Jump height is a poor indicator of lower limb maximal power output: theoretical demonstration, experimental evidence and practical solutions

Abstract

KEY POINTS
1. Despite a widespread use, we contended that jump height as measured during vertical jump tests is not a good indicator of lower limb power or maximal power output capability. 2. We showed this based on several confounding factors: body mass, push-off distance, individual force-velocity profile and optimal force-velocity profile. Some experimental data were also shown and discussed to further illustrate the not very-good correlation between jump height and power output.
3. Finally, in order to address this issue, we discussed the possible practical solutions, and advocate for the use of a simple, accurate computation method based on jump height as an input.

Full text

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
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OPINION!PAPER!
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JUMP!HEIGHT!IS!A!POOR!INDICATOR!OF!LOWER!LIMB!MAXIMAL!POWER!OUTPUT:!!
THEORETICAL!DEMONSTRATION,!EXPERIMENTAL!EVIDENCE!AND!PRACTICAL!SOLUTIONS!
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Jean-Benoit!Morin1,3,!Pedro!Jiménez-Reyes2,!Matt!Brughelli3,!Pierre!Samozino4!
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1!Université!Côte!d’Azur,!LAMHESS,!Nice,!France!
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2!Faculty!of!Physical!Sciences!and!Sport,!Catholic!University!of!San!Antonio,!Murcia,!Spain!
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3!Sports!Performance!Research!Institute!New!Zealand,!Auckland!University!of!Technology,!
Auckland,!New!Zealand!
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4!Univ!Savoie!Mont!Blanc,!Laboratoire!Interuniversitaire!de!Biologie!de!la!Motricité,!EA!7424,!F-
73000!Chambéry,!France!
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Corresponding!author!
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Pr!Jean-Benoit!Morin!
Faculty!of!Sport!Science!
261!Boulevard!du!Mercantour!
06205!NICE,!France!
Tel:!0033489153956!
Email:!jean-benoit.morin@unice.fr!
Web:!jbmorin.net!
Twitter:!@jb_morin!
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All authors have approved this manuscript and agree with the fact that it is shared as a pre-print
DOI: 10.31236/osf.io/6nxyu
Cite as:
Morin, J., Jiménez-Reyes, P., Brughelli, M., & Samozino, P. (2018, September 4). Jump height is a
poor indicator of lower limb maximal power output: theoretical demonstration, experimental
evidence and practical solutions. https://doi.org/10.31236/osf.io/6nxyu

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
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!
!
KEY$POINTS$
$
1. Despite!a!widespread! use,! we!contended!that! jump! height!as!measured! during! vertical!
jump! tests! is! not! a! good! indicator! of! lower! limb! power! or! maximal! power! output!
capability.!
!
2. We! showed! this! based! on! several! confounding! factors:! body! mass,! push-off! distance,!
individual! force-velocity! profile! and! optimal! force-velocity! profile.! Some! experimental!
data!were!also! shown!and!discussed! to! further!illustrate!the! not! very-good!correlation!
between!jump!height!and!power!output.!
!
!
3. Finally,!in!order!to!address!this!issue,!we!discussed!the!possible!practical!solutions,!and!
advocate!for!the!use!of!a!simple,!accurate!computation!method!based!on!jump!height!as!
an!input.!
!
$
$
ABSTRACT$
!
Lower!limb!maximal!power!output!(Pmax)!is!a!key!physical!component!of!performance!in!many!
sports.!During!squat!jump! (SJ)! and! countermovement!jump!(CMJ)!tests,!athletes!produce!high!
amounts!of!mechanical!work!over!a!short!duration!to!displace!their!body!mass!(i.e.!the!dimension!
of!mechanical! power).!Thus,! jump! height! has! been! frequently! used! by! the!sports! science!and!
medicine!communities!as!an!indicator!of!Pmax.!However,!in!this!article,!we!contended!that!SJ!and!
CMJ!height!are!in!fact!poor!indicators!of!Pmax!in!trained!populations.!!
To!support! our!opinion,!we!first!detailed!why,!theoretically,!jump!height!and!Pmax!are!not! fully!
related.!Specifically,!we!demonstrated!that!individual!body!mass,!distance!of!push-off,!optimal!
loading!and!force-velocity!characteristics!confound!the!jump!height-Pmax!relationship.!!
We!also!discussed!the!poor!relationship!between!SJ!or!CMJ!height!and!Pmax!measured!with!a!force!
plate!based!on!data!reported!in!the!literature,!which!added!to!our!own!experimental!evidence.!
