Original Paper
Biomedical Human Kinetics, 6, 69–76, 2014
DOI: 10.2478/bhk-2014-0012
“Work curve” as a distinguishing mark of athletes’ work performance
Mirosław Mikicin
Józef Piłsudski University of Physical Education, Warsaw
Summary
Study aim: The aim of the study was to determine work performance in the aspect of work rate, energy, persistence, adaptation
rate, and accuracy based on the indices of an athlete’s work curve.
Material and methods: Thirty athletes (15 women and 15 men) who practised five sports (swimming, track and field, fencing,
judo, and taekwondo) and a control group (30 university students, 15 women and 15 men) participated in a work curve test
(Kraepelin). Both groups were equivalent. They were aged 18–25 years, all of them had finished secondary education, and
studied at the same university. The analysis concerned indices grouped into 6 factors: quantitative measures of performance,
measures of energy and persistence, measures of quick adaptation and efforts without self-restraint, measures of variability,
measures of accuracy and diligence, and measures of additional factors.
Results: Factor analysis of the work curve revealed a significant difference to the benefit of the athletes (p < 0.001) in the measures of energy and persistence. The results obtained in this study revealed good adaptation of athletes to exercise, resistance to
fatigue, and quick process of learning.
Conclusions: The results obtained may reflect the adaptation of athletes to long-term physical activity. Therefore, they are characterized by greater involvement and patience. Therefore, it can be concluded that monotonous training that necessitates much
energy, concentration of attention, and endurance, and, consequently, high work performance, is one of the most important
predictors of athletic activity.
Keywords: Psychodiagnosis – Sport – Work curve – Work performance
Introduction
In the 1930s, scientists emphasized that civilization
synchronizers played an essential role in the regulation of
human activity [1, 13]. Kraepelin developed a work curve
that took into consideration the arithmetic sum of all positive (motivation) and negative (fatigue) effects, which he
found to determine the level of human work performance
at any moment of activity. It has been demonstrated that the
work curve in its early phase of development is ­U-shaped,
whereas later it falls toward the right side. The mean level
of work performance in the later period is higher than at
previous stages and increases proportionally with the age.
Moreover, the differences in the mean level of work performance can be concluded between people of different
age and both sexes.
Other views were presented by Graf [14], who found
the effect of other factors on changes in daily work performance. His study of the best workers (who found their
work easy) found the following work rhythm: the phase of
Author’s address
initiation (30–60 minutes); the phase of further increase in
work performance that reaching a peak between the second
and third working hour; the phase of a gradual decline to
a minimum that occurs at around midday (fourth working
hour); the phase of afternoon increase to the peak performance (fifth working hour); and the phase of a decline in
performance after the end of working (Fig. 1). The pattern
of daily work performance led to the creation of a double
work curve. Graf concluded that it is consistent with physiological human properties, naming it “physiological work
curve”, which only took into consideration daily working
hours. The research carried out by this author has demonstrated that the work curve falls from the afternoon peak to
the midnight hours and reaches its minimum at around 2
to 3 a.m.
Biological function of the human body often depends
on a number of external (exogenous) factors, i.e., the
Earth’s rotation around its own axis, the revolution of
the Earth around the Sun, and the revolution of the Moon
around the Earth, which affect the biological rhythms (daily, seasonal, “lunar”) There are also endogenous (internal)
Mirosław Mikicin, Józef Piłsudski University of Physical Education, ul. Marymoncka 34, 00-968 Warsaw, Poland
[email protected]
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Performance
M. Mikicin
1
2
3
4
5
6
7
8
9
Working hours
Fig. 1. The work curve according to Otto Graf
rhythms in the human body, the causes of which remain
still unknown.
The problems of biorhythms have been the focus of interest since ancient times and the Middle Ages [14]. The
concepts developed in these periods remained unchanged
until the first half of the 20th century. However, the second half of the century saw a new approach to biorhythms.
Biochemistry, psychology, and physiology provided the
ground for development of a new science: chronobiology. Research centres that dealt with these problems also
started to be established. One of the first centres was the
International Society for Biological Rhythm Research established in 1935 in Ronneby, Sweden.
