understanding the influence of population size on athletic performance

Available online at www.sciencedirect.com

Procedia Engineering 00 (2009) 000–000

Procedia Engineering

www.elsevier.com/locate/procedia

8th

Conference of the International Sports Engineering Association (ISEA)

Understanding the influence of population size on athletic

performance

Leon Fostera*, David James

a, Steve Haake

a

aSports Engineering Research Group, Centre for Sport and Exercise Science, Sheffield Hallam University, Sheffield, S10 2BP, United Kingdom

Received 31 January 2010; revised 7 March 2010; accepted 21 March 2010

Abstract

It is widely accepted that sports technology has made a major contribution to human athletic performance. In order to quantify the effect of sports technology one must first understand the influence of other factors. Human athletic performance is also related to the number of participants competing. As such it is hypothesised that the size of the global human population will be factor in athletic performance. Human performance in running events has been correlated with global gender population size. The data shows exponential decay trends which have been subsequently modelled using an exponential decay function (t = L+ aexp-bP). Results show that a further increase in global population will have little or no effect on running performances. © 2009 Published by Elsevier Ltd.

Keywords: Population; Athletic performance; Running performance; Athletics statistics; Empirical modelling; Exponetial decay

1. Introduction

Athletic performance in all sports has visibly increased since the inception of modern international competitions

at the end of the 19th

century. Evidence for this can be seen in the result statistics collected from a range of different

athletic competitions, and clearly seen in the progression of world records [1-4]. One factor that can explain the

improvements seen in athletic performances is the continued development of sports technology. The term sports

technology refers to any technology used in sports which can aid in sporting performance. However its influence

cannot explain all athletic improvements; as in the case of sports with little or no technology, there are still large

improvements in performance. For example the male marathon world record has been broken 36 times since 1908.

There are clearly many other factors that influence athletic performance: for instance, improved nutrition, coaching

or population changes.

* Corresponding author. Tel.: +44 (0) 114 225 2465; fax: +44 (0) 114 225 4356.

E-mail address: [email protected].

c© 2010 Published by Elsevier Ltd.

Procedia Engineering 2 (2010) 3183–3189

www.elsevier.com/locate/procedia

1877-7058 c© 2010 Published by Elsevier Ltd.doi:10.1016/j.proeng.2010.04.130

http://www.elsevier.com/locate/procedia

http://dx.doi.org/10.1016/j.proeng.2010.04.130

2 L. Foster et al. / Procedia Engineering 00 (2010) 000–000

The measured improvement of human athletic performance over the past 150 years has been accompanied by a

substantial increase in global population. Yang [5] proposed that the larger the population from which a human is

selected each year, the higher the probability that an exceptional athlete will be found by chance alone. Hence if the

population size grows over time, athletic performance may also increase. This leads on to the hypothesis, that global

human population size is an influencing factor in human athletic performance and needs to be assessed before other

influences such as sports technology are to be evaluated.

Running is an athletic sport in which human performance has improved since the start of modern competition. It

is hypothesised that technology in the sport of running has relatively little influence on performance in comparison

to many other sports. As the 'simplest' sport running statistics have been used to determine the effect, if any of

population on performance. Statistics for male and female running events have been collected and correlated against

global gender population size when the performance records were made.

2. Historic improvements in running performance

Performance improvements in various athletic events including running have been gauged in a recent paper by

Haake [6]. Haake proposed the use of a performance improvement index (PII) to allow comparisons between

different athletes and sports, with the main aim of quantifying the effects of technology in various sports. To

evaluate performance improvements in running a PII has been applied to various male and female running events.

The PII devised for the 100 metres which can be applied to other running events is given as:

Equation 1

where t is the reference performance time, t0 is the comparison performance time in seconds and E/E0 is the ratio

of energies required to undertake the running event. Data for world records and the average of the top 25 times for

each event was collected from a number of sources [1,4,7] and cross-verified to check their validity. Only the top

time of each athlete is included in any one year so that 25 different athletes are used. This type data is more

representative of human running performance on a yearly basis; and reduces the influence of extreme performance

data, such as world records on the overall trend.

