Metrics Reference¶

Complete documentation of all 25+ climbing metrics including calculation methods, scientific rationale, and practical interpretation.

Understanding the Coordinate System¶

All metrics use normalized coordinates (0.0 - 1.0) from MediaPipe Pose estimation:

X-axis: 0.0 = left edge, 1.0 = right edge
Y-axis: 0.0 = top edge, 1.0 = bottom edge (inverted from typical graphics)

This normalization ensures metrics work across different video resolutions and climbing wall sizes.

Time-based metrics use the video frame rate (default 30 fps) to convert frame-based measurements into per-second values.

Core Movement Metrics¶

Hip Height¶

Key: hip_height Type: float Range: 0.0 (top) to 1.0 (bottom)

Calculation¶

left_hip_y = landmarks[LEFT_HIP].y
right_hip_y = landmarks[RIGHT_HIP].y
hip_height = (left_hip_y + right_hip_y) / 2.0

Rationale¶

The hips represent the body's center of mass more consistently than other landmarks (shoulders move with arm positions, knees with leg positions). Averaging both hips reduces noise from asymmetric positions like hip flags or body rotation.

Interpretation¶

Lower values (→ 0.0) = higher in frame = climbing up
Higher values (→ 1.0) = lower in frame = descending
Decreasing trend = vertical progress
Constant value = static position (rest/lock-off/stuck)

What You Can Learn¶

✅ Total ascent: initial_hip_height - final_hip_height ✅ Climb efficiency: Smooth decrease = good beta, fluctuations = wasted height ✅ Rest positions: Plateaus in the graph ✅ Crux sections: Prolonged plateaus or increases (downclimbing)

Center of Mass Velocity¶

Key: com_velocity Type: float Units: Normalized units per second

Calculation¶

# Center of mass from shoulders and hips
core_points = [left_shoulder, right_shoulder, left_hip, right_hip]
com_current = weighted_average(core_points)
com_previous = com_at_previous_frame

# Euclidean distance
dx = com_current.x - com_previous.x
dy = com_current.y - com_previous.y
distance = sqrt(dx² + dy²)

# Convert to velocity
velocity = distance / (1/fps)  # Distance per second

Rationale¶

Center of mass (COM) provides a single point representing the entire body's movement. Using core points (shoulders + hips) excludes limb movements that don't represent whole-body displacement. Velocity captures movement speed regardless of direction (up, down, or lateral).

Interpretation¶

0.01 - 0.1: Normal climbing pace
> 0.15: Very fast/dynamic moves
< 0.005: Near stationary (rest, lock-off, stuck)
Spikes: Dynamic movements, jumps, quick repositioning

What You Can Learn¶

✅ Climbing style: Consistent velocity = static climbing, spikes = dynamic ✅ Fatigue onset: Decreasing average velocity over time ✅ Route difficulty: Sections with low velocity = technical/difficult ✅ Movement efficiency: High velocity with low energy expenditure = skilled

Center of Mass Sway¶

Key: com_sway Type: float Units: Normalized units (standard deviation)

Calculation¶

# Collect horizontal positions over window (default 30 frames = 1 second)
com_x_positions = [com.x for com in last_30_frames]

# Standard deviation of lateral position
sway = std_dev(com_x_positions)

Rationale¶

Lateral stability is a key indicator of control and technique. Experienced climbers minimize unnecessary horizontal movement, keeping their center of mass aligned with the line of ascent. Standard deviation captures the variability in side-to-side movement over a sliding time window.

Interpretation¶

< 0.01: Excellent stability (competition-level technique)
0.01 - 0.02: Good stability (experienced climber)
0.02 - 0.03: Moderate stability (intermediate)
> 0.03: Poor stability (beginner, pumped, or very overhung)

What You Can Learn¶

✅ Technical skill: Lower sway = better body positioning ✅ Route character: High sway on slab = poor footwork, on overhang = expected ✅ Fatigue indicator: Increasing sway = losing control ✅ Specific weaknesses: Compare sway on different hold types (crimps vs slopers)

Jerk¶

Key: jerk Type: float Units: Normalized units per second²

Calculation¶

# Jerk is the rate of change of acceleration
# Requires at least 4 frames for numerical differentiation

# Velocities
v1 = distance(frame[n-3], frame[n-2]) * fps
v2 = distance(frame[n-2], frame[n-1]) * fps
v3 = distance(frame[n-1], frame[n]) * fps

# Accelerations
a1 = (v2 - v1) * fps
a2 = (v3 - v2) * fps

# Jerk
jerk = abs(a2 - a1) * fps

Rationale¶

Jerk measures movement smoothness. Smooth, controlled climbing has low jerk (gradual accelerations). Jerky movement indicates:

Overgripping (tension-release cycles)
Poor technique (fighting the wall instead of flowing)
Fatigue (muscle control degradation)
Fear/hesitation (stop-start movements)

This is a second-order derivative, making it sensitive to movement quality.

