Resources

Metric Library

A reference for every metric Axioforce computes from force-plate data.

Airborne Displacement

Estimated horizontal center of mass displacement during airborne phase using takeoff velocity.

d=v_xy × (2 × v_z / g)

Average

The average value of the dataset

average=sum(x) / n

Average Force

% BW

The average force during a phase, multiple phases, or a capture.

average_force=average(force)

Average over 1 Second

Get the average of the data for the last 1 second.

average=sum(x[t−1s:]) / len(x[t−1s:])

Average Power

The average power during a phase, multiple phases, or a capture.

average_power=average(force × velocity)

Average Relative Power

W/kg

The average power relative to the system mass during a phase, multiple phases, or a capture.

average_power=average(force × velocity) / system_mass

Average RFD

N/s

The rate at which force is developed

RFD=ΔF / Δt

Average Velocity

m/s

The average velocity during a phase, multiple phases, or a capture.

average_velocity=average(velocity)

Body Mass

The body mass of the individual.

body_mass=mass

Count

The number of data points in the dataset

count=n

Countermovement Depth

The peak negative vertical displacement during the braking and propulsive phases of a CMJ.

countermovement_depth=min(Pz)

Estimated Airborne Displacement

Estimated horizontal center of mass displacement during airborne phase using takeoff velocity.

d=v_xy × (2 × v_z / g)

Estimated Jump Distance

Estimated jump distance from center of mass displacement and takeoff velocity, assuming a symmetric flight arc.

Z: h = vz^2 / (2g)

X/Y: d = 2 × Δx_contact + vx × (2 × vz / g)

Estimated Jump Distance From Impulse

Estimate jump distance from net impulse and time in air.

distance=Δv × t_air

where Δv = impulse / m and t_air = 2×vz/g

Estimated Time in air

Estimate the time spent in the air based on the vertical velocity at takeoff.

time_in_air=2 × vz / g

Exit Velocity

kph

Ball speed off the bat, manually entered or from external source (e.g., Trackman, Rapsodo)

Manual Entry

First Quartile

The value below which the first quartile of the data falls

Q1=0.25 × (n + 1)

Force at Minimum Displacement

% BW

The vertical ground reaction force applied to the system center of mass at the instant of peak negative vertical displacement of the system center of mass.

force_at_minimum_displacement=Fz(t_min,Pz)

Hang Time

The time the athlete is in the air.

hang_time=land_time − lift_off,time

Hip Rotation Magnitude

Sum of absolute peak vertical free moments (Tz) from back foot and front foot during the Swing.

hip_rot_mag=|peak_Tz,back| + |peak_Tz,front|

Hip Rotation Symmetry

Difference of absolute peak vertical free moments (Tz): back foot minus front foot.

hip_rot_sym=|peak_Tz,back| − |peak_Tz,front|

Impulse

The change in momentum of the athlete

impulse=force × time

Impulse Ratio

The ratio between the impulse during the propulsive phase and the braking phase during a CMJ.

impulse_ratio=propulsive_impulse / braking_impulse

Interquartile Range

The range between the first and third quartiles

IQR=Q3 − Q1

Jump Height

The height of the jump, calculated using the hang time.

jump_height=hang_time^2 × g / 8

Jump Height from Takeoff Velocity

Calculate the vertical leap height based on the takeoff velocity.

vertical_leap_takeoff_velocity=vz^2 / (2 × g)

Jump Momentum

kg*m/s

Calculate the jump momentum based on the takeoff velocity and the athlete's mass.

jump_momentum=mass × vz

JumpingStiffness

N/m

The vertical ground reaction force applied to the system center of mass at the instant of peak negative vertical displacement of the system center of mass divided by the peak negative vertical displacement of the system center of mass during the jumping phases.

jumping_stiffness=Fz(t_min,Pz) / abs(min(Pz))

Kurtosis

A measure of the 'tailedness' of the data distribution compared to a normal distribution

kurtosis=(1/n) × sum((x − mean)^4) / (std_dev^4)

L/R Asymmetry Average Force

The asymmetry between the left and right average force (either positive or negative) during a phase, multiple phases, or a capture.