Historic periods of athletic improvement have been defined by five periods: Period 1 (1891-1912) the start of

organised competition; Period 2 (1913-1929) influenced by World War I; Period 3 (1921-1936) interwar; Period 4

(1937 - 1947) influence by World War II, and finally Period 5 (1948 - present day) post World War competition up

until the modern day. The percentage change in PII in male running events for these different historic periods is

represented in Figure 1.

-20%

-10%

0%

10%

20%

30%

40%

50%

Ch

an

ge

in

in

de

x (

%)

100m200m400m800m1500m5000m10000mMarathon 42195m

[3] 1920 - 1936

[2] 1913 - 1919 [4] 1937- 1947[5] 1948 - Present day[1] 1891-1912

200 m

400 m

800 m

1500 m

5000 m

10000m

Mara

thon

100 m

200 m

400 m

800 m

1500 m

5000 m

10000m

Mara

thon

100 m

200 m

400 m

800 m

1500 m

5000 m

10000m

Mara

thon

100 m

200 m

400 m

800 m

1500 m

5000 m

10000m

Mara

thon

100 m

200 m

400 m

800 m

1500 m

5000 m

10000m

Mara

thon

100 m

Figure 1: Male PII for the different historic periods (NB data is only available from 1921 onwards that, in the standard 42195m marathon)



Figure 1 illustrates that the PII is detrimentally affected in both period 2 and period 4, the World War influenced

periods. This indicates that the World Wars have a negative effect on running performances and looking at the

entirety of running data from 1891, these periods need to be considered when modelling performance

improvements. For this study, data from period 5 was examined as this was outside the any war influenced period.

3. Performance versus population

Figure 2 shows the estimation of the global population size since year 1000 up until 2200 given by the United

Nations Population Division, medium variant model [8]. It is shown that from the start of the 19th century the global

population has increased rapidly, with a peak value estimated to reach around 10 billion in 2200. For the purpose of

this study it was assumed that the ratio of male to females in the world was 1:1, however the true ratio varies

somewhat throughout the world. It was also assumed, that the fraction of the population which participates in sport

has stayed the same throughout the era of modern athletic competition (1850 to 2009). An increasing global

population size would mean an increase in participation levels in sport. Figure 3 shows the population of males for

the recent period of modern athletic competitions plotted with the male 100 metre world records each year. This

shows that the male population has progressively increased alongside an increase in the maximum performance of

the 100 metres.

0

1

2

3

4

5

6

7

8

9

10

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

2100

2200

Glo

bal p

op

ula

tio

n (b

illio

ns)

Year

9.5

9.6

9.7

9.8

9.9

10.0

10.1

10.2

10.3

10.4

10.50.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

1800

1820

1840

1860

1880

1900

1920

1940

1960

1980

2000

2020

100 m

wo

rld

reco

rd tim

e (s)

Esti

mate

d m

ale

po

pu

lati

on

(b

illio

ns)

Year

Population estimates (U.N.)

Male 100 metres World Record

Figure 2: Estimated global population of the world with year

(U.N. population division)

Figure 3: Global population of males shown with the 100 m

world records, against year

A simplified model for calculating human population size, for a given year was used to estimate the global

human population size throughout the history of modern athletic competitions. This is given by the equation,

Equation 2

where N is the estimated global population size in billions and X is the centuries since 1800. (R2>0.999) and is valid

from 1850 to 2008 [9].

L. Foster et al. / Procedia Engineering 2 (2010) 3183–3189 3185


Figure 4: Average of the top twenty five performances plotted against gender population for male and female events in: (a) 100 metres (b) 800

metres and (c) Marathon.

Shown in Figure 4 are the averages of the top 25 performances for the (a) 100 metres, (b) 800 metres and (c)

marathon events for both male and females plotted against gender population size in billions. Figure 4 all show

exponential decay trends and are representative of performance versus population graphs in all events, both male

and female. Note that Figure 4 shows data from all historic periods, and any war influenced periods have not been

taken in to account. These exponential decay trends can be subsequently modelled using an exponential decay

function.

4. Method

An exponential decay model previously used by Morton [10] is given by,

Equation 3

where L is the limit of human performance in a specific event; a and b are parameters of the decay curve, P is the

population size in billions and t is the predicted performance for a given population size.

The exponential decay function was fitted to the collected running performance data versus gender population

size using Microsoft ExcelTM and SPSSTM software packages, to give best-fit P values of a, b and L, with 95%

confidence limits.