A many-year study by Voss, Gamper, Berger, Fliess,
and Graf [14] helped separate around 80 rhythms categorized according to different criteria. Using knowledge of
biorhythms in such domains of science as planning and
management, one can divide biorhythms as follows:
1. Biological rhythms of physical, mental, and intellectual
capacity. 2. Rhythms with annual, weekly, and daily periods. Seasonal training cycles, especially in individual disciplines, planned for individual biological rhythm, might
result in better preparation for athletic competitions.
The rhythmics of human body capacity is also connected to the work curve obtained by Hildebrandt [14],
who found two peaks of activity: the first between 9 and
11 a.m. and the second between 6 and 8 p.m. Between
them, at about 1 to 3 p.m., a phase of reduced capacity
occurs, whereas a sharp decline is observed after 10 p.m.
until the minimum from about 2–3 a.m. to 5 a.m. Therefore, the above data show that the most effective hours
of human work (e.g., an athlete’s work) are at around 8
to 11 a.m. and 4 to 9 p.m. If athletes plan to train with
different rhythm, a week-long adaptive period should be
planned in order for an athlete to adjust to the varied conditions.
Furthermore, it should be noted that an athlete’s body
signals the reduced ability to work and fatigue, which is
often ignored. The signals include: the need for a break,
stretching, sighing, yawning, a wandering mind, deteriorated concentration of attention, increased muscle tension,
slipping of the tongue, and small problems with memory.
After the phase of demobilization, one can observe the
phase of increase, which, in the final period, is often sustained by various stimulants.
Daily fluctuations of various psychical and physical
human capacities have also been analysed during laboratory studies and diagnosed as those which are affected
by the daily rhythm [23]. The aim of these analyses was
to determine the effect of daily rhythm on basic abilities,
e.g., divided attention, concentration of attention, reaction
time, mental capacity, and visual-motor coordination. The
maximum decline occurs between 3 and 6 a.m., whereas
a “plateau” occurs between midday and 4 p.m. (flat area of
the curve). Variability in the level of performing the tasks
and factors that determine the differences between individuals (overall psychophysical condition, mental condition, level of motivation, training degree, certain characteristics of personality and temperament), and the forced
sleep cycle or sleep deprivation [5].
One theory [11] assumes that human abilities are divided into: potential (that define human abilities at the optimum conditions of development) and actual (that show
what a person is able to do at optimum conditions for the
expression of abilities). People develop only a part of their
abilities and only a part of them is revealed through observations and measurements.
Strenberg attributes human abilities to fast automation
of the cognitive processes [24]. This researcher argues that
an activity, if performed repeatedly, is automated, which in
psychology means that its control moves from the global
level (that requires conscious control of the activity performed) to local level (connected with performance of the
activity in an uncontrolled and automated manner, without
effort). According to Strenberg [24], the cognitive processes are faster automated in people with a higher level
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“Work curve” as a distinguishing mark of athletes’ work performence
of intelligence, which is associated with performance of
activities without effort in a fluent manner and without the
necessity for conscious control [16]. People with lower
intelligence perform the same activity slower and with
more effort. Intelligence can be perceived in two ways:
“as a driving factor of the speed, effectiveness, and persistence in acquiring knowledge or as a complex characteristic which is attributable to molecular phenomena of the
automation of cognitive processes” [20, p. 750].
With respect to athletes, McLelland and Atkinson [4]
determined two essential dimensions of work performance
that relate to motivation. The first is the motive for success, i.e., strong willingness to compete, the need for facing other people, and achieving success. Another dimension is the motive to avoid failure, i.e., a very strong fear
for failure, expressed in the tendency to avoid the situations of competition, and lack of confidence in success.
The Kraepelin test, also termed the Kraepelin fatigue
test [1, 13], provides a lot of precious information concerning human functions. This offers opportunities to determine cognitive properties of the entity and their intelligence, temperament, abilities and even personality [7].
The work curve obtained in the test provides several indicators that determine its shape Furthermore, the indicators
help calculate the factors which reveal the work curve.
