![Correlation between sports events and energy expenditure
(a) The total daily energy expenditure (TEE) and its proportions of active energy expenditure (AEE), resting energy expenditure (REE) and Feeding, the sum of each type of active energy expenditure (AEEi) constitutes AEE, the sum of each type of resting energy expenditure (REEi) and the basal energy expenditure to maintain the body (REE0) constitutes REE. Thus, TEE = AEE+ REE+ Feeding [9]. (b) According to the normal function-specific signal transduction pathway (NSP) [16] diagram of energy expenditure of marathon adapted, the red line is the energy expenditure of marathon (AEEi) and the blue line is the resting energy expenditure of swimming or other sports (REEi). (c) AEE and REE diagrams of different sports events. (d) Subject training and fitness training improve the level of sports performance through the relationship between AEE and REE.](https://www.researchgate.net/publication/384151496/figure/fig4/AS:11431281278970539@1726779459453/Correlation-between-sports-events-and-energy-expenditure-a-The-total-daily-energy_Q320.jpg)
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RESEARCH ARTICLE
Exploring the dynamics of sports records
evolution through the gembris prediction
model and network relevance analysis
Lu TangID
1,2
, Mingliang Yang
1,2
*
1Department of Physical Education, Civil Aviation Flight University of China, Guanghan, China, 2Institute of
aviation sports, Civil Aviation Flight University of China, Guanghan, China
*yml9999@126.com
Abstract
Background
Sports records hold valuable insights into human physiological limits. However, presently,
there is a lack of integration and evolutionary patterns in the recorded information across
various sports.
Methods
We selected sports records from 1992 to 2018, covering 24 events in men’s track, field, and
swimming. The Gembris prediction model calculated performance randomness, and Pear-
son correlation analysis assessed network relevance between projects. Quantitative study
of model parameters revealed the impact of various world records’ change range, predicted
value, and network correlation on evolutionary patterns.
Results
1) The evolution range indicates that swimming events generally have a larger annual world
record variation than track and field events; 2) Gembris’s predictions show that sprint, mara-
thon, and swimming records outperform their predicted values annually; 3) Network rele-
vance analysis reveals highly significant correlations between all swimming events and
sprints, as well as significant correlations between marathon and all swimming events.
Conclusion
Sports record evolution is closely linked not only to specific sports technology but also to
energy expenditure. Strengthening basic physical training is recommended to enhance
sports performance.
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OPEN ACCESS
Citation: Tang L, Yang M (2024) Exploring the
dynamics of sports records evolution through the
gembris prediction model and network relevance
analysis. PLoS ONE 19(9): e0307796. https://doi.
org/10.1371/journal.pone.0307796
Editor: Mukesh Kumar Sinha, Manipal Academy of
Higher Education, INDIA
Received: February 6, 2024
Accepted: July 11, 2024
Published: September 19, 2024
Peer Review History: PLOS recognizes the
benefits of transparency in the peer review
process; therefore, we enable the publication of
all of the content of peer review and author
responses alongside final, published articles. The
editorial history of this article is available here:
https://doi.org/10.1371/journal.pone.0307796
Copyright: ©2024 Tang, Yang. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: The data that was
used during this study was already publicly
available. The sports records were obtained from
from the International Amateur Athletic Federation
(IAAF) (https://worldathletics.org/records/toplists)
Introduction
In competitive sports, achieving a new world record is always gratifying. However, it’s not just
about representing the pinnacle of a specific sports specialty, it’s crucial to assess the valuable
information and patterns behind the record [1]. Sports records, over time, follow a monotonic
function on a time scale and spatial function [2]. Hence, every sports records is bound to be
surpassed eventually. Factors like gender, age, genetics, participant numbers, geopolitics, dop-
ing, technological prowess, and athletic training contribute to creating sports records, with
athletic training playing a decisive role [1,2].
Sports training serves as a synthesis of research outcomes from diverse disciplines to
enhance athletic performance and applies the laws and characteristics of one sport to training
in others. It advances sports science by integrating insights from mathematics, physics,
computational science, engineering, anatomy, and physiology. Simultaneously, it extrapolates
laws and features from training theories like item clusters, integration, parallelism, crossover,
and multimodality, guiding training practices [3–6], and offering a theoretical foundation for
selecting athletes across sports.