Finally,!we!discussed!the!limitations!of!existing!practical!solutions!(regression-based!estimation!
equations!and!allometric!scaling),!and!advocated!using!a! valid,! reliable!and! simple! field-based!
procedure! to! compute! individual!Pmax!directly! from! jump! height,! body! mass! and! push-off!
distance.!The!latter!may!allow!researchers!and!practitioners!to!reduce!bias!in!their!assessment!
of!Pmax!by!using!jump!height!as!an!input!with!a!simple!yet!accurate!computation!method,!and!not!
as!the!first/only!variable!of!interest.!
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Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
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!
1. INTRODUCTION+
!
Vertical!jump!tests!such!as!the!squat!jump!(SJ)!and!countermovement!jump!(CMJ)!have!been!long!
and!widely!used!to!assess!an!athlete’s!lower!limb!ballistic!performance!and!indirectly!quantify!
their!mechanical!power!output!capability,!i.e.!the!ability!to!produce!mechanical!work!over!the!
duration! of! the! push-off![1–3].! Although! measuring! technologies! have! differed! over! the! past!
century,!vertical!jump!tests!are!still!very!popular!due!to!their!simple!and!easy!implementation,!
good! reproducibility! and! time-energy! saving! feature! [4].! The! main! metric! used! to! describe!
jumping!performance!is!maximal!height!after!the!athlete!leaves!the!ground.!For!these!reasons,!
vertical!jump!tests!have!been!popularized!with!classic!testing!batteries!and!procedures![1–3,5,6].!
Since!maximal!power!output!(Pmax)!is!a!key!physical!component!of!performance!in!many!sports,!
and!because!vertical!jumps!like!SJ!and!CMJ!require!athletes!to!produce!mechanical!(potential)!
work!over!a!short!duration!to!displace!their!body!mass!(i.e.!the!dimension!of!mechanical!power),!
jump!height!is!frequently!used!as!an!indicator!of!Pmax![3].!For!example,!in!a!recent!survey!about!
strength! and! conditioning! practice! in!elite! rugby! union! [4],! the! authors! report! that! the! most!
commonly!used!test!of!muscular!power!was!maximum!CMJ!height.!
In!this!article,!we!contend!that!maximum!SJ!and!CMJ!height!are!in!fact!poor!indicators!of!lower!
limb!Pmax!in!trained!populations.!To!support!our!opinion,!we!have!first!detailed!the!theoretical!
reasons! explaining! why! jump! height! and! Pmax!are! not! fully! related.! We! then! provided!
experimental!evidence!of!the!poor!to!very!poor!associations!between!SJ!or!CMJ!height!and!Pmax.!
Finally,!we!detailed!a! simple! and!field-based!procedure!to!accurately!compute! Pmax! from! SJ!or!
CMJ!height!measurements.!The!latter!may!allow!researchers!and!practitioners!to!improve!their!
assessment! of! Pmax,! using! SJ! or! CMJ! height!as! inputs! with! a! simple! yet! accurate! computation!
method![7–9],!of!which!calculation!spreadsheets!are!freely!available!online!!
(https://www.researchgate.net/publication/320146284_JUMP_FVP_profile_spreadsheet).!
!
!
2. THEORETICAL+DEMONSTRATION+
!
We!detailed!the!three!main!factors!that!account!for!the!discrepancy!between!jump! height! and!
lower! limb! Pmax!in! this! section:!individual! push-off! distance! (hPO),! optimal! loading! (Lopt)! and!
force-velocity!(Fv)!profile.!!
!
2.1. +Push-off+distance+
The!SJ!and!CMJ!motions!require!the!athlete!to!produce!(mainly!with!their!lower!limb!extensor!
muscles)!and!exert!force!onto!the!supporting!ground!during!the!push-off!phase.!This!phase!lasts!
from!the!starting!(SJ)!or!most!downward!(CMJ)!position!classically!set!at!~90°!knee!angle!to!the!
take-off!position!with!fully!extended!lower!limb.!The!distance!over!which!the!lower!limb!extends!
during!the! push-off!phase!(hPO)!thus!represents!the!distance!over!which!muscles!will!generate!
force! and! mechanical! work! [8].! Thus,! it! is! clear! that! two! athletes! with! different! lower! limb!
segment!lengths!(even!for!a!given!same!body!stature)!may!have!very!different!hPO!values!while!