Characteristics such as work rate, energy, persistence, adaptation rate, making the effort without self-restraint, level
of variability, accuracy, and diligence determine the traits
of the subject.
Work curve in psychological tests
The study [25], which examined 2,900 people, revealed that the Kraepelin test [1, 2, 13] is a useful tool for
psychological examinations, as it can be used to determine
the work curve and calculate the level of other variables
for each age group. The studies [12] analysed correlations with the Uchida-Kraepelin psychodiagnostic test and
performed factor analyses for multiple personality traits.
It was demonstrated that there is an opportunity for the
evaluation of personality traits based on five personality
factors and the work curve.
It is highly probable that the work curve is also connected with human temperament [24], which is a relatively constant characteristic of the human body, determined
biologically, and manifested in formal characteristics of
behaviour. The Regulative Theory of Temperament [24]
assumes that the temperament manifests itself in all types
of human behaviour. Temperament is defined as a two-dimensional concept: at the energy level and temporal level,
which is considerably consistent with the Kraepelin work
curve [1, 13]. Activity and emotional activity characterize
temperament at the energy level.
Factor analysis of the variables of performance of the
test demonstrated that the quantitative indices obtained,
based on the results of the Kraepelin test [13], measure six
separate and independent factors which were categorized
into the respective groups: quantitative measures of performance, measures of energy and persistence, measures
of quick adaptation and efforts without self-restraint, measures of variability or stability, measures of accuracy and
diligence, and measures of. and measures of the additional
factor.
Quantitative measures of performance, with high results denoting the tendency for quick starting and performing the work.
A high level of the measures of energy and persistence
is connected with improvement in performance with time,
and, consequently, with a rising work curve. In such cases
[19], a learning process occurs, resulting from the experience, with the subject not exposed to fatigue. Learning [8]
is a purposive, conscious, organized, and controlled process. Fisher [8] regards overall intelligence, motivation,
memory, special abilities, interest, and the environment of
the learning person as the most important factors that affect learning.
Convexity and concavity of the work curve reflect the
rate of adaptation and effort without self-restraint. People
with a high index of convexity react to stimuli faster and
more spontaneously, and are more prone to variability, impulsiveness. This is also attributable to their fast starting
work and fast onset of fatigue. A small convexity or even
concavity of the work curve shows that it takes longer for
the subject to adapt to new situations. However, after a period of adaptation, this subject is able to maintain the rate
for a longer time as they have reserves of energy. It seems
that the convexity relates to deep nervous processes, as
a positive relationship occurs between these processes and
EEG wave frequency [1, 13].
Oscillation indices [1, 13], which are dependent on
a number of factors, represent the measure of variability
and stability. The first of them is individual situation of
a human and their attitude to the requirements they have
to meet. Work monotony is difficult to tolerate by a person
with a high level of variability, and it is even possible that
the person “suspends” the work due to being impatient.
On the other hand, if a problem to be solved occurs, this
person might reveal their abilities. Ignoring other factors,
high level of oscillation points to emotional stress of the
subject or neuroticism. According to Strelau [24], “people
with high intensity of this characteristic are susceptible to
irrational ideas, less able to control their own impulses and
cope with stress, they strongly react to fear, tension and
show tendency for distress and are willing to be discouraged and depressed in difficult situations and show low
self-esteem, shyness and confusion in the presence of
others” [24, p. 554]. The opposite reaction is observed in
emotionally balanced people as they are stable, relaxed,
and cope with stress easier, without tension, fear or anger.
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The measures of accuracy and diligence are likely to
be connected with conscientiousness, which, according
to Costa and McCrae [17] is characterized by strong will,
motivation for action, and consistent achievement of their
goals. Conscientious people are scrupulous, responsible,
diligent, consistent in the achievement of goals, deliberate
in planning and performing new tasks, as well as organized
and reliable at work. Furthermore, conscientious individual are characterized by the above-discussed motivation
and autotelic engagement [16], which determines energy,
choice of direction, and level of activity [3]. A low percentage of mistakes and corrections suggests a natural and
habitual tendency for accurate and diligent work. A high
percentage of corrections shows that the person studied is
tense, nervous, and has difficulties with external attention
(concentration on the task).