The essence of sports lies in the amalgamation of external movements and internal bodily
functions. The variability in function among different sports is a crucial factor influencing
the existence of laws between them. Sports records, epitomizing the pinnacle of human
body movement function for a given year, not only reflect the highest sports training stan-
dards but also encapsulate the features and laws governing diverse disciplines. Conse-
quently, this study aims to correlate and analyze 24 sports records from 1992 to 2018,
exploring the interaction laws between world records and the evolving human function in
each sport. This endeavor enriches quantitative research in sports training science and exer-
cise physiology.
Methods
Data source
Data were sourced from the International Amateur Athletic Federation (IAAF) (www.
worldathletics.org) and the International Swimming Federation (Fe
´de
´ration Internationale de
Natation Association, FINA) (www.fina.org). Considering the prevalent use of banned sub-
stances to enhance athletic performance in the 1970s and 1980s, this study selected the annual
world records of 648 male athletes from 1992 to 2018 in track (100m sprint, 200m sprint,
400m running, 800m running, 3000m running, 10,000m running, 400m hurdles, and mara-
thon), field (high jump, long jump, and triple jump), and swimming (100m backstroke, 200m
backstroke, 100m breaststroke, 200m breaststroke, 100m butterfly, 200m butterfly, 50m free-
style, 100m freestyle, 200m freestyle, 400m freestyle, 800m freestyle, 200m medley, and 400m
medley). These events span competitions like the Olympic Games, the World Championships
in Athletics, and the World Swimming Championships.
Statistical analysis
Gembris predictive model. Correlations between data fluctuations would be meaningless
if random factors caused fluctuations in sports world records. To explore the presence of ran-
domness in these fluctuations, the impact of random factors on world record fluctuations was
evaluated using Gembris predictive statistical model [1,7]. The annual world record fluctua-
tion is presumed to be a smooth stochastic process devoid of systematic progression and
adheres to a Gaussian distribution (mean μand standard deviation σ). The anticipated value of
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and the International Swimming Federation
(Fe
´de
´ration Internationale de Natation Association,
FINA) (https://www.worldaquatics.com/swimming/
rankings).
Funding: This work was supported by
Fundamental Research Funds for the Central
University (PHD2023-02 to LT); Aviation Sports
Research Institute project of Civil Aviation Flight
University of China (24CAFUC09034 to MY). There
are no financial conflicts of interest to disclose.
Competing interests: The authors declare that the
research was conducted in the absence of any
commercial or financial relationships that could be
construed as a potential conflict of interest.
the record over the next Nyears can be estimated as:
xmax ¼mþsða0þa1ln lnðNÞÞ2ð1Þ
where the optimal coefficients are a
0
= 0.818, a
1
= 0.574, and a
2
= 0.349. These coefficients,
along with σ= 1, ensure that the error in approximating xmax remains below 0.06 within a
specified interval. Similarly, the standard deviation of the approximation of x
max
is:
sE¼sðb0þb1ln ln Nþb2ðln ln NÞÞ2ð2Þ
The optimal parameters, b
0
= 0.8023, b
1
= -0.2751, and b
2
= 0.0020, result in an approximation
error of under 0.15 percent. This paper utilizes data from 1992–2001 to project trends in world
records from 1992–2018, and the estimated fluctuations are subsequently compared with
actual sports performance results.
Network relevance. The records were documented as relative fluctuations by taking the
1992 world records as the baseline for each subsequent year’s records. The division of the
world records of other years by the baseline determined the relative fluctuations. Using SPSS
22.0 software (IBM, NY, USA), we calculated the Pearson correlation coefficients for the fluc-
tuation patterns of each world record, setting the significance level for statistical analysis at
P= 0.05. The time series of relative fluctuation (TSRF) for each world record x can be
expressed as follows:
TSRFxjð Þ ¼ xj
xi
;i¼1992;j¼1993;1994;. . . ;2018ð Þ ð3Þ
The number of interrelationships between any two TSRFs reflects the temporal correlation of
the evolution of world records. Given that speed events and jumping events set world records
based on the minimum and maximum values, respectively, this paper transforms the world
records of jumping events inversely to facilitate a direct comparison with the former. The cor-
relation coefficient (R) is employed to assess the strength of correlation in the fluctuation of
world records between events. A value of Rcloser to 1 indicates a stronger positive correlation.