pushing!from!the!90°!starting!position!to!their!extended!limb!take-off!position.!In!turn,!should!
they!have!the!same!maximal!SJ!or!CMJ!height,!they!would!present!different!push-off! distances!
and!times,!leading!to!very!different!levels! of! power! output.!The!athlete!with!a!greater!hPO!will!
also! show,! ceteris* paribus,! a! lower! mechanical! power! output,! and! vice* versa.! The! theoretical!
importance!of!hPO!in!the!SJ!height!performance!equation!has!been!demonstrated!by!Samozino!et!
al.![10]!and!is!not!negligible.!Furthermore,!Markovic!et!al.![11]!showed!that!body!mass!and!CMJ!
depth!(which!is!equivalent!to!hPO)!clearly!confounded!the!relationship! between! muscle! power!
output!and!jumping!performance.!These!authors!also!suggested!that!the!effect!of!hPO!should!be!
controlled!when!interpreting!the!inter-individual!results!of!SJ!or!CMJ!tests.!

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
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This% crucial% importance% of% hPO%helps% to% explain% the% outstanding% jumping% capability% in% some%
animals%with%muscular%force%outputs%that%are%not%clearly%superior%to%human%athletes%[12].%In%the%
sports%performance%context,%not%taking%into%account%the%effect%of%hPO%on%SJ%or%CMJ%performance%
may%result%in%misleading%interpretations%of%jump%tests%as%predictors%of%power%output,%with%a%bias%
toward% underestimating% the% power% capability% of% an% athlete% with% a% small% hPO%and% conversely%
overestimating%that%of%an%athlete%with%a%great%hPO.%This%issue%may%be%of%particular%importance%in%
young% age% categories% (in% which% variable% hPO% may% be% observed% among% athletes% of% the% same%
chronological%age)% when%using%SJ%or%CMJ%height%as%a% screening-selection%test.%Finally,%hPO%is%not%
only%determined%by%individual%anthropometrical%factors,%but%also,%when%it%is%freely%chosen,%by%the%
self-selected%starting%position%(SJ)%or%countermovement%depth%(CMJ).%The%latter%are%associated%to%
muscle%force-length% properties,%training% history% or% sport% specificities,%which% supports%the% fact%
that%hPO%should%be%carefully%controlled.%
%
2.2. #Optimal#loading#
In%any% type%of% exercise%allowing% maximal%muscular% exertions%(e.g.% throwing,%jumping,% cycling,%
running),% the% loading% conditions% influence% movement%velocity% (following%the% laws%of% motion),%
which%in%turn%influences%power%output,%with%Pmax%achieved%only%in%an%optimal%loading%condition%
(Lopt)%[13–15].%For%example,%should%the%external%loading%be%too%heavy%or%too%light,%the%conditions%
would%lead%the%athlete%to%produce%higher%levels%of%force%or%velocity,%respectively,%but%in%both%cases%
this%would%be%associated%with%sub-maximal%levels%of%power%output.%This%is%well%described%by%the%
second%degree%polynomial%relationship%observed%between%movement%velocity%output%and%power%
output%in%various%types%of%exercises%[16–20].%%
In%the%specific%context%of%vertical%jumps,%external%loading%influences%the%power%output%[14,15,21]%
and%Pmax%is%only%produced%in%Lopt%conditions.%Thus,%Pmax%is%achieved%by%a%given%individual%in%a%SJ%or%
CMJ%only%if%their%individual%Lopt%is%equal%to%their%body%mass.%This%corresponds%to%the%“maximum%
dynamic% output% hypothesis”% [13,22–24].% However,% due% to% individual% neuromuscular%
characteristics,%and%training%history,%some%athletes%have%a%Lopt%that%differs%from%their%own%body%
mass,% and% would% need% either% positive% (additional% load)% or% negative% (assistance,% unloaded%
conditions)%loading%to%jump%with%their%Lopt%[23,25].%%
As%a%conclusion%to%this%section,%it%is%important%to%distinguish%the%power%output%developed%during%
a%maximal%(i.e.%all-out)%single%effort%(e.g.%SJ%or%CMJ)%to%the%maximal%power%output.%Inferring%that%