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry Average RFD

The asymmetry between the left and right RFD (either positive or negative) during a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry Average RFD

The asymmetry index between the left and right RFD (either positive or negative) during a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Impulse

The asymmetry between the left and right impulse (either positive or negative) during a phase, multiple phases, or a capture.

impulse=integral(Fz × dt)

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry Index Average Force

The asymmetry index between the left and right average force (either positive or negative) during a phase, multiple phases, or a capture.

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Index Impulse

The asymmetry index between the left and right impulse (either positive or negative) during a phase, multiple phases, or a capture.

impulse=integral(Fz × dt)

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Index Peak Force

The asymmetry index between the left and right force (either positive or negative) during a phase, multiple phases, or a capture.

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Index Peak RFD

The asymmetry index between the left and right at the peak combined (left + right) instantaneous RFD (either positive or negative) during a phase, multiple phases, or a test.

RFD=dF / dt

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100 at peak (L+R) RFD

L/R Asymmetry Index RFD

The asymmetry index between the left and right RFD (either positive or negative) during a phase, multiple phases, or a capture.

RFD=ΔF / Δt

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Index RFD 100

The asymmetry index between the left and right RFD (either positive or negative) during the first 100 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Index RFD 150

The asymmetry index between the left and right RFD (either positive or negative) during the first 150 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Index RFD 200

The asymmetry index between the left and right RFD (either positive or negative) during the first 200 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry_index=((Right − Left) / (Total × 0.5))

L/R Asymmetry Index RFD 50

The asymmetry index between the left and right RFD (either positive or negative) during the first 50 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry_index=((Right − Left) / (Total × 0.5)) × 100

L/R Asymmetry Peak Force

The asymmetry between the left and right force (either positive or negative) during a phase, multiple phases, or a capture.

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry Peak Landing Force

Percent difference between the left and right peak landing forces.

asymmetry=100 × (PeakLandingRight − PeakLandingLeft) / max(PeakLandingRight, PeakLandingLeft)

L/R Asymmetry Peak RFD

The asymmetry between the left and right at the peak combined (left + right) instantaneous RFD (either positive or negative) during a phase, multiple phases, or a test.

RFD=dF / dt

asymmetry=((Right − Left) / max(Right, Left)) × 100 at peak (L+R) RFD

L/R Asymmetry RFD

The asymmetry between the left and right RFD (either positive or negative) during a phase, multiple phases, or a capture.

RFD=ΔF / Δt

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry RFD 100

The asymmetry between the left and right RFD (either positive or negative) during the first 100 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry RFD 150

The asymmetry between the left and right RFD (either positive or negative) during the first 150 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry RFD 200

The asymmetry between the left and right RFD (either positive or negative) during the first 200 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry=((Right − Left) / max(Right, Left)) × 100

L/R Asymmetry RFD 50

The asymmetry between the left and right RFD (either positive or negative) during the first 50 ms of a phase, multiple phases, or a test.

RFD=ΔF / Δt

asymmetry=((Right − Left) / max(Right, Left)) × 100

LandingStiffness

N/m

landing_stiffness=Fz(t_min,Pz) / abs(min(Pz))

Left Force at Minimum Displacement

% BW

The left-side vertical ground reaction force at the instant of peak negative vertical displacement of the system center of mass (Parent).

left_force_at_minimum_displacement=Fz_left(t_{min,Pz,parent})

Left Force at Peak Force

% BW

The left ground reaction force applied to the system center of mass at the point of the peak instantaneous ground reaction force applied to the system center of mass.

left_force_at_peak_force=Fz_left(t_peak,parent)

Max

The maximum value in the dataset

max=max(x)

Median

The median value of the dataset

median=Q2 = 0.5 × (n + 1)