Results
Evolution of sports records
To avoid errors caused by random fluctuations in data, we selected the best world records for
each year from 1992 to 2005 to compare with the records for each year from 2005 to 2018. Fig
1provides a general overview, indicating that swimming events generally exhibit a greater
magnitude of change than track and field events. Notably, the 200m backstroke world record
saw a remarkable 10% improvement in 2018 compared to 1992. Significance is the marathon,
the only track and field event surpassing certain swimming events in improvement over the
years, with a direct 5% enhancement in 2018 over the 1992 record. The marathon ranks 7th
among all events in the spans of 1992–2002 and 2018–2008. Except for the marathon, other
track and field events experienced a substantial decrease in change magnitude compared to
swimming records. Specifically, the 400m freestyle, with the smallest increase in 2018 com-
pared to 1992, was 3.46 times higher than the 100m sprint, which had the largest increase in
track and field events. Furthermore, high jump, long jump, 400m hurdles, 200m running,
400m running, 800m running, 3,000m running, and 10,000m running all exhibited negative
growth in all year span comparisons (Fig 1).
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Fig 1. Magnitude of change in sports records. White columns show growth in sports records; black columns show negative
growth in sports records.
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Prediction of sports records
The prediction results indicate that except for middle and long-distance running, track and
field events fall within the σ
E
interval (Fig 2). However, all statistics related to sprinting, mara-
thon, and swimming events deviate from the σ
E
interval. Fig 2e and 2f reveal that the stochastic
variation process of the world records for 400m and 3000m running aligns with the actual per-
formance evolution. In contrast, the 100m sprint, 200m sprint, 50m freestyle, and marathon
events exhibit significant deviations (Fig 2a and 2d).
Network correlations in the evolution of sports records
The correlation analysis results (Fig 3a) reveal a high positive correlation (R>0.7, P<0.05)
among the TSRFs of all swimming events. Additionally, a high positive correlation (R>0.7,
P<0.05) is observed between the 100m and 200m sprint events. Furthermore, there exists a
high or moderate positive correlation between the marathon and all swimming events (R= 0.4
~ 1.0, P<0.05). A moderate positive correlation is found between the 100m sprint and all
swimming events (R= 0.4 ~ 0.7, P<0.05). Conversely, a moderate negative correlation is iden-
tified between the 3000m middle and long-distance running and all swimming events (R=
-0.4 ~ -0.7, P<0.05). Notably, the network correlation analysis (Fig 3b) indicates a high posi-
tive correlation (R>0.7, P<0.05) and network connectivity between the TSRF of the annual
world record in the marathon and all swimming events.
Fig 2. Gembris predicts the evolution of sports records between 2002–2018. (a) 100m sprint; (b) 200m sprint; (c)
50m freestyle; (d) marathon; (e) 400m running; (f) 3000m running. The black solid line and the red solid line indicate
the theoretical estimate and the actual value, respectively, and the dashed line indicates the data change σ
E
interval.
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Discussion
Predictive analyses of sports world records from 1992 to 2018 can be conducted using Gembris
algorithmic model [1,7]. The stochastic variation process of 400m and 3000m middle-distance
running world records aligns well with the actual performance evolution, indicating a small
approximation error and a superior fit of the prediction model for these two sports. This sug-
gests no significant breakthrough in their performance over the 27 years, consistent with the
generally low growth rate in track events in Result 3.1. Annual world records in sprinting, mar-
athon, and swimming surpass predicted values, implying a substantial performance increase
and systematic improvement from 1992 to 2018. This aligns with the notable growth rate
change in sprinting, marathon, and swimming performance.
In the correlation analysis, a high positive correlation emerged among the TSRFs of all
swimming events, suggesting no correlation between strokes (backstroke, breaststroke, butter-
fly, and freestyle) and event distances (sprints, intermediate, and long distances). This absence
of a clear relationship allows for the emergence of "super athletes" like Michael Phelps (USA),
Ian James Thorpe (Australia), and Sun Yang (China), who set new world records across vari-
ous strokes and distances. Notably, the 100m and 200m sprints in track events exhibit a high
positive correlation in TSRFs, exemplified by Jamaican sprinter Usain Bolt, holding world rec-
ords in both (as of October 2023). Intriguingly, the marathon shows a similar strong positive
correlation with all swimming events [8], and others, indicating a fractal relationship between
time and events in top runners and swimmers’ athletic performance.