SJ%or%CMJ%height%is%associated%with%optimal%loading%conditions%(and%thus%Pmax)%is%only%correct%if%
the%individual%athlete%tested%has%their%own%body%mass%as%Lopt,%which%is%a%substantial%assumption.%
#
2.3. #Force-velocity#profile#and#optimal#profile#
Samozino% et% al.% [9,21]%have% clearly% shown,% using% a% theoretical% approach% [10]% confirmed% by%
experimental% evidence% [19,26],% that% SJ% height% was% almost% entirely% explained% by% the% following%
variables:%Pmax,%hPO%and%the%slope%of%the%Fv%profile.%Thus,%added%to%the%previous%section%about%the%
influence% of% hPO,% it% is% clear% that% the% relationship% between% maximal% jump% height% and% Pmax%is%
confounded%by%the%balance%between%the%athletes’%force%and%velocity%capabilities,%as%described%by%
their%Fv% profile.%The%two%implications%shown%by%Samozino%et%al.’s%works%are%that%(i)%for%a% same%
hPO%and%Pmax,% different%levels% of%SJ% height%may% be% achieved% depending% on% the% Fv% profile% of% the%
athletes%and%(ii)%the%theoretical%maximal%SJ%height%for%a%given%individual%(given%their%hPO%and%Pmax)%
is%only%reached% if% the%actual%Fv%profile%is%equal%to%the%calculated%optimal%Fv%profile%(and%in%this%
case,%body%mass%is%the%Lopt)%[8,10,19,26].%In%other%words,%an%athlete%with%an%optimal%Fv%profile%for%
jump%height% will%have% his%own% body%mass% as%Lopt,% and%thus% produce%Pmax% during% vertical%jump%
without%additional%load.%
The% relative% influences% of% hPO,% Pmax% and% Fv% profile% on% SJ% performance% are% summarized% in% the%
following%equation,%that%has%been%validated%experimentally%[19,26]:%
!"#$ %&'()
*+
,-./01)
23*
&45
6 78
"#$9:;<=> 7? 3,-. /01
*
*
%%%%%Eq.1%

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
5
In#this#equation,#hmax#is#the#maximal#possible#SJ#height#reached#with#an#optimal#Fv#profile#SFvopt.#
Note#that#these#demonstrations#have#been#initially#published#using#SJ#as#the#jump#modality,#but#
subsequent#works#by#Jimenez-Reyes#et#al.#have#shown#that#similar#conclusions#could#be#drawn#
for#the#CMJ#modality#[7].##
A#practical#summary#of#the#above-mentioned#theoretical#points#is#that#the#relationship#between#
SJ#or#CMJ#height#is#clearly#confounded#by#individual#anthropometrical#and#physiological#factors#
inherent# to# each# athlete# tested.# Not# taking# these# factors# into# account# may# lead# to# bias# when#
quantifying# Pmax#via# single# jump# tests# without# additional# load,# as# will# be# evidenced# with# the#
following#simulations#(Table#1)#and#the#experimental#measurements#discussed#in#section#3.#
#
3. EXPERIMENTAL-EVIDENCE-
#
To#support#our#point#that#the#relationship#between#SJ#or#CMJ#height#and#lower#limb#Pmax#is#poor#
to#very#poor#with#experimental#evidence,#we#will#first#list#and#discuss#the#published#correlations#
between#these#variables.#Then,#we#will#present#some#experimental#data#we#have#collected.#
Table#2#shows#a#few#examples#limited#to#studies#reporting#jump#height#measurements#and#the#
magnitude# of# their# correlation# to# lower# limb# maximal# power# output# as# measured# with# the#
reference# force# plate# method,# and# expressed# in# Watts.# Independently# from# their# statistical#
significance,#these#correlations#are#of#rather#low#magnitude#to#accurately#estimate#power#output#
and#Pmax#from#jump#height,#on#an#individual#basis.##
-
Table&2.)Pearson’s)correlation)coefficients)and)linear)regression)coefficients)between)jump)height)
and)lower)limb)peak)instantaneous)power)measured)with)force)plates)and)expressed)in)Watts.)The)
population)age)is)displayed)as)an)average)value) or)range)of)values)for)the)group.)SJ:)Squat)Jump.)
CMJ:)Counter)Movement)Jump.))