Interpretation¶

< 0.001: Very smooth (expert technique)
0.001 - 0.005: Normal climbing smoothness
> 0.005: Jerky movement (technical issues or fatigue)
High variance: Inconsistent movement quality

What You Can Learn¶

✅ Technical proficiency: Lower jerk = better movement control ✅ Fatigue detection: Increasing jerk = muscle control degradation ✅ Learning progress: Jerk decreases as climber learns route ✅ Crux identification: Jerk spikes at difficult sections

Body Angle¶

Key: body_angle Type: float Units: Degrees (0° - 90°)

Calculation¶

# Vector from hips to shoulders
hip_center = (left_hip + right_hip) / 2
shoulder_center = (left_shoulder + right_shoulder) / 2

dx = abs(shoulder_center.x - hip_center.x)  # Horizontal component
dy = abs(shoulder_center.y - hip_center.y)  # Vertical component

# Angle from vertical
body_angle = atan(dx / dy) * (180 / π)

Rationale¶

Body angle indicates lean from vertical. This metric reveals:

Wall angle compensation: More lean on overhangs
Rest positions: Near-vertical (0-15°) positions are less strenuous
Dynamic loading: Large angles = more force on arms
Technique choices: Keeping hips close (low angle) vs. away from wall

Using atan(dx/dy) gives angle from vertical (not horizontal), making 0° = vertical stance, which is more intuitive for climbing.

Interpretation¶

0-15°: Vertical/slab stance (efficient, restable)
15-30°: Moderate lean (typical vert climbing)
30-50°: Significant lean (overhang, roof approach)
50-90°: Extreme lean (steep overhang, horizontal roof)

What You Can Learn¶

✅ Wall angle estimation: Average body angle correlates with route steepness ✅ Rest technique: Low angles indicate good rest positions ✅ Energy expenditure: Higher angles = more arm loading = faster fatigue ✅ Style analysis: Consistent vs. variable angles = different climbing approaches

Hand Span¶

Key: hand_span Type: float Units: Normalized distance

Calculation¶

left_wrist = landmarks[LEFT_WRIST]
right_wrist = landmarks[RIGHT_WRIST]

dx = right_wrist.x - left_wrist.x
dy = right_wrist.y - left_wrist.y
hand_span = sqrt(dx² + dy²)

Rationale¶

Hand span indicates reach width and body compression. Wide spans suggest:

Underclings or gastons
Mantling or compression moves
Open body position

Narrow spans suggest:

Tight hand positions (chimneys, arêtes)
Crossed hands (sideways movement)
Compressed body position

Interpretation¶

> 0.4: Very wide (full extension, underclings)
0.2 - 0.4: Normal climbing reach
< 0.2: Narrow (mantling, compression, or sideways)

What You Can Learn¶

✅ Movement type: Rapid changes = dynamic repositioning ✅ Route character: Consistently wide = horizontal traverse, narrow = vertical crack ✅ Reach efficiency: Compare span to vertical progress (wide ≠ always better) ✅ Technique variety: High variance = diverse move types

Foot Span¶

Key: foot_span Type: float Units: Normalized distance

Calculation¶

left_ankle = landmarks[LEFT_ANKLE]
right_ankle = landmarks[RIGHT_ANKLE]

dx = right_ankle.x - left_ankle.x
dy = right_ankle.y - left_ankle.y
foot_span = sqrt(dx² + dy²)

Rationale¶

Foot span reveals base of support and leg positioning:

Wide stance: Stability, slab technique, stemming
Narrow stance: Vertical climbing, drop knees, heel hooks

Changes in foot span indicate footwork adjustments and weight shifts.

Interpretation¶

> 0.3: Wide stance (slab, stemming, stability)
0.1 - 0.3: Normal footwork
< 0.1: Feet together (flagging, drop knee, barn door prevention)

What You Can Learn¶

✅ Base of support: Wider = more stable but less mobile ✅ Footwork quality: Smooth transitions = good technique ✅ Route type: Wide spans = slab/chimney, narrow = overhang ✅ Efficiency: Excessive foot movement = wasted energy

Vertical Progress¶

Key: vertical_progress Type: float Units: Normalized distance (cumulative)

Calculation¶

initial_hip_height = hip_height_at_frame_0
current_hip_height = hip_height_at_current_frame

vertical_progress = initial_hip_height - current_hip_height

Since Y-axis is inverted (0=top), decreasing hip height = climbing up, so progress is initial minus current.