SPSSTM

could not accurately fit the decay model to data for the female events of 1500m and larger. This was

because there was insufficient historic data to allow the model to be fitted accurately, leading to very large

confidence intervals being formed.

For the comparison of these exponential curves in the different events, a normalising process was carried out.

This entailed the changing of the performance measure plotted on the Y axis to the percentage away from the

predicted minimum limit of performance time. Gender population size stayed the same and the curves were placed

all on one graph. The gradient of each curve at a specific gender population size shows the rate of improvement in

the different events. The gradient of the curve was found by differentiating Equation 2 with respect to population

size to give,

Equation 4

The rates of change were then normalised using the previously mentioned method of taking all performance

values and expressing them as a percentage away from the ultimate limit, L.



5. Results

Table 1 and Table 2 show the parameters gained after the process of fitting the exponential decay function to the

historic period 5 data sets of both male and female events. Shown below this in Figure 5 and 6 are the male and

female running performance in the (a) 100 metres, (b) 800 metres and (c) marathon versus the gender population,

shown with these exponential decay models. Upper and lower bounds to the model were found by using the 95%

confidence intervals gained from SPSS. The lower limit L was also plotted on these graphs.

Table 1: Model parameters cacluated for male running events based on

the average of the top 25, shown with 95% confidence intervals

Table 2: Model parameters cacluated for female running events based

on the average of the top 25, shown with 95% confidence intervals

9.6

9.8

10.0

10.2

10.4

10.6

10.8

11.0

11.2

11.4

0 1 2 3 4

Perf

orm

an

ce

tim

e (

s)

Lower limit, L

(a) 100m

100

102

104

106

108

110

112

114

0 1 2 3 4

Male population (Billions)

(b) 800m

Lower limit, L

7000

7500

8000

8500

9000

9500

10000

10500

11000

0 1 2 3 4

(c) Marathon

Lower limit, L

Figure 5: Male performance figures against male population size in billions for the average of the top 25 performances in: (a) 100 metres (b) 800

metres (c) Marathon, shown with best fit exponential function model with 95% confidence intervals

10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

0 1 2 3 4

Pe

rfo

rm

an

ce

tim

e (s

)

(a) 100m

Lower limit, L

100

110

120

130

140

150

160

170

0 1 2 3 4

(b) 800m

Lower limit, L

Female population (Billions)

Figure 6: Female performance figures against female population size in billions for the average of the top 25 performances in the (a) 100 metres

(b) 800 metres, shown with the best-fit exponential function model with 95% confidence intervals

Race Distance L (+/-) a (+/-) b (+/-)

100m 9.88 0.05 3.02 0.48 1.02 0.16

200m 20.08 0.05 9.60 2.03 1.51 0.18

400m 44.59 0.12 21.69 6.23 1.65 0.23

800m 104.09 0.20 79.91 25.01 2.02 0.25

1500m 211.92 0.67 129.11 33.95 1.63 0.21

5000m 778.52 3.24 557.76 117.14 1.49 0.17

10000m 1637.89 5.27 1795.62 406.18 1.80 0.18

Marathon 7686.78 34.06 27231.22 8028.99 2.33 0.23

Race Distance L (+/-) a (+/-) b (+/-)

100m 10.94 0.05 9.14 2.04 1.53 0.18

200m 22.32 0.09 31.88 8.59 1.89 0.21

400m 50.14 0.22 149.66 62.87 2.21 0.29

800m 117.93 0.44 627.46 233.40 2.76 0.29



0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

0 0.5 1 1.5 2 2.5 3 3.5 4

Dis

tan

ce

a

wa

y f

rom

lim

it, L

(%

)

Global population of males (Billions)

Marathon

10,000m

5000m

800m

200m

100m

1500m

400m

(a) Male

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

0 0.5 1 1.5 2 2.5 3 3.5 4

Global population of females (Billions)

800m

200m

100m

400m

(a) Female

Figure 7: Magnitude away from the predicted limit using exponential decay model, against gender population size in the different events for (a)

males and (b) females

Figure 7 (a) and (b) show the normalized curves for the male and female events. Shown below in Table 3 is a

summary of the rates of change in performance for the different events, male and female. Improvement rates are

stated at the population size at the inauguration of the event, in 2009 and 2050. The rates of change are in units of %

billion-1. (Note that the global population in 2050 is estimated to be 8.7 billion)

Table 3: Summary of the rate of changes from normalized performance versus for both male and female events

Gender Event (m)

Current lowest

average of the

top 25 (s)

Predicted

lower bound

limit, L (s)

Surpassed model

predicted ultimate

limit?