Factor analysis of the Kraepelin test revealed another
factor, which has not been identified so far. It was observed that can be connected with the two situations: experience connected with proficient addition and difficulty
in adaptation to the new situation. Several stages of adaptation can be distinguished: learning new patterns and then
using them in practice, i.e., psychological reorientation,
tolerance, and total adaptation of an individual or community to the current conditions, i.e., assimilation. Social
adaptation is affected by [10]: intelligence, socialization
of the entity, knowing your own abilities, responsibility,
independence, and membership in social groups. Through
adaptation, humans satisfy their natural needs and are well
adjusted to living in society.
As a predictor of sports activity, the work curve is also
likely to be connected with attention [15]. This is due to
the fact that concentration of attention might modify brain
activity, which consequently is likely to transform the
work curve.
Material and methods
The study examined 30 athletes (15 women and
15 men) who practised one of the five sports: swimming,
track and field, fencing, judo, and taekwondo. The control
group (30 subjects, 15 women and 15 men) was comprised
of university students. Both groups were equivalent. They
were aged 18–25 years, all of them had finished secondary education, and studied at the same university. Each
person participated in one individual session, and thus the
diagnostic process lasted 17 months. The study of athletes
and the control group was carried out in the Interfaculty
Laboratory of Neurophysiology at the University of Physical Education in Warsaw, Poland. None of the tests was
rejected due to erratic filling out of the questionnaire by
the persons studied. The examinations were not disturbed
by anything. Young people were willing to fill out the
M. Mikicin
questionnaire and were interested in the results. All of the
study participants gave their written consent to participate
in the experiment. All of the procedures were approved
by the Ministry of Science and Higher Education in Poland and were consistent with the standards of the Bioethics Committee of the University of Physical Education in
Warsaw, Poland, and the standards of the Declaration of
Helsinki.
The Kraepelin’s test [1, 2, 13] was created for the
examination of the speed, persistence, and accuracy
of work. During the test, the person examined is supposed to perform as many operations of the addition of
two digits in adjacent columns as they could within one
hour, with the obtained score written to the right. The
total of proper scores calculated in consecutive 3-minute
time periods creates the work curve. The shape of the
curve, with the general number of addition operations
performed, and the number of mistakes and corrections,
provides the basis for the interpretation of the test results. The values in the work curve allows for calculation of the six separate and largely independent factors
(partial measure). Their interpretation is based on Kraepelin’s studies described in a study by Arnold [1] and
studies published by his followers, including Takigasaki
[26] and Kashiwagi et al. [12].
Partial measures:
a) Performance measures:
– total number of addition operations (number of operations a person performed during the test, including mistakes and corrections);
– number of operations in the first 3-minute time period (Y1, the score obtained during the first 3 minutes of the test, which is the indicator of previous
experience in addition),
– maximum number of addition operations in the
3-minute time period (without the first time period,
which reflects the highest possible work rate of the
person studied);
b) Measures of energy and persistence:
– percentage increase (difference between means of
the first and the last four 3-minute time periods expressed in percentage terms);
– half ratio (quotient of the total number of addition
operations from the period that consists of the ten
last 3-minute time periods (11–20) and the first ten
windows (1–10);
– location of the maximum (3-minute period number
when a person performed the highest number of addition operations (without the first period);
c) Measures of fast adaptation and effort without selfrestraint:
– convexity I (the difference between the general
number of addition operations during the first and
last four time periods, multiplied by the mean
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“Work curve” as a distinguishing mark of athletes’ work performence
elevation of the curve and divided by the number of
time periods):
– convexity II (the difference between the overall
number of addition operations during the first and
last five time periods, and the number of addition
operations in the other middle ten time periods);
d) Measure of variability (or constancy), which determines
indices of oscillation around the even curve (average deviation from the third to the 18th time period);
e) Measures of accuracy and diligence are determined by:
the mistake ratio (the overall number of mistakes as
a percentage result of the general number of addition
operations) and the correction ratio (percentage result
of the overall number of addition operations);
f) Measures of additional factors are determined by the
initial decline (the difference between the number of
addition operations in the first time period and the lowest number in time periods 1 to 4) and the duration of
the decline (determined in the first four periods when
the fewest addition operations were performed).