Sports records embody the human pursuit of optimal performance, a continual refinement
of behavior with both explicit and implicit functions in each activity. Poehlman and Dvorak
(9)utilizing the double-labelled water method to measure energy expenditure, revealed that
activity energy expenditure (AEE) constitutes 15–35% of total energy expenditure (TEE) per
day, contrasting with the dominant 60–75% of TEE attributed to resting energy expenditure
(REE), leaving approximately 10% for feeding activity (Fig 4a). Enhancing the optimal exercise
level primarily involves elevating AEE, markedly reducing the risk of all-cause mortality. A
Fig 3. Network relevance of sports records. (a) Matrix of correlation coefficients; (b) Connected network of 24 sports records
evolved, two TSRFs with correlation coefficients greater than 0.7 are defined as connected. (1, 100m sprint; 2, 200m sprint; 3,
400m running; 4, 800m running; 5, 3000m running; 6, 10,000m running; 7, marathon; 8, 100m backstroke; 9, 200m backstroke;
10, 100m breaststroke; 11, 200m breaststroke; 12, 100m butterfly; 13, 200m butterfly; 14, 50m freestyle; 15. 100m freestyle; 16,
200m freestyle; 17, 400m freestyle; 18, 800m freestyle; 19, 200m medley; 20, 400m medley; 21, 400m hurdles; 22, long jump; 23,
high jump; 24, triple jump).
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cohort study on over 2 million individuals found a positive association between higher AEE
levels, increased activity skills, and reduced mortality risk [10]. Higher AEE levels were also
linked to modulated rhythmic gene expression, manifesting as decreased body mass and
increased maximal oxygen uptake [11]. Another avenue for intensifying activity is the reduc-
tion of REE. Studies indicate significant post-training reductions in REE after 40 weeks [12]
and during 30 weeks of weight loss training [13]. Athletes commonly exhibit a lower resting
heart rate, known as heart rate reserve or cardiac reserve function, contrasting with the general
population. Therefore, the objective of exercise training may involve augmenting overall func-
tional performance by increasing active energy expenditure and subsequently decreasing rest-
ing energy expenditure.
This paper marks the inaugural identification of a robust connection between the evolution
of world records in the marathon and all swimming events. This seemingly counterintuitive
revelation necessitates revisiting Aristotle’s primary principle of nature [14]. The foundational
nature of exercise encompasses both external action and internal energy expenditure. Despite
the marked distinctions in movement and energy expenditure between marathon and swim-
ming, a profound interconnection emerges when scrutinized through the lens of activity and
resting energy expenditure, as delineated in the preceding section. In elite marathon runners,
the marathon assumes a paramount role in all activities. When engaged in marathon running,
the associated activity energy expenditure (AEE) substantially rises, concurrently suppressing
Fig 4. Correlation between sports events and energy expenditure. (a) The total daily energy expenditure (TEE) and its
proportions of active energy expenditure (AEE), resting energy expenditure (REE) and Feeding, the sum of each type of active
energy expenditure (AEE
i
) constitutes AEE, the sum of each type of resting energy expenditure (REE
i
) and the basal energy
expenditure to maintain the body (REE
0
) constitutes REE. Thus, TEE = AEE+ REE+ Feeding [9]. (b) According to the normal
function-specific signal transduction pathway (NSP) [16] diagram of energy expenditure of marathon adapted, the red line is the
energy expenditure of marathon (AEE
i
) and the blue line is the resting energy expenditure of swimming or other sports (REE
i
). (c)
AEE and REE diagrams of different sports events. (d) Subject training and fitness training improve the level of sports performance
through the relationship between AEE and REE.
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swimming’s resting energy expenditure (REE) linked with other sports. This phenomenon
aligns with the normal function-specific signal transduction pathway (NSP) effect—a negative
feedback mechanism. This mechanism ensures that the specific exercise’s function inhibits the
activation of alternative signal transduction pathways in target tissue cells [15,16]. Marathon-
related target tissue cells, through cytokines or exosomes, activate the marathon NSP in a wide-
spread manner. This strategically conserves energy expenditure, facilitating a more efficient
marathon activity by suppressing swimming or analogous functions (Fig 4b).
