sport training is based on the optimal prescription of exercise mode , duration and intensity .
a daily task of coaches and fitness trainers is to plan an exercise program of adequate intensity . on the contrary , special care
when working with athletes , coaches and fitness trainers often establish training heart rate ( hr ) intensities for aerobic exercise based on maximal hr ( hrmax ) , for example karvonen method.1 hrmax is measured as the maximal value recorded in the end of graded exercise test ( gxt ) either in a laboratory or in field . however , occasionally it is desirable not to perform a gxt , for example to avoid the fatigue induced by maximal testing during the competitive period .
when it is not possible to measure hrmax , its prediction from an age - based equation is an alternative , which is widely used by coaches and fitness trainers .
two popular equations used in the daily sport practice are those of fox , naughton and haskell ( fox - hrmax = 220-age)2 and tanaka , monahan and seals ( tanaka - hrmax = 208 - 0.7age).3 the validity of these equations has been examined extensively in large samples of adults ( e.g.34567891011 ) and in specific categories of population , for example healthy,312 sedentary,510 overweight,7 sport813 and individuals with mental retardation.6 the aforementioned studies have used a gxt in a laboratory setting to elicit hrmax . in contrast , only a few studies have been conducted in children and adolescents91415 and using a field protocol.16 few studies had a longitudinal design.1718 while available studies provide important data regarding the estimation of hrmax , the research is by no means complete nor has it has been consistent .
one particular area of concern is that athletes and adolescents are under - represented in this body of research . in a recent study
, it was shown that athletes of speed / power sports had similar measured - hrmax with endurance athletes and both had lower values than those who were untrained.19 this difference between trained and untrained individuals highlights the need to examine the popular prediction equations in sport samples .
in addition , the various protocols of gxt in laboratory and in field may elicit different values of hrmax .
for instance , a study on soccer players revealed higher hrmax in a field test ( multistage shuttle run ) than in a gxt on treadmill.20 in a recent study of the validity of prediction equations in soccer players , fox - hrmax overestimated and tanaka - hrmax underestimated measured - hrmax , a new formula was suggested for adolescent soccer players ( 223 - 1.44age ) and the need to examine the validity of these equations in more sport populations was highlighted.21 therefore , the aim of this study was to examine the validity of fox - hrmax , tanaka - hrmax and nikolaidis - hrmax in a large sample of young team sport athletes .
in addition , we investigated whether these relationships vary according to age group ( u-12 , 9 - 12 years vs. u-15 , 12 - 15 years vs. u-18 , 15 - 18 years ) .
a total of 147 athletes from soccer , futsal , basketball and water polo clubs in the region of athens were recruited to participate in this study , which was conducted in 2 days .
on the 1 day , the participants visited the laboratory , where they were examined for anthropometry . on the 2 day , within a week from the first session , they performed a gxt ( 20 m shuttle run test , srt ) in an indoor court .
an electronic weight scale ( hd-351 tanita , illinois , usa ) was employed for weight measurement ( in the nearest 0.1 kg ) , a portable stadiometer ( seca , leicester , uk ) for height ( 0.001 m ) and a caliper ( harpenden , west sussex , uk ) for skinfolds ( 0.5 mm ) .
body mass index ( bmi ) was calculated as the quotient of body mass ( kg ) to height squared ( m ) , and body fat percentage ( bf ) was estimated from the sum of 10 skinfolds ( cheek , wattle , chest i , triceps , subscapular , abdominal , chest ii , suprailiac , thigh and calf ; bf = 41.32 + 12.59  logex , where x the sum of 10 skinfolds).22 gxt .
aerobic capacity was tested with the widely used 20 m srt.2324 briefly , after a 20 min warm - up including jogging and stretching exercises , participants performed an incremental running test in an indoor court between two lines 20 m apart .
initial speed was set at 8.5 km.h and increased every minute by 0.5 km.h till exhaustion . during the late stages of the test
in addition , they had been instructed to adhere strictly to the speed that was dictated by audio signals .
hr was recorded continuously during the test by team2 pro ( polar electro oy , kempele , finland ) .
statistical analyses were performed using ibm spss v.20.0 ( spss , chicago , usa ) .
one - way analysis of variance ( anova ) was used to examine differences between the age groups ( u-12 , u-15 and u-18 ) .
one - way repeated measures anova was used to examine differences between measured and predicted hrmax . to interpret effect sizes for statistical differences in the anova we used eta square classified as small ( 0.010 <   0.059 ) , medium ( 0.059 <   0.138 ) and large (  > 0.138).25
bland - altman26 analysis was used to examine the accuracy and variability of prediction equations .
associations between measured hrmax and age were examined using pearson 's product moment correlation coefficient ( r ) .
magnitude of correlation coefficients were considered as trivial ( r  0.1 ) , small ( 0.1  r < 0.3 ) moderate ( 0.3  r < 0.5 ) , large ( 0.5  r < 0.7 ) , very large ( 0.7  r < 0.9 ) and nearly perfect ( r  0.9 ) and perfect ( r = 1 ) .
statistical analyses were performed using ibm spss v.20.0 ( spss , chicago , usa ) .