Reference-
Number-and-Type-of-
subjects-
Type-
of-
jump-
Correlation-
Coefficient-and-
Magnitude-
Linear-
Regression-
Coefficient-
Bridgeman#
et# al.# 2016#
[27]#
12#
Males#(25.4#±#3.5#yrs),#
strength#trained#
CMJ#
0.62#-#Large#
0.38#
Young#et#al.#
2011#[28]#
23#
Males#(22.3#±#2.1#yrs),#
elite#Australian#
football#players#
CMJ#
0.41#-#Moderate#
0.17#
Amonette#
et# al.# 2012#
[29]#
415#
Males#(15.7#±#2.8#yrs),#
soccer,#American#
football,#kinesiology#
students#
CMJ#
0.65#-#Large#
0.42#
Markovic#
and# Jaric.#
2007#[30]#
159#
Males#(18-25#yrs),#
physical#education#
students#
SJ#
CMJ#
0.47#-#Moderate#
0.66#-#Large#
0.22#
0.44#
#
#
Although# the# magnitude# of# the# correlation# between# jump# height# and# Pmax# may# be# improved#
through# allometric# scaling# (see# 4.# Practical# solutions),# the# relationship# between# these# two#
variables#is#not#acceptable,#in#our#opinion,#to#accurately#infer#Pmax#from#SJ#or#CMJ#measurements,#
on#an#individual#athlete’s#basis.#Not#to#mention#the#use#of#this#estimation#in#the#context#of#sports#
performance#monitoring#or#athlete’s#screening/selection#process.##

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
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Table&1.!Theoretical!simulation!of!the!relative!error!induced!in!squat!jump!power!output!computations!when!not!taking!the!potential!effects!
of!body!mass,!push-off! distance,!force-velocity!profile,!optimal!profile! and!optimal!load!into!account.! Typical!values!for!a!male! athlete!are!
taken!as!reference!(athlete!1)!and!compared!to!other!athletes!showing!the!same!jump!height!in!standard!(no!additional!load)!conditions,!but!
different!values!for!other!mechanical!variables.!Note!that!the!analysis!would!be!similar!for!countermovement!jump.!Athletes!#2,!#3!and!#4!
only!show!one!different!variable!from!athlete!#1,!whereas!athlete!#5!shows!differences!in!all!variables.!In!the!real!world,!an!almost!infinite!
number! of! combinations! and! ranges! is! theoretically! possible! for! different! mechanical! variables! of! importance.! In! the! current! example,! a!
maximal!error!of!38%!has!been!computed!between!two!individuals!showing!the!same!jump!performance!of!27!cm.!Negative!additional!loading!
indicates!an!unloaded!jump!condition!(e.g.!with!assistance!provided!by!elastic!bands).!Note!that!only!one!type!of!change!(increase/decrease)!
has!been!shown!for!each!variable!(for!clarity!reasons),!but!errors!magnitudes!induced!by!opposite!changes!are!similar.!
The!equations!used!to!perform!these!computations!have!been!validated!and!discussed!by!Samozino!et!al.!
[
8,10,19,26
]
.!
Athlete&ID&
and&
comparisons&
Body&
mass&
(kg)&
Push-off&
distance&
hPO&(m)&
Standard&
jump&height&
(no&
additional&
load)&(m)&
Power&
output&
during&the&
standard&
jump&(m)&
Slope&of&the&
Fv&
relationship&
SFv&(in&%&of&
SFvopt)&
Optimal&
load&
(BW)&
Optimal&
additional&
load&(kg)&
Maximal&
power&
output&
Pmax&(W)&
Maximal&
power&
output&
Pmax&
(W/kg)&
!"#
$%#
%&'(#
%&)*#
"+%%#
"%%#
"&%%#
%#
"+%%#
)%&%#
!)#
*%#
%&'(#
%&)*#
",%%#
"%%#
"&%%#
%#
",%%#
)%&%#
!)#-./010#!"2#345#567839#5:.#"%#79#;4<./#=4>?#@600#8354#6AA4135#;.6>0#54#6#")&(B#>8CC./.3A.#83#6=04;15.#D4<./#C4/#5:.#06@.#E1@D#:.89:5#
!'#
$%#
%&)(#
%&)*#
"$*F#
"%%#
"&%%#
%#
"$*F#
)'&(#
!'#-./010#!"2#345#567839#5:.#"%#A@#;4<./#hGH#8354#6AA4135#;.6>0#54#6#"*&(B#>8CC./.3A.#83#@6I8@6;#D4<./#C4/#5:.#06@.#E1@D#:.89:5#
!,#
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!,#-./010#!"2#345#567839#5:.#∼',B#>8CC./.3A.#83#4D58@6;#D/4C8;.#4/#;46>#8354#6AA4135#;.6>0#54#6#∼,B#>8CC./.3A.#83#6=04;15.#D4<./#C4/#5:.#06@.#E1@D#:.89:5#
!(#
F%#
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)""'#
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),&(#
!(#-./010#!"2#-6/8410#A4@=83658430#4C#5:.#041/A.0#4C#=860#@6?#;.6>#54#6#'$B#>8CC./.3A.#K13>./.058@65843L#83#@6I8@6;#D4<./#415D15#C4/#5:.#06@.#E1@D#:.89:5#

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
