Pacing of Human Locomotion on Land and in Water: 1500 m Swimming vs. 5000 m Running

dy of pace strategy in different environments could help to understand its depen- dence on athletes' energetic limits or on sport-speci c factors. The aim of this study was to analyse the pacing strategy of nalists during seven swimming and running world events held in 2021–2022. The speed of 32 swimmers every 50 m in 1500 m freestyle competitions, and the speed of 55 runners every 100 m in 5000 m track competitions, were analysed. Differences between swimming and running were statistically signi cant for Total Time (p= 0.00, ES = 1.9), Average Time of splits (p= 0.00,ES = 2.0), Median Time of splits (p= 0.00, ES = 2.0), and Maximal length of split sequences (p= 0.00,ES = 1.3), and non-signi cantly different for number of Sequences of splits (p= 0.12, ES = 0.5), Percentage of total splits faster than the median speed (p= 0.08, ES = 0.2), Percentage of splits faster than the median speed in the rst half (p= 0.16, ES = 0.4) and Percentage of splits faster than the median speed in the second half (p= 0.21,

non-signi cantly different for number of Sequences of splits (p= 0.12, ES = 0.5), Percentage of total splits faster than the median speed (p= 0.08, ES = 0.2), Percentage of splits faster than the median speed in the rst half (p= 0.16, ES = 0.4) and Percentage of splits faster than the median speed in the second half (p= 0.21, ES = 0.3). In conclusion, despite similar metabolic requirements of 1500 m swimming and 5000 m running, the in uence of speci c environment and sport type on the pacing strategy of world level competitions seems to be supported. Keywords: energy cost; endurance; training; technique; tactic; fatigue; performance; time series; mathematical modelling 1. Introduction Effective guidance for the best targeted training program can be provided by study- ing more speci cally for energy optimization of previous high-level winning perfor- mances[1–4]. An analysis of word records for various forms of human locomotion in the range of 3.5–230 min demonstrated that time and distance of all sport disciplines are linked by a linear relationship [4]. Nevertheless, because of the different nature of the demands placed on the athletes, the average speed declines as the distance increases at dif- ferent rates for each speciality [4,5]. There is evidence that, throughout prolonged exercise, the overall pacing strategy is modulated to avoid early exhaustion brought on by a malfunc- tion of one or more physiological systems. It is argued, therefore, that pacing strategies are markers of the physiological regulation that underlie them, and that pacing strategies are in uenced by changes in muscle activation that are anticipatory in nature [6–8]. Moreover, in competition, athletes are constantly and simultaneously presented with various external stimuli. Different competition environments in uence pacing behaviour, highlighting the importance of athlete–environment interactions. To understand pacing decision-making, both the athlete's internal state and the external environment must be considered [9]. In this regard, studying the pace strategy in radically different environments, such as land and water, in run and swim races of similar durations, could help to understand if the pacing strategy is more in uenced by athletes' energetic limits or by

interactions. To understand pacing decision-making, both the athlete's internal state and the external environment must be considered [9]. In this regard, studying the pace strategy in radically different environments, such as land and water, in run and swim races of similar durations, could help to understand if the pacing strategy is more in uenced by athletes' energetic limits or by sport-speci c factors, such as environmental, biomechanical, technical, and training method differences [9–11]. Appl. Sci.2023,13, 6455.