The work curve test has been standardized and adapted
in Germany and the Czech Republic: Arbeitskurve nach
Kraepelin und Pauli-Test, Mainzer Revision.
Statistical Analyses
The statistical analyses used in the study were aimed
at finding the work curve for the athletes’ studies. We used
non-parametric tests (Mann-Whitney U test and factor
analysis).
Results
Analysis of the results showed significant differences
that occur between the subjects. Table 1 presents mean
values and standard deviations of the indices of the work
curve obtained for the athletes and the control group.
A significant difference was demonstrated concerning the work curve between the athletes and the control
group. This means that, over time, the athletes are characterized by improvement in performance (i.e. II/I ratio),
which is the only statistically significant result (z = 4.638,
p < 0.001) and, consequently, increasing work curve. This
shows that the athletes are less prone to fatigue.
Factors in the work curve
Differences observed in the work curve were originally
regarded as a series of partial measures which describe
the work performance for a task in the test [1, 13]. Most
of the mean indices that describe partial measures of the
work curve for the athletes and control group (students)
differ insignificantly, apart from one significant index (at
p < 0.001). The measures are presented in Table 2, whereas their interpretation was based on Kraepelin’s studies [1]
and studies by his followers [12, 26].
Among the three measures of performance (I), differences were found in two of them: the total number of
addition operations performed in the test, that points to
a higher work rate; and the increase in the number of op-
Table 1. Indices of the work curve in the group of athletes, (N = 30) and the control group, (N = 30)
Variable
Athletes
Control group
M
SD
min
max
M
SD
min
max
total number
2213.43
496.20
1549.00
3379.00
2458.06
505.66
1697.00
3657.00
Peak
132.96
25.89
96.00
190.00
141.33
28.89
89.00
217.00
Period I
103.54
25.48
59.00
151.00
110.20
23.32
60.00
155.00
% increment
18.33
18.50
–42.32
37.74
15.47
23.11
–97.69
55.61
1.23***
0.12
0.62
1.39
1.12
0.13
0.82
1.61
Peak location
16.70
2.65
11.00
20.00
16.66
3.20
7.00
20.00
Convexity I
31.12
37.47
–8.80
208.80
33.07
26.88
–27.20
87.20
Convexity II
71.09
90.68
–8.00
523.00
68.33
49.73
–12.00
187.00
Oscillation I
0.0007
0.0315
–0.05
0.07
–0.006
0.03
–0.13
0.052
Mistake ratio
1.09
1.00
0.10
4.42
0.95
0.82
0.03
3.65
Correction ratio
1.11
1.40
0.00
7.18
1.24
0.79
0.04
2.82
Initial decline
10.96
8.61
0.00
34.00
11.36
7.93
0.01
27.00
Duration of the decline
2.69
1.16
0.00
4.00
2.50
0.90
1.00
4.00
II/I ratio
M – mean, SD – standard deviation, min – the lowest score, max – the highest score, *** – different from control group p < 0.001
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M. Mikicin
Table 2. Factors in the work curve according to Kraepelin for the athletes (N = 30) and the control group (N = 30)
Factor
Athletes
Control group
I. Performance measures:
2.86
2.65
II. Measures of energy and persistence
2.12
2.04
III. Measures of fast adaptation and effort
1.97
1.88
IV. Measure of variability (or constancy)
1.97
1.98
Measures of accuracy and diligence
1.56
1.52
VI. Measures of the additional factor
1.52
1.59
erations in the first 3-minute time period, that points to
better experience with addition.
The biggest significant difference (p < 0.001) to the
benefit of the athletes was found in one of three parameters that measured energy and persistence (II). It concerns
the half ratio for the last ten and the first ten time periods.
These results obtained for partial measures suggest that
the work curve increases more in the group of athletes,
whereas the lower level in the control group might be attributable to fatigue with the high rate of work in the first
half hour performing the test.