In the realm of sports, variations in energy expenditure directly impact the interconnection
between athletic specialties. Fig 4c illustrates the correlation between energy expenditure in
different sports [17,18]. When subjected to identical conditions, swimming events exhibit
comparatively higher activity energy expenditure (AEE) levels due to the necessity of overcom-
ing water resistance. Conversely, cycling or skating events demonstrate relatively lower AEE
levels by utilizing tools to hasten movement. Swimming, on the other hand, boasts the lowest
resting energy expenditure (REE) level, with running, walking, skating, and riding showcasing
descending resting metabolic levels. Specialized training aims to elevate the AEE level of a spe-
cific event and diminish the non-specialized training REE level. Essentially, reducing REE lev-
els in non-specific training compensates for the AEE levels in specific training. Therefore,
alongside specialized training, reinforcing and supplementing non-specific training [4–6].
Furthermore, physical fitness represents the fundamental athletic prowess of the human body,
encompassing strength, speed, endurance, coordination, flexibility, sensitivity, and other ath-
letic qualities. It is a pivotal component of athletes’ competitive capabilities. Physical fitness
training predominantly involves aerobic training, anaerobic training, and muscle strength
training to enhance AEE levels across different abilities. Similarly, while augmenting the AEE
level of a specific athletic ability, it concurrently diminishes the REE level of other athletic abili-
ties. This approach ultimately serves the purpose of enhancing sports performance and athletic
achievements (Fig 4d). In conclusion, alongside advancing the AEE level of specialization and
physical abilities, it is imperative to consider the AEE level of non-specialized sports and
diverse physical training. Ultimately, reducing the corresponding REE level broadens the
scope of energy expenditure compensation, ensuring the full realization of sports
performance.
The study acknowledges several limitations. Firstly, our results come from group data and
do not provide a comprehensive evaluation of the long-term sports performance of specific
athletes. Additionally, our model encounters challenges stemming from non-physiological fac-
tors such as environmental conditions, participation in the sport, and doping [19]. Particularly
noteworthy is the trend of doping practices becoming more covert and sophisticated, which
could potentially impact the progression of sports records in manners that current statistical
models may fail to accurately capture [20]. Finally, The study’s primary focus on male sports
records aimed to delve deeply into the evolution of sports records within specific gender
groups. This targeted approach not only minimized the influence of confounding variables but
also facilitated a more precise understanding of the mechanisms underlying male sports record
evolution. However, acknowledging gender disparities is crucial for ensuring the comprehen-
sive applicability of our findings. For future investigations, we advocate for similar in-depth
analyses of female athletes’ sports records to enrich insight into gender-specific sports perfor-
mance dynamics within specific contexts. Such comparative studies would contribute signifi-
cantly to our understanding of how gender influences athletic performance under varying
conditions. In addition, future research should include longitudinal studies in other sports or
across longer periods, this would provide valuable insights for coaches to design more targeted
training programs and interventions to optimize sports performance.
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Conclusion
This paper quantitatively analyzes the evolution of annual world records in 24 track and field
and swimming events from 1992 to 2018. Specifically, swimming records have outpaced those
in field and track events, with all field events showing negative growth. Correlation analyses
reveal strong connections not only between swimming and sprint events but also between
marathons and all swimming events. Additionally, the predictive model analysis confirms that
these high correlations between events are non-random. Lastly, the paper explores the interac-
tion pattern of the annual world records’ evolution from the perspective of energy expenditure.
This perspective elevates active energy expenditure during high-quality performance in a spe-
cific sport (specialized or physical training). Simultaneously, it considers the active energy
expenditure in non-specialized sports and diversified physical training, significantly reducing
the corresponding resting energy expenditure. This broadens the space for energy expenditure
compensation, providing an optimal physiological basis for full performance and
enhancement.
Author Contributions
Conceptualization: Lu Tang, Mingliang Yang.
Data curation: Lu Tang, Mingliang Yang.
Funding acquisition: Mingliang Yang.
Investigation: Mingliang Yang.
Methodology: Mingliang Yang.
Resources: Mingliang Yang.
Software: Lu Tang.
Writing – original draft: Lu Tang, Mingliang Yang.
Writing – review & editing: Lu Tang, Mingliang Yang.
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