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By#adding#experimental#data#to#illustrate#our#point,#we#have#measured#SJ#or#CMJ#height#and#!max#
values#in#trained#populations#(sprint,# weightlifting#and# elite# rugby#league#competitors)#within#
various# published# and# in-review# research# protocols# [7,31].# Both# jump# height# and# !max#were#
assessed# using# a# force# plate# system,# and# !max# was# determined# as# the# apex# of# the# load-power#
relationship#for#several#loaded#jump#conditions#(see#[19,26]#for#details).#Note#that#most#studies#
cited#in#this#paper#did#not#use#this#approach#to#determine#!max,#but#rather#the#“peak”or#“maximal”#
value#of#instantaneous#power#output#measured#during#a#single#jump.##
It#is#clear#from# this# dataset# (Fig.#1#and#2)#of#trained#to#elite#athletes#(n=90#for#SJ#and#n=68#for#
CMJ)# that# the# correlations# between# !max# and# jump# height# were# not# systematically# very# large#
(r=0.493#to#0.877),# although# improved#(not#for#CMJ# in#sprinters#and#jumpers,# Figure# 2)#when#
normalizing#!max#to#body#mass.#
!
Fig.&1.&"#$$%&'()#*+,-!%'$+#*.+,$/,0%(1%%*,+23'(,4356,7%)87(,'*9,'0+#&3(%,-6'*%&,':/,#$,$%&'();%,(#,
0#9<,5'++, -6'*%&,0:/,5'=)5'&, 6#1%$,#3(63(, )*, 7)87&<>($')*%9, +6$)*(%$+?, 1%)87(&)@(%$+,'*9, $380<,
&%'83%,6&'<%$+,,
!
!
!
Fig.&2.&"#$$%&'()#*+,-!%'$+#*.+,$/,0%(1%%*,A#3*(%$5#;%5%*(,4356,7%)87(,'*9,'0+#&3(%,-6'*%&, ':/,
#$,$%&'();%,(#,0#9<,5'++,-6'*%&,0:/,5'=)5'&,6#1%$,#3(63(,)*,7)87&<>($')*%9,+6$)*(%$+,'*9,4356%$+:,,
!
!

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
7
Furthermore,*the*corresponding*low*regression*coefficients*(overall*r2*<*0.56)*show*that*a*large*
part*of*the*variance*in*Pmax*is*not*directly*explained*by*the*variance*in*jump*height.*Jump*height*
and*Pmax*are*significantly*correlated,*but*the*magnitude*of*the*correlations*is*not*high*enough*to*
estimate*the*latter*accurately*from*the*former.*In*line*with*the*theoretical*points*listed*above,*
possible*explanations*for*the*relatively*low*correlations*observed*for*the*overall*group*(Fig.*1)*
include:*variable* hPO* values*among*athletes,* heterogeneous*individual*Fv*profiles* and* optimal*
profiles,*and*in*turn*optimal*load*that*differs*from*body*mass*for*some*athletes*(which*was*the*
case*for*most*rugby*players).*
Finally,*two*recent*studies*show*that*athlete’s*absolute*lower*limb*power*output*capability*could*
not*be*appropriately*categorized*or*estimated,*in*most*sports,*from*jump*height*measurements*
[32,33].*Among* the*practical* solutions*to* solve*this* issue,*the* current*authors*propose* to* use*
estimations*based*on*regressions,*and*allometric*scaling*of*raw,*absolute*power*values.*In*the*
next*section* we* will*discuss* these*possibilities* and* their*limitations,* and*support* the* use*of* a*
more*direct,*accurate*and*practical*method*we*recently*validated.*
*
4. PRACTICAL*SOLUTIONS*
*
4.1. Regression-based*estimation*equations**
One*solution*to*better*estimate*Pmax*from*SJ*or*CMJ*measurements*has*been*the*use*of*regression-
based*equations.*Briefly,* a* regression*(usually* linear)* equation*is* generated* from*actual*jump*
height*and*Pmax*measured*with*reference*methods*(e.g.*force*plate)*in*a*set*of*subjects.*Then,*the*
accuracy*of*the*Pmax*values*“predicted”*by*the*equation*(which*inputs*are*often*jump*height*and*
a*few*simple*variables*such*as*body*mass*or*height)*is*assessed*by*comparison*to*those*obtained*
with*the*reference*methods.* Numerous* regression*equations*have*been*published* to* estimate*
Pmax* (e.g.[34–39]).* However,* although* practical,* this* estimation* method* has* several* major*
limitations.*The*first*limitation*is*the*lack*of* theoretical* rationale* supporting*the*link*between*
Pmax,* jump* height* and* body* mass,* notably* via* a* simple* weighted* addition*of* the* two* latter*
variables*(see*2.*Theoretical*demonstration).*Another*limitation*of*such*equations*is*that*they*
are* population-dependent,* which* may* lead* to* a* lower* accuracy* for* estimating* power* on* an*