Appl. Sci.2023,13, 6455 2 of 13 The velocity pattern and kinetic energy of every race are strongly dependent on the drag of the medium in which the athlete moves. The drag coef cient for swimming is thirty-fold that of running [10]. In addition to the air and water environmental differences, such as propulsion and drag, which in swimming are against the same environment, while in running propulsion and friction are against the ground and drag against the air, in pool swimming, the speed uctuations at each stroke are small as compared to running, and drafting cannot take place [12]. As small changes in swimming velocity can cause a disproportionate rise in water resistance, a faster stroke rate will increase the amount of energy lost to the environment [13–15]. Large swimming velocity uctuations increase the work needed to proceed at a certain velocity, both for the need to overcome inertia and drag. A “smooth motor pattern” is thus expected to minimize the energy cost of swimming [16]. Top-level performance in competition is a combination of variability within laps and stability between laps [17]. Hence, due to the importance of stroke technique in in uencing energy cost and aerobic performance, the incorporation of the stroke rate count into the speed–time relationship analysis could be a useful criterion for controlling pacing, technical parameters, and training intensity [18–23]. On the contrary, in running, it seems that competing at a perfectly even pace is nearly impossible [24,25]. A notable intraindividual variability of the measurements is reported when high level endurance runners are tested to determine their aerobic ability and exercise ef ciency [26]. In a prediction of 5000 m track running performance, it was shown that critical power increases when the trials are self-paced compared with constant power in laboratory conditions, thus emphasizing that gait pacing in uences the speed–time relationship [27,28]. Nonetheless, both in 1500 m running and 400 m swimming, a more conservative initial speed that allowed for increases later appears to be associated with success [11]. To understand the importance of these environmental and biomechanical differences, we hypothesised that human optimisation of

with constant power in laboratory conditions, thus emphasizing that gait pacing in uences the speed–time relationship [27,28]. Nonetheless, both in 1500 m running and 400 m swimming, a more conservative initial speed that allowed for increases later appears to be associated with success [11]. To understand the importance of these environmental and biomechanical differences, we hypothesised that human optimisation of energy distribution in function of exercise duration, according to the metabolic requests, could lead to speci c pacing strategy back- grounds in different environments. Therefore, the aim of the study was to analyse and compare the pacing strategy of 1500 m freestyle swimming and 5000 m track running of male nals at world level competitions, and to differentiate medallist from non-medallist behaviours. 2. Materials and Methods 2.1. Experimental Approach All procedures were conducted according to the Helsinki Declaration. The ethics committee of the University of Rome Foro Italico approved and authorised this project, assigning the code CAR 155/2023. Informed consent from athletes was not deemed necessary, since only publicly available information was used. Competitions data on the male 1500 m freestyle swimming in long and short course pools and 5000 m running on track were downloaded from the websites,, www.diamondleague.com, and, accessed 9–31 January 2023. All data were gathered and retrospectively analysed anonymously. Each competition report included a subject identi cation number for each athlete, the name of the competition, distance, overall nishing position (ranking), split times (split) every 50 m for swimming and every 100 m for running, and the completion time (Tot time). A total of 87 results of 7 world events held in 2021 and 2022 were analysed. For the 1500 m freestyle swimming, the male long course nals of the Olympic Games 2021 (Tokyo 2020), FINA World Championships 2022 (Budapest), short course nals FINA Swimming World Cup 2021 (Berlin), and FINA Swimming World Cup 2021 (Budapest) were analysed. For the 5000 m running, the male nals of the Olympic Games 2021 (Tokyo 2020), World Championships in Athletics 2022 (Oregon), Diamond League 2022 (Eugene), and Diamond League 2022 (Rome), were considered. Results of 87 participants were investigated.

World Championships 2022 (Budapest), short course nals FINA Swimming World Cup 2021 (Berlin), and FINA Swimming World Cup 2021 (Budapest) were analysed. For the 5000 m running, the male nals of the Olympic Games 2021 (Tokyo 2020), World Championships in Athletics 2022 (Oregon), Diamond League 2022 (Eugene), and Diamond League 2022 (Rome), were considered. Results of 87 participants were investigated. A total of 32 swimming speeds, taken every 50 m in the 1500 m freestyle competitions, and 55 running speeds, taken every 100 m in the 5000 m track competitions, were analysed.

Appl. Sci.2023,13, 6455 3 of 13 2.2. Time Series An analysis was applied to test the randomness through both median and the as- cendent and descendent analysis of the time series. The time series analysis consists of assessing whether the times of each split should be considered, mathematically speaking, as a true time series, and not as a random sample. In other words, is the order of the index-set t1, t2,. . .material, not accidental, as it would be for a sample x1, x2,. . .(a sequence of values of independent and identically distributed random variables), in which suf xes are arbitrary. The study of some data indexed by time, with tools from the theory of time series, is mathematically meaningless if a statistical test performed on the data did not lead to the rejection of randomness. In 1968, Kendall and Stuart exempli ed this issue of randomness with 56 values of barley yields between 1884 and 1936, concluding that these measurements behave as those of a random sample [29]. The authors enumerate the standard statistical tests at our disposal to reject, or not, the null hypothesis that a sequence is a random sample: turning points, phase lengths, difference-sign, rank correlation, records, and rank serial correlation. In Aivazian 1978, two tests of randomness are discussed: the median test and a test based on the number and maximal length of monotonous phases [30]. The latter test, used in our study, is based on a statistic denoted by ( , ), with critical values given by and de ned as follows. The authors call a series a maximal sequence of consecutive measurements that is monotonous. Then, is the number of such series and the length of the longest one. If one of the inequalities v(n)> " 1 3 (2n 1) 1.96 r 16n 29 9 0 # ,t(n)<[3.3(log 10n+1)] where [x] denotes the integer part of x, we reject randomness; in other words, we conclude that the sequence x1,. . ., xn can be considered as a true time series, not as a random sample. In our case, n = so that

the inequalities v(n)> " 1 3 (2n 1) 1.96 r 16n 29 9 0 # ,t(n)<[3.3(log 10n+1)] where [x] denotes the integer part of x, we reject randomness; in other words, we conclude that the sequence x1,. . ., xn can be considered as a true time series, not as a random sample. In our case, n = so that the critical region is given by > 9.723 or < 6 for swimming and > 18.140 or < 6 for running 2.3. Time of Competition and Split Speed For each nalist, the length of split sequences was calculated as the count of how many consecutive splits were held faster (indicated with “minus” sign) or slower (indicated with + “plus” sign) than the median velocity. The Maximal length of split sequences was assessed as the longest sequence holding the same or + sign. The number of Sequences of splits was assessed as the count of the number of or + sequence. For each athlete, we also considered the nish time of the competition (Tot Time), the average and the median time of the splits, the differences among the time at each split, and the average time of the competition. Afterwards, for all athletes, the percentage of splits that were held faster than the average time was calculated for the whole competition and separately for the rst and the second half. 2.4. Comparison between Swimming and Running Total Time, Average Time of splits, Median Time of splits, Sequences of splits, Maximal length of split sequences, Percentage of total splits faster than the average speed, and Percentage of splits faster than the average speed in the rst half and in the second half, were compared by searching for statistically signi cant differences between swimmers and runners. To graphically depict the speed variation along the competitions of both disciplines, the differences among each split time and the average time was calculated for all athletes. 2.5. Athlete Ranking To differentiate athletes by their competitive level, the speed variations along splits were calculated separately and compared between medallists, from 1 to 3 , and non- medallists,

swimmers and runners. To graphically depict the speed variation along the competitions of both disciplines, the differences among each split time and the average time was calculated for all athletes. 2.5. Athlete Ranking To differentiate athletes by their competitive level, the speed variations along splits were calculated separately and compared between medallists, from 1 to 3 , and non- medallists, from 4 to last.

Appl. Sci.2023,13, 6455 4 of 13 2.6. Statistical Analysis Descriptive statistics (mean and SD) are reported for each category. The normality of the data was analysed by the Shapiro–Wilk test. ANOVA, Mann–Whitney U, or Friedman, for repeated measures with post-hoc corrected for Bonferroni tests, were applied when appropriate depending on data distribution. Statistical analyses were performed using IBM SPSS Statistics for Windows, version 26.0 (