Rationale¶

Cumulative metric tracking total height gained from start position. Unlike instantaneous hip height, this provides:

Absolute climb progress
Ability to detect downclimbing (negative progress)
Performance comparison across attempts

Interpretation¶

Increasing: Making upward progress
Plateauing: Static position or horizontal traversing
Decreasing: Downclimbing or lowering
Final value: Total vertical distance climbed

What You Can Learn¶

✅ Climb completion: Compare to route height ✅ Efficiency metric: Use in economy calculation ✅ Attempt comparison: Normalize performance across tries ✅ Crux identification: Progress stalls = difficult sections

Efficiency & Technique Metrics¶

Movement Economy¶

Key: movement_economy Type: float Units: Ratio (0.0 - 1.0)

Calculation¶

# Track cumulative distance traveled by COM
total_distance = sum(distance_between_consecutive_frames)

# Vertical progress (from Hip Height metric)
vertical_progress = initial_hip_height - current_hip_height

# Economy ratio
movement_economy = vertical_progress / total_distance

Rationale¶

Perfect efficiency would be moving straight up (economy = 1.0). In reality, climbers move laterally to reach holds, creating a less efficient path. Movement economy quantifies this:

High economy (0.7-1.0): Efficient movement, good route reading, minimal deviation
Low economy (< 0.5): Excessive lateral/vertical wandering, poor beta, wasted energy

This metric combines spatial efficiency with strategic climbing choices.

Interpretation¶

0.9 - 1.0: Nearly perfect (impossible on real routes with holds)
0.7 - 0.9: Excellent efficiency (competition level, well-known route)
0.5 - 0.7: Good efficiency (normal recreational climbing)
< 0.5: Poor efficiency (onsight, poor beta, beginner)

What You Can Learn¶

✅ Route knowledge: Increases with practice (better beta) ✅ Climb grade impact: More efficient on easier grades ✅ Style differences: Boulder (lower) vs. route (higher) ✅ Energy expenditure: Lower economy = faster fatigue

Lock-off Detection¶

Keys: is_lock_off, left_lock_off, right_lock_off Type: bool Units: Boolean

Calculation¶

# For each arm independently
elbow_angle = calculate_joint_angle(shoulder, elbow, wrist)
velocity = current_com_velocity

# Detection criteria
is_locked_off = (elbow_angle < 110°) AND (velocity < 0.005)

# Both arms
is_lock_off = left_lock_off OR right_lock_off

Rationale¶

Lock-offs are static strength positions where climbers hold themselves with bent arms while reaching for the next hold. Detection requires:

Bent elbow (< 110°): Holding with arm flexion, not straight-arm hanging
Low velocity (< 0.005): Static position, not dynamic movement

This identifies high-intensity strength moments that contribute to fatigue.

Interpretation¶

True: Currently in static strength position
High percentage: Route requires significant static strength
Frequent transitions: Dynamic climbing with many lock-offs
Duration: Time in lock-off = strength demand

What You Can Learn¶

✅ Strength requirements: High lock-off % = power-endurance route ✅ Technique quality: Fewer lock-offs = better efficiency (where possible) ✅ Fatigue contribution: Lock-offs are metabolically expensive ✅ Training needs: Frequent lock-offs = train static strength

Rest Position Detection¶

Key: is_rest_position Type: bool Units: Boolean

Calculation¶

body_angle = calculate_body_angle(landmarks)
velocity = current_com_velocity

# Detection criteria
is_rest_position = (body_angle < 20°) AND (velocity < 0.005)

Rationale¶

Rest positions are characterized by:

Near-vertical body (< 20°): Minimal arm loading, weight on skeleton
Static position: Not moving, allowing recovery

Identifying rests reveals route reading and pacing strategy. Good climbers find and use rests even on hard routes.

Interpretation¶

True: Currently in recovery position
High percentage: Route has many rests (easier) or climber is pacing well
Low percentage: Sustained difficulty or poor route reading
Rest duration: Longer = more recovery, but slower time

What You Can Learn¶

✅ Route character: Rest availability indicates sustained vs. intermittent difficulty ✅ Pacing strategy: Using rests = good tactics, rushing through = poor pacing ✅ Fitness level: Need for rests on easier routes = endurance limitation ✅ Competitive analysis: Rest usage in competition (risk vs. recovery trade-off)

Joint Angle Metrics¶

All joint angles use the same calculation method but different landmark triplets. Understanding one explains all eight.