individual*basis.*For*instance,*Quagliarella*et*al.*[40]*performed*a*detailed*comparative*study*of*
several*equations,*and*reported*very*high*error*values*(>50%)*and*concluded*that*the*use*of*Pmax*
estimates,*can* only* be*useful*to*compare*the*performance*of*groups*of*subjects.* Discrepancies*
and*equation-dependant*accuracy*of*prediction*were*also*observed*in*other*comparative*studies*
[8,36,41,42],* making* the* use* of* regression-based* estimates* irrelevant* for* an* individually*
accurate*determination*of*lower*limb*Pmax.*
*
4.2. Allometric*scaling*
Accounting*for*the*potential*influence*of*body*dimensions*(mostly*stature*and*mass)*on*Pmax*as*
estimated*through*SJ*or*CMJ*measurements*can*be*done*by*scaling*the*raw,*absolute*value*of*Pmax*
to*a*power*of*these*body*dimensions*[43,44].*For*instance,*scaling*Pmax*to*body*mass*(SJ)*or*body*
mass* and* countermovement* depth* (CMJ)* at* the* power* 1* resulted* in* markedly* increased*
correlation*coefficients*with*jump*height*[11].*This*led*to*researchers*recommending*the*use*of*
allometric*scaling*to*more*accurately*estimate*Pmax*from*jump*height*[30,32,33].*In*particular,*
Markovic*and*Jaric*[30]*proposed*that*the*most*justified*and*accurate*scaling*was*when*muscle*
power*was*proportional* to* body*mass*raised*to* the* power*of*0.67*(and* even* more*accurately*
0.75*as*discussed*by*these*authors)*to*account*for*the*theory*of*geometric*similarity,*that*states*
that*some*physiological*features*of* mammals* bodies*(e.g.*muscle*physiological*cross-sectional*
area)*are*not*directly*proportional*to*body*mass*[45].**
However,*allometric*scaling*is*a*correction*method*that*is*also*based*on*assumptions,*and*may*
not* apply* correctly* in* heterogeneous* populations,* and/or*in* the* case* of* very* specific* body*
composition*and*especially*skeletal*muscle*mass*as*developed*through*years*of*specific*training*
in*elite*athletes.*Kons*et*al.*recently*showed*that*the*improvement*of*correlations*between*jump*

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
8
height& and& Pmax& through& allometric& scaling& was& highly& sport-specific&[33].& Interestingly,& Fig.&1&
shows& that& the& correlation& strongly& differs& between& elite& rugby& players& and& other& athletes&
compared&when&normalizing&Pmax&to&body&mass,&leading&to&an&overall&lower&correlation&when&all&
athletes& are& considered.& This& tends,& again,& to& show& that& indirect& methods& (regression-based&
estimates&or&allometric&scaling)&may&not&totally&solve&the&individual&accuracy&issue&discussed&in&
this&article.&To&this&aim,&an&alternative&method&has&been&proposed&10&years&ago&[8],&that&directly&
computes&jumping&power&output&and&Pmax,&based&on&a&biomechanical&model&and&simple&inputs,&
as&described&in&the&following&section.&&
&
4.3. Direct*computation*using*a*simple*field*method*
In&order&to&solve&most&of&the&previously&described&issues&and&provide&a&simple&and&practical&yet&
accurate&way&to&compute&force,&velocity&and&power&output&during&a&SJ&push-off,&Samozino&et&al.&
have& proposed& and& validated& a& computation& method& in& 2008& [8].& This& method,& based& on&
macroscopic&modelling&of&body&mass&displacement&and&the&associated&mechanical&external&work,&
requires&only&body&mass,&hPO&and&jump&height.&The&initial&reliability&and&concurrent&validity&was&
tested&against&reference&force&plate&measurements&[8],&and&was&confirmed&in&subsequent&studies&
from&other&authors,&including&additional&load&conditions&and&application&to&CMJ&[7,46,47].&
In&this&method,&the&mean&power&produced&during&a&jump&was&computed&as:&
! " #$ %
%&'
( ) *%
+&&&&&&&&&Eq.&2&
&
with&m&the&body&mass,&g&the&gravitational&acceleration,&hPO&the&vertical&push-off&distance,&and&h&
the& jump& height.& In& this& work,& jump& height& was& defined& as& the& aerial& distance& covered& by& the&
center&of&mass&between&the&take-off&and&vertical&apex&instants.&
It& has& also& been& confirmed& that& Pmax& can& be& accurately& computed& from& multiple-load& jump&
protocols&as:&
!