Rate of

improvement in

1948 (% billion-1

)

Rate of

improvement in

2009 (% billion-1

)

Rate of

improvement in

2050 (% billion-1

)

Gender population

size at 0.999 L

(Billions)

100 9.95 9.82 NO 8.886 1.016 0.371 5.626

200 20.07 20.03 NO 11.273 0.452 0.101 4.088

400 44.50 44.48 NO 10.566 0.316 0.062 3.758

800 103.80 103.89 YES 12.935 0.175 0.024 3.291

1500 211.52 211.26 NO 13.407 0.420 0.084 3.945

5000 777.34 775.29 NO 17.078 0.715 0.163 4.415

10000 1624.15 1632.62 YES 21.532 0.464 0.078 3.886

42195 7600.00 7652.72 YES 46.843 0.325 0.032 3.503

100 10.96 10.91 NO 19.404 0.743 0.163 4.393

200 22.29 22.20 NO 26.496 0.476 0.074 3.853

400 49.91 49.69 NO 43.627 0.391 0.044 3.620

800 117.34 116.90 NO 49.512 0.139 0.009 3.112

Male

Female

6. Discussion

The aim of this study was to investigate the effect of population size on running performance. The graphs in

Figures 4 5 and 6, and the data in Table 3 indicate that population can be used as reasonable estimate of sporting

performance in running. This is quite surprising given the number of parameters that could affect an individual's

performance.

Ultimate limits for each different event were predicted by the fit of the exponential decay model. All of these

predicted limits have either been surpassed or are very close to being surpassed, illustrated by the predicted

improvement rates approaching zero. This implies that currently, performance is independent of population size and

if global population continues to increase, it is likely that there will not be a substantial increase in running

performance. However in the early period of population growth the trends show a strong relationship between

population size and running performance. This indicates that running performances were at one stage heavily

influenced by population size.

The normalised graphs shown in Figure 7 allow for the comparison of all the population predictor models for

different events; both male and female. It seems that the longer the event distance, the greater the improvement

level. For example in 1948 the male 100 metres event was 8.7% away from the predicted limit of performance

where as the male marathon was 20.2% away from the predicted limit. The reasons why this is the case is not clear

and subject to further study.



7. Conclusion

Correlating running performance times against global population produces exponential decay trends. As running

performances have or are close to reaching limits in performance, it is concluded that increases in global population

size will have little influence on current or future running performances. Conversely, during the mid 20th century

changes in global population size are likely to have had a significant effect of running performances.

References [1] International Amateur Athletics Federation, Progressive World Record Lists 1913 - 1970 (Including 1970-1971 supplements), International

Amateur Athletic Federation, London, 1972.

[2] MH Lietzke. An Analytical Study of World and Olympic Racing Records, Science. 119 (1954) 333-336.

[3] GP Meade. An Analytical Study of Athletic Records, The Scientific Monthly. 2 (1916) 596-600.

[4] M Nonna. Track and Field Statistics, (2008) [Online] Available from: http://trackfield.brinkster.net [Accessed: December/17 2008].

[5] MCK Yang. On the Distribution of the Inter-Record Times in an Increasing Population, Journal of Applied Probability. 12 (1975) 148-154.

[6] SJ Haake. The impact of technology on sporting performance in Olympic sports, J.Sports Sci. 27 (2009) 1421.

[7] RL Quercetani, A World History of Track and Field Athletics, Oxford University Press, London, 1964.

[8] U.N. The World at Six Billion, United nations publucations - Population Division, Department of Economic and Social Affairs, United

Nations Secretariat. (1999).

[9] MW Denny. Limits to running speed in dogs, horses and humans, Journal of Experimental Biology. 211 (2008) 3836-3849.

[10] RH Morton. The Supreme Runner: What Evidence Now? The Australian Journal of Sport Sciences. 3 (1983) 7-10.


understanding the influence of population size on athletic performance

Documents