one - way analysis of variance ( anova ) was used to examine differences between the age groups ( u-12 , u-15 and u-18 ) .
one - way repeated measures anova was used to examine differences between measured and predicted hrmax . to interpret effect sizes for statistical differences in the anova we used eta square classified as small ( 0.010 <   0.059 ) , medium ( 0.059 <   0.138 ) and large (  > 0.138).25 bland - altman26 analysis was used to examine the accuracy and variability of prediction equations .
associations between measured hrmax and age were examined using pearson 's product moment correlation coefficient ( r ) .
magnitude of correlation coefficients were considered as trivial ( r  0.1 ) , small ( 0.1  r < 0.3 ) moderate ( 0.3  r < 0.5 ) , large ( 0.5  r < 0.7 ) , very large ( 0.7  r < 0.9 ) and nearly perfect ( r  0.9 ) and perfect ( r = 1 ) .
briefly , our sample was comprised of u-12 ( 34% ) , u-15 ( 27% ) and u-18 athletes ( 39% ) .
there were significant differences between age groups for age , weight , height and bmi .
the older the age group , the heavier , taller with higher bmi and aerobic capacity were the athletes .
moreover , u-18 had lower bf than u-12 ( 2.3% ) and u-15 ( 2.9% ) , while there was no difference with regard to the measured - hrmax ( f2,144 = 1.2 , p = 0.308 ,  = 0.02 ) .
descriptive characteristics , shown as mean ( standard deviation ) values of participants by age group the measured - hrmax and predicted - hrmax can be found in table 2 . when using an anova with repeated measures with a greenhouse - geisser correction , the mean score for hrmax differed statistically significantly between measured and predicted values in the total sample ( f1.072,156.441 = 103.0 , p < 0.001 ,  = 0.41 ) , in u-12 ( f1.007,49.348 = 51.2 , p < 0.001 ,  = 0.51 ) , in u-15 ( f1.006,39.224 = 26.4 , p < 0.001 ,  = 0.40 ) and in u-18 ( f1.010,56.569 = 43.0 , p < 0.001 ,  = 0.43 ) .
post hoc tests using the bonferroni correction revealed that in the total sample , fox - hrmax and nikolaidis - hrmax overestimated measured - hrmax [ 5.5 bpm ( 3.7 ; 7.2 ) , mean difference ( 95% confidence intervals ) and 2.5 bpm ( 0.7 ; 4.3 ) , respectively ] , while tanaka - hrmax underestimated measured - hrmax [ 2.4 bpm ( 4.2 ; 0.7 ) ] . measured - heart rate ( hr)max and age - predicted hrmax , shown as mean ( standard deviation ) values of participants by age group in addition
fox - hrmax and nikolaidis - hrmax overestimated measured - hrmax [ 7.1 bpm ( 3.8 ; 10.3 ) and 5.4 bpm ( 2.1 ; 8.6 ) , respectively ] , whereas tanaka - hrmax provided similar values as measured - hrmax [ 1.7 bpm ( -5.0 ; 1.5 ) - . in u-15 ,
fox - hrmax overestimated measured - hrmax [ 6.2 bpm ( 2.4 ; 10.3 ) ] , while nikolaidis - hrmax and tanaka - hrmax provided similar values as measured - hrmax [ 3.3 bpm ( 0.6;7.1 ) and 1.8 bpm ( -5.6;2.0 ) , respectively ] . in u-18 ,
fox - hrmax overestimated [ 3.6 bpm ( 1.2 ; 6.0 ) ] , tanaka - hrmax underestimated [ 3.5 bpm ( -5.9 ; 1.1 ) ] , while nikolaidis - hrmax provided similar values as measured - hrmax [ 0.6 bpm ( 3.0 ; 1.8 ) ] .
hrmax was not correlated with age in the total sample ( r = 0.11 , p = 0.201 ) .
the respective correlations separately for u-12 , u-15 and u-18 were also trivial to small and non - significant : r = 0.03 ( p = 0.829 ) , r = 0.22 ( p = 0.181 ) and r = 0.16 ( p = 0.242 ) , respectively .
relationship between age and maximal heart rate ( hrmax ) in participants figures 2 , 3 and 4 show bland - altman plots of the difference between predicted - hrmax and measured - hrmax in total and in each age group for fox - hrmax tanaka - hrmax and nikolaidis - hrmax , respectively . in general
, we observed that there was overestimation of hrmax at low values of hrmax and underestimation of hrmax at high values of hrmax .
bland - altman plots of the difference between fox - hrmax and measured - hrmax in the total sample ( a ) , u-12 ( b ) , u-15 ( c ) and u-18 participants ( d ) bland - altman plots of the difference between tanaka - hrmax and measured - hrmax in the total sample ( a ) , u-12 ( b ) , u-15 ( c ) and u-18 participants ( d ) bland - altman plots of the difference between nikolaidis - hrmax and measured - hrmax in the total sample ( a ) , u-12 ( b ) , u-15 ( c ) and u-18 participants ( d )
the main finding of this study was that neither fox , tanaka nor nikolaidis equation provide accurate values of hrmax in the total sample of young athletes [ table 3 ] .