Min

The minimum value in the dataset

min=min(x)

Mode

The most frequently occurring value in the dataset

mode=most_frequent(x)

Momentum at Peak Force

kg*m/s

Calculate the momentum at peak force during a phase, multiple phases, or a capture.

momentum_at_peak_force=v_{at,peak,force} × body_mass

mRSI

m/s

Calculate the modified Reactive Strength Index (mRSI). How much "jump" per second of effort.

mRSI=jump_height / (contact_time or time_to,takeoff)

mRSI-Lateral

m/s

Calculate the modified Reactive Strength Index (mRSI) adapted for lateral jumps. How much "jump" per second of effort.

mRSI_lateral=jump_distance / (contact_time or time_to,takeoff)

Net Impulse

Calculate the net impulse.

net_impulse=(F × dt)

Peak

The largest absolute value in the dataset

peak=max(abs(x))

Peak Direction

The direction of the peak value in the dataset

????

Peak Direction Phi

The phi value of the peak direction

????

Peak Direction Rho

The rho value of the peak direction

????

Peak Direction Theta

The theta value of the peak direction

????

Peak Force

% BW

The peak force (either positive or negative) during a phase, multiple phases, or a capture.

peak_force=max(abs(Force))

Peak Free Moment

Peak vertical free moment (Tz) — pure rotational torque about the vertical axis. Returns value at peak |Tz| with sign preserved.

peak_Tz=Tz at max(|Tz|)

Peak Impulse

The maximum impulse value in the dataset

peak_impulse=max(impulse)

Peak Momentum XY

kg*m/s

Calculate the peak momentum in the XY plane during a phase, multiple phases, or a capture.

peak_momentum_xy=max(sqrt(Vx^2 + Vy^2) × dt)

Peak Power

The peak instantaneous power (either positive or negative) during a phase, multiple phases, or a capture.

peak_power=max(abs(force × velocity))

Peak Relative Power

W/kg

The peak instantaneous power relative to the system mass (either positive or negative) during a phase, multiple phases, or a capture.

peak_power=max(abs(force × velocity)) / system_mass

Peak RFD

N/s

Peak instantaneous rate of force development

peak(RFD) = max(dF / dt)

Peak to Peak Amplitude

The difference between the maximum and minimum values in the dataset

peak_to_peak_amplitude=max(x) − min(x)

Peak Velocity

m/s

The peak velocity (either positive or negative) during a phase, multiple phases, or a capture.

peak_velocity=max(abs(Velocity))

Pitch Tempo

Time between the last upward crossing of |Fy| = 10 N in Loading and the peak |Fy| in Delivery.

pitch_tempo=time_of,peak,|Fy|_delivery − time_when,|Fy|_loading_last_crosses_10N

Pitch Velocity

kph

Ball velocity at release, manually entered or from external source (e.g., Trackman)

Manual Entry

Positive Impulse

The impulse during the braking and propulsive phases.

positive_impulse=(F × dt)

Positive Net Impulse

The net impulse during the braking and propulsive phases.

positive_impulse=(F × dt)

Positive Net Impulse Asymmetry

The asymmetry between the left and right positive net impulse during the propulsive phase.

positive_impulse_per_leg=integral((F − bodyweight) × dt) over propulsive phase

asymmetry=((Right − Left) / max(Right, Left)) × 100

Pre-Takeoff Displacement

Horizontal center of mass displacement at the end of the propulsive phase.

Pvector=sqrt(Px^2 + Py^2)

Range

The difference between the maximum and minimum values in the dataset

range=max(x) − min(x)

Rate of Force Development

N/s

The rate at which force is developed

RFD=Î”Force / Î”Time

Reaction Time

The duration of the reaction phase.

duration=t2 − t1

Reaction Time to Takeoff

The total time taken from the start of the visual stimulus to the takeoff.

reaction_time_to_takeoff=time_of,takeoff − time_of,stimulus

Recoil Time

Time from first negative Fy after Delivery contact (Landing Zone) to the first zero-crossing of Fy back to >= 0.

recoil_time_ms=t(Fy crosses 0 up) − t(first Fy < 0 after contact)

Relative Net Impulse

Ns/kg

Calculate the net impulse relative to body mass.

net_impulse=(F × dt) / system_mass

Relative Positive Impulse

Ns/kg

The impulse during the braking and propulsive phases relative to body mass.

positive_impulse=(F × dt) / system_mass

RFD 100

N/s

The rate at which force is developed during the first 100 ms of the test or phase.

RFD=ΔF / Δt

RFD 150

N/s

The rate at which force is developed during the first 150 ms of the test or phase.

RFD=ΔF / Δt

RFD 200

N/s

The rate at which force is developed during the first 200 ms of the test or phase.

RFD=ΔF / Δt

RFD 50

N/s

The rate at which force is developed during the first 50 ms of the test or phase

RFD=ΔF / Δt

Right Force at Minimum Displacement

% BW

The right-side vertical ground reaction force at the instant of peak negative vertical displacement of the system center of mass (Parent).

right_force_at_minimum_displacement=Fz_right(t_{min,Pz,parent})

Right Force at Peak Force

% BW

The right ground reaction force applied to the system center of mass at the point of the peak instantaneous ground reaction force applied to the system center of mass.

right_force_at_peak_force=Fz_right(t_peak,parent)

RSI

Calculate the Reactive Strength Index (RSI).

RSI=flight_time / (contact_time or time_to,takeoff)

Skewness

A measure of the asymmetry of the data distribution

skewness=(1/n) × sum((x − mean)^3) / (std_dev^3)

Standard Deviation

A measure of the amount of variation or dispersion in the dataset

std_dev=sqrt((1/n) × sum((x − mean)^2))

Stride Length

Forward distance between Launch Zone COP at Loading peak Fz and Landing Zone COP at Delivery peak Fz.

stride_length_cm=COPy_delivery − COPy_loading

Stride Width

Lateral distance between Launch Zone COP at Loading peak Fz and Landing Zone COP at Delivery peak Fz.

stride_width_cm=COPx_delivery − COPx_loading

Swing Stride Length

Forward (Y) COP displacement on the lead-foot plate from capture start to lead foot strike.

stride_length_cm=(COPy_at,strike − COPy_at,start) × 100

Swing Stride Tempo

Time from peak back-foot propulsive force (|Fy|) to lead-foot strike.

tempo_ms=t_foot,strike − t_peak,back,Fy

Swing Stride Width

Lateral (X) COP displacement on the lead-foot plate from capture start to lead foot strike.

stride_width_cm=(COPx_at,strike − COPx_at,start) × 100

System Weight

The body mass of the individual

system_weight=weight

Takeoff Velocity

m/s

Velocity of the center of mass at the instant of take-off.

takeoff_velocity=velocity at time of take−off

Third Quartile

The value below which the third quartile of the data falls

Q3=0.75 × (n + 1)

Time to Peak Force

The total time taken from the initiation of movement to the peak force.

time_to_peak_force=time_{of,peak,force} − time_{of,initial,movement}

Time to Takeoff

The total time taken from the initiation of movement to the instant of take-off.

time_to_takeoff=time_of,takeoff − time_{of,initial,movement}

Trend

The overall direction of the data over time

trend=(y2 − y1) / (x2 − x1)

True Quickness

Time from the start of the visual stimulus until the estimated center of mass displacement reaches 61 cm (~2 ft).

reactive_61cm_displacement_time=time_{at,61cm,displacement} − time_of,stimulus

Variance

A measure of how far a set of numbers is spread out from their average value

variance=(1/n) × sum((x − mean)^2)

Vertical Leap

The vertical distance the athlete jumps

vertical_leap=(initial_velocity^2 × sin(angle)^2) / (2 × g)