Calculation Method (Generic)¶

def calculate_joint_angle(point_a, point_b, point_c):
    """
    Calculate angle at point_b formed by points a-b-c.
    Uses law of cosines via dot product.
    """
    # Vectors from joint to adjacent landmarks
    ba = point_a - point_b
    bc = point_c - point_b

    # Dot product
    dot_product = ba.x * bc.x + ba.y * bc.y

    # Magnitudes
    mag_ba = sqrt(ba.x² + ba.y²)
    mag_bc = sqrt(bc.x² + bc.y²)

    # Angle from dot product formula: cos(θ) = (a·b)/(|a||b|)
    cos_angle = dot_product / (mag_ba * mag_bc)
    cos_angle = clamp(cos_angle, -1.0, 1.0)  # Numerical safety

    angle = arccos(cos_angle) * (180/π)  # Convert to degrees
    return angle

This returns the interior angle (0° - 180°) at the middle point.

Elbow Angles¶

Keys: left_elbow, right_elbow Type: float Units: Degrees (0° - 180°)

Specific Calculation¶

left_elbow_angle = calculate_joint_angle(
    left_shoulder,   # Point A
    left_elbow,      # Point B (vertex)
    left_wrist       # Point C
)

Interpretation¶

170° - 180°: Nearly straight (passive hanging, efficient)
120° - 170°: Slightly bent (active engagement)
90° - 120°: Moderate flexion (holding position)
< 90°: Deep flexion (lock-off, gaston, high power demand)

What You Can Learn¶

✅ Arm efficiency: More time with straight arms (>160°) = better technique ✅ Lock-off identification: Values < 110° during static holds ✅ Fatigue progression: Increasing average angle = arms tiring, straightening out ✅ Move type: Rapid changes = dynamic, stable values = static

Shoulder Angles¶

Keys: left_shoulder, right_shoulder Type: float Units: Degrees (0° - 180°)

Specific Calculation¶

left_shoulder_angle = calculate_joint_angle(
    left_hip,        # Point A
    left_shoulder,   # Point B (vertex)
    left_elbow       # Point C
)

Interpretation¶

< 90°: Arm below shoulder (low reach, underclings)
90°: Arm perpendicular to body (neutral)
> 90°: Arm above shoulder (overhead reaches, typical climbing)
> 120°: High reach (extended overhead, dyno preparation)

What You Can Learn¶

✅ Reach height: Higher angles = reaching high ✅ Overhang adaptation: Consistently high angles on steep terrain ✅ Move variety: Angle range shows movement diversity ✅ Shoulder stress: Prolonged extreme angles (>150° or <60°) = injury risk

Knee Angles¶

Keys: left_knee, right_knee Type: float Units: Degrees (0° - 180°)

Specific Calculation¶

left_knee_angle = calculate_joint_angle(
    left_hip,        # Point A
    left_knee,       # Point B (vertex)
    left_ankle       # Point C
)

Interpretation¶

170° - 180°: Straight leg (standing on holds, heel hooks)
120° - 170°: Slight bend (normal standing/stepping)
90° - 120°: Moderate flexion (squatting, high step preparation)
< 90°: Deep flexion (high steps, knee bars, drop knees)

What You Can Learn¶

✅ Footwork type: Deep flexion = high steps, straight = standing ✅ Leg strength demand: More time in 90-120° = quad-intensive ✅ Drop knee detection: One knee deep, other straight ✅ Efficiency: Excessive knee bend = inefficient leg use

Hip Angles¶

Keys: left_hip, right_hip Type: float Units: Degrees (0° - 180°)

Specific Calculation¶

left_hip_angle = calculate_joint_angle(
    left_shoulder,   # Point A
    left_hip,        # Point B (vertex)
    left_knee        # Point C
)

Interpretation¶

170° - 180°: Fully extended (straight body, slab)
140° - 170°: Normal climbing position
120° - 140°: Moderate bend (bringing hips to wall)
< 120°: Deep bend (compression moves, bicycles, knee-chest positions)

What You Can Learn¶

✅ Body position: Lower angles = hips closer to wall = better technique on overhangs ✅ Compression moves: Very low angles (< 120°) during compression ✅ Flexibility requirements: Sustained low angles = hip flexibility needed ✅ Efficiency indicator: Keeping hips in optimal for wall angle

Summary Statistics¶

These are computed from the full history of frame-by-frame metrics.