fox - hrmax overestimated measured - hrmax in total as well as in each age group .
thus , tanaka - hrmax was valid in u-12 and u-15 , while nikolaidis - hrmax was valid in u-15 and u-18 .
summary of the main findings our study did not confirm the findings of previous research supporting that fox - hrmax underestimates hrmax with increasing age,317 which should be attributed to the younger age of the participants in the present study .
in contrast , our findings confirmed that fox - hrmax overestimate hrmax in adolescents.15 this finding practically implies that adopting this widely used prediction equation in young athletes leads athletes to work at higher intensities than what it is desired .
the basic characteristics of participants were similar with those reported recently27 and the differences in weight , height , bmi and endurance between adolescent and adult players were in line with previous research.2728 the comparison between age groups with regard to their mean hrmax revealed no statistical difference , despite a trend for lower values in u15 ( 1.9 bpm ) and u18 ( 2.2 bpm ) than in the younger group , finding which was in accordance with the trivial , but not statistically significant , negative correlation between hrmax and age . however , these findings on the relationship between hrmax and age were not in agreement with the existing literature .
the variation of the span of chronological age may explain the discrepancy between this study and previous research with regard to the above mentioned correlation . in a previous study covering a relatively short span of ages ( 1016 years )
the correlation between hrmax and age was 0.10,15 while in studies with large span we observed large to very large correlations ( e.g. 15 - 75 years , r = 0.56,8 14 - 77 years , r = 0.60,11 16 - 71 years , r = 0.67,29 19 - 89 years , r = 0.60,12 16 - 65 years , r = 0.60,10 18 - 81 years , r = 0.79 ) .
therefore , it should not be a surprise the lack of significant and large correlation when the sample of participants , independently from its size , covers only a few years . compared with boys of similar age ( 10 - 16 years)15 who performed a gxt on treadmill , the athletes in the present study achieved similar hrmax . in addition , we found also similar values with another study on individuals aged 7 - 17 years.9 the main limitation of this study was that it presents the common drawbacks of any field gxt ; in opposition to the criteria of maximal effort [ e.g. plateau of oxygen uptake , hr > 90%-95% of hrmax , respiratory quotient > 1.15 and lactate > 9 - 10 mmol.l ] used typically in a laboratory setting , the only criterion to evaluate participants effort was their oral confirmation that they have run till exhaustion .
in addition , we examined only the relationship between hrmax and age and not the effect of other confounders on this relationship .
it has been suggested that the overestimation of hrmax might be associated with increased weight and smoking , while its underestimation with rest hr.11 however , an issue with important practical implications is to recognize the risks that coaches and fitness trainers undertake depending on which their choice of prediction equation is .
adopting tanaka equation , which consistently tends to provide low values of hrmax , might result in prescribing exercise of lower intensity than what it is desired .
in contrast , using fox or nikolaidis equation , which tend to overestimate hrmax , might result in prescribing high exercise intensity . to deal with this issue
, it is recommended to apply higher intensity in the first case and lower intensity in the other two cases.30
the results of this study failed to validate two widely used and one recently developed prediction equations in a large sample of young athletes , indicating the need for specific equation in different age groups .
based on the findings of the present study , coaches and fitness trainers are advised to prefer tanaka - hrmax when desiring to avoid overtraining , while fox - hrmax and nikolaidis - hrmax should be their choice in order to ensure adequate exercise intensity .
 background : although maximal heart rate ( hr)max is used widely to assess exercise intensity in sport training and particularly in various team sports , there are limited data with regards to the use of age - based prediction equations of hrmax in sport populations . 
 the aim of this study was to compare the measured - hrmax with three prediction equations ( fox - hrmax = 220-age and tanaka - hrmax = 208 - 0.7age and nikolaidis - hrmax = 223 - 1.44age ) in young team sport athletes.materials and methods : athletes of soccer , futsal , basketball and water polo , classified into three age groups ( u-12 , 912 years , n = 50 ; u-15 , 1215 years , 
 n = 40 ; u-18 , 1518 years , n = 57 ) , all members of competitive clubs , voluntarily performed a graded exercise field test ( 20 m shuttle run endurance test ) to assess hrmax.results:fox-hrmax and nikolaidis - hrmax overestimated measured - hrmax , while tanaka - hrmax underestimated it ( p < 0.001 ) . 
 however , this trend was not consistent when examining each group separately ; measured - hrmax was similar with tanaka - hrmax in u-12 and u-15 , while it was similar with nikolaidis - hrmax in u-18.conclusion:the results of this study failed to validate two widely used and one recently developed prediction equations in a large sample of young athletes , indicating the need for specific equation in different age groups . 
 therefore , coaches and fitness trainers should prefer tanaka - hrmax when desiring to avoid overtraining , while fox - hrmax and nikolaidis - hrmax should be their choice in order to ensure adequate exercise intensity . 
INTRODUCTION
MATERIALS AND METHODS
Statistical analyses
RESULTS
DISCUSSION
CONCLUSION