In both parameters (Convexity I and Convexity II) of
the measures of adaptation and effort without self-restraint
(III), higher scores obtained by the athletes might suggest
longer maintenance of the work rate [1, 13].
The index of oscillation around the work curve, presented as a measure of variability (IV) that points to the
consequence and level of emotional distress during the
test [1, 13], was also evaluated. No differences were observed in this result.
The correction ratio (10, p < 0.05), calculated as a percentage of the total number of addition operations is interpreted as an improvement in the measure of accuracy and
diligence (V) during performance of the work. Another
significant observation is the increase in the percentage of
corrections that occurs with the reduction in the percentage of mistakes.
With regard to the additional measures (VI), the difference in the duration of the initial decline is insignificant,
which is interpreted as an experience and adaptation to the
new situation [1, 13].
The above data were illustrated graphically by means
of the diagram in Figure 3.
Discussion and conclusions
Interpretation of the results is based on the difference
demonstrated between the indices of the work curve obtained for the athletes and the control group, which reveal
the level of activity, speed, persistence, external attention
during the activity, sensory-motor rhythm, and accuracy
of the activity.
The work curve obtained for the athletes reveals an increasing tendency, which means that a learning process resulting from active experiencing occurs. Moreover, location of the maximum results in the control group occurred
earlier than in the athletes, which suggests that the persons in the control group get tired faster. Furthermore, the
people from the control group had a higher peak level and,
consequently, a higher work rate. Fast decision-making,
efficient performance of work, and a high level of overall
intelligence can be observed in the control group.
Our findings are consistent with the results obtained for
the work performance, particularly the attention and stamina of mountaineers during climbing [26]. In that study, the
Uchida-Kraepelin work curve test was carried out twice
[21, 22]. The first test was performed at rest, whereas in
the second test, one group (mountaineers) was tested in
the mountains after three hours of climbing and the second group (non-mountaineers) was well rested. Subjects
from the group of mountaineers demonstrated more incorrect characteristics in the work curve of the second test
compared to the non-mountaineers. Improper functions,
such as a decline in the performance in the second half
of the test and expansion in the performance range, show
that many of the mountaineers studied were physically exhausted. This suggests that fatigue decreased the ability to
cope with crises. On the other hand, some subjects from
the group of mountaineers showed significantly higher
performance in the mountains (second test) compared to
the performance in the college (first test). These findings
suggest higher work performance in mountaineers.
In the future, athletes’ work curves should be analysed
with respect to the specific sport [27]. Presumably, the tendency for making quick decisions and a high level of overall intelligence are the most demanded traits in technical
sports, as the athletes have to show both quick reflexes and
unconventional thinking. Another factor is the measure of
quick adaptation and effort without self-restraint, which
makes a person with a high index of convexity react faster
to the stimuli, be more spontaneous in action, and show
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“Work curve” as a distinguishing mark of athletes’ work performence
that their abilities of unconventional thinking are necessary. Accuracy and diligence should be the traits typical
of fencers, as these athletes need thoroughness to reach
a high level of skill.
The factor that is likely to be the most important in
sports based on speed and stamina is energy and persistence
[18]. Since these sports need much patience and stamina,
both physical and psychical, an athlete should show a high
level of convexity or even concavity of the work curve and
a low level of oscillation. This means that after a period
of adaptation, these athletes are able to maintain the work
rate for a long time. They keep some energy in reserve and
are able to cope with work monotony, which is essential
during training sessions. In the first case, a person with
high convexity reacts quickly and spontaneously to the
stimuli, which represents an invaluable asset for sprinting
performance. However, longer distances need the ability
to maintain speed and lower impulsiveness for a longer
time. Furthermore, another important trait is accuracy and
diligence [18], which should be noticeable especially in
sports that require perfect technique, such as pole vaulting, high jump, and shot put.
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Received 19.02.2014
Accepted 04.09.2014
© University of Physical Education, Warsaw, Poland
Acknowledgements
The study was financed from budgetary means for
scientific research in 2011-2014 as a research project
No. NRSA1 000751.
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