Average Metrics¶

All metrics prefixed with avg_ are simple means:

avg_velocity = mean(all_velocity_values)
avg_sway = mean(all_sway_values)
# etc.

Use: Characterize overall climb performance, compare attempts, track improvement.

Maximum Metrics¶

Metrics like max_velocity, max_sway identify peak values:

max_velocity = max(all_velocity_values)
max_jerk = max(all_jerk_values)

Use: Identify hardest moments, dynamic peaks, loss of control incidents.

Count Metrics¶

lock_off_count and rest_count sum boolean frames:

lock_off_count = sum(1 for frame in frames if frame.is_lock_off)

Use: Quantify specific technique occurrences.

Percentage Metrics¶

Convert counts to percentages of total climb time:

lock_off_percentage = (lock_off_count / total_frames) * 100

Use: Normalize for climb duration, enable cross-climb comparison.

Fatigue Score¶

Calculation:

# Split climb into thirds
first_third_quality = mean(movement_smoothness[:N/3])
last_third_quality = mean(movement_smoothness[-N/3:])

# Degradation ratio
fatigue_score = (first_third_quality - last_third_quality) / first_third_quality

Interpretation:

0.0: No quality degradation
0.3: Moderate fatigue
> 0.5: Significant fatigue
Negative: Actually improving (learning route during climb)

Use: Detect endurance limitations, compare climb pacing strategies.

Practical Application Examples¶

Analyzing a Training Session¶

summary = analyzer.get_summary()

# Technique efficiency
if summary['avg_movement_economy'] > 0.7:
    print("✅ Good route reading and efficiency")
else:
    print("❌ Work on beta optimization")

# Endurance assessment
if summary['fatigue_score'] > 0.4:
    print("❌ Endurance limitation - train power endurance")

# Strength requirements
if summary['lock_off_percentage'] > 30:
    print("💪 Route requires significant static strength")

Comparing Climb Attempts¶

attempt1_economy = 0.65
attempt2_economy = 0.73

improvement = ((attempt2_economy - attempt1_economy) / attempt1_economy) * 100
print(f"Efficiency improved by {improvement:.1f}%")

Identifying Weaknesses¶

history = analyzer.get_history()

# Find high-sway sections
high_sway_frames = [i for i, s in enumerate(history['sways']) if s > 0.03]

# Cross-reference with video timestamps
problem_timestamps = [frame/fps for frame in high_sway_frames]
print(f"Loss of control at: {problem_timestamps} seconds")

Route Characterization¶

summary = analyzer.get_summary()

avg_body_angle = summary['avg_body_angle']
lock_off_pct = summary['lock_off_percentage']
rest_pct = summary['rest_percentage']

if avg_body_angle < 20 and rest_pct > 20:
    print("Route: Vertical, technical, good rests")
elif avg_body_angle > 40 and lock_off_pct > 25:
    print("Route: Overhung, powerful, sustained")

Metric Relationships and Dependencies¶

Dependent Metrics¶

Some metrics are calculated from others:

movement_economy requires: vertical_progress, total_distance_traveled
jerk requires: at least 4 frames of velocity history
is_lock_off requires: elbow_angle, velocity
fatigue_score requires: full climb history

Inversely Correlated¶

velocity ↑ → sway ↑ (faster = less stable)
body_angle ↑ → rest_percentage ↓ (lean = harder)
movement_economy ↑ → total_distance ↓ (efficient = less wandering)

Independently Varying¶

hand_span vs foot_span: Different body configurations
elbow_angle vs shoulder_angle: Joint-specific positioning

Limitations and Considerations¶

MediaPipe Accuracy¶

Occluded landmarks (behind wall/body): May cause brief metric errors
2D projection from 3D space: Distance metrics less accurate on angle to camera
Confidence thresholds: Low-confidence frames should be filtered

Metric Reliability¶

Most reliable: Hip height, velocity, joint angles (use core visible landmarks)
Moderate: Sway, body angle (sensitive to camera angle)
Least reliable: Spans on routes with camera not perpendicular to wall

Interpretation Context¶

Always consider:

Wall angle: Overhangs naturally have higher body angles
Route style: Slab vs. overhang climbing have different normal ranges
Climber experience: Beginners have higher variance in all metrics
Video quality: Poor lighting/resolution affects MediaPipe accuracy

Future Metric Development¶

Potential additions:

3D depth estimation: More accurate distance calculations
Reach efficiency: Hand movement relative to height gained
Breathing rate: From shoulder movement patterns
Chalk usage: Hand stops indicating shake-outs
Route-specific learning: Metrics improvement over multiple attempts