghue, P. (2010) — "Research Methods for Sports Performance Analysis." Routledge. Methodological foundation for z-score percentile calculations and benchmark normalization.

Glossary

Term	Definition
X-Factor	Angular separation between hip and shoulder rotation axes during the swing loading phase
Kinetic Chain	Sequential activation of body segments from proximal (hips) to distal (wrist) for power transfer
Contact Frame	The frame at which peak wrist speed occurs — proxy for ball-racquet contact moment
COM	Center of Mass — weighted average of shoulder and hip midpoints (40/60 split)
Pronation	Inward rotation of the forearm — critical for serve power and spin
Continental Grip	Base knuckle on bevel 2 — the universal grip for serves, volleys, and slices
Semi-Western Grip	Base knuckle on bevel 4 — default modern forehand grip for topspin
Swing Plane	Angle of the racquet path relative to horizontal — steeper planes produce more topspin
SmartSwing Score	Composite 0-100 metric combining biomechanics (62%), timing (14%), footwork (8%), positioning (8%), readiness (8%)
Diagonal Covariance	Gaussian classifier that treats each indicator independently — assumes no cross-indicator correlation

SmartSwing AI — Proprietary & Confidential. This document is for internal engineering reference only.
Generated April 8, 2026. Engine v2.0.