,-. "/
01
0
2&&&&&&&&&&&Eq.&3&
&
F0&and&V0&being&the&force&and&velocity-axes&intercepts&of&the&linear&Fv&relationship&obtained&from&
the&multiple-load& measurements&[19].&However,& since&many& human& subjects&(especially& those&
with&no&extensive&force-&or&velocity-oriented&training)&show&a&Pmax&that&is&close&to&their&SJ&power&
output,&Pmax&might&be&correctly&computed&by&using&the&SJ&power&value.&
Like& all& biomechanical& models,& this& method& has& assumptions& and& limitations& that& have& been&
discussed&extensively&elsewhere&[8,21,48].&In&addition,&these&computations&lead&to&mean&values&
during&the&push-off&phase,&as&opposed&to&peak&values&estimated&in& many& studies& (e.g.& [27,49]).&
That&said,&even&if&instantaneous&and&mean&values&may&reasonably&be&assumed&to&be&linked&during&
vertical& jumps,& mean& values& (i.e.& averaged& over& the& whole& movement)& appeared& to& be& more&
representative&of&the&muscular&effort&[9,50].&&
That&being&said,&given&the&reliability&and&external&validity&of&this&equation&to&compute&SJ&and&CMJ&
power& output& (and& also& easy& to& obtain& Pmax),& we& believe& these& limitations& do& not& induce&
meaningful& errors& and& bias,& and& are&largely&outweighed& by& the& possibility& to& simply& and&
practically&calculate&jump&power,&from&jump& height.& This& is&all&the&more&important&since&jump&
height& measurements/estimations& alone& show& some& clear& limitations,& as& discussed& in& the&
previous&sections.&Interestingly,&this&method&has&been&integrated&in&a&very&practical&and&reliable&
[51–53]& smartphone& app& (MyJump2),& allowing& cheaper& yet& accurate& computations& of& jump&
height&and&power&output,&from&a&simple&high-speed&video&recording&of&the&jumps.&
&
&
&
&
&

Morin&et&al.&Pre-Print&–&2018&–&Jump&height&is&a&poor&indicator&of&lower&limb&maximal&power&output&
9
!
5. CONCLUSIONS*
Given! (i)! the! several! limitations! of! using! jump! height! measurements! to! accurately! infer! an!
athlete’s! lower! limb! power! output! capabilities,! and! (ii)! the! possibility! to! more! accurately!
calculate!mean!power!output!during!SJ!or!CMJ!based!on!body!mass,!lower!limb!length!and!jump!
height!using! Equation! 2,! we! strongly! recommend! that! sports! performance,! medicine,! and!
research!colleagues!use!the!method!proposed!by!Samozino!et!al.![8,26],!instead!of!the!standard!
measure!of!jump!height!alone.!This!may!lead!to!a!richer!level!of!information,!from!the!very!same!
input!measurements.!
*
ACKNOWLEDGEMENTS*
*
The! authors! wish! to! thank! Dr! Slobodan! Jaric,! who! has! influenced! some! of! the! concepts! and!
thinking! behind! this! work,! through! his! major! contributions! to! the! field,! and! his! friendly!
discussions!and!remarks.!We!were!very!sad!to!learn!that!Dr!Jaric!had!passed!away! during! the!
writing!process!of!this!paper.!
Authors!have!no!source!of!funding!or!conflict!of!interest!to!declare!regarding!this!paper.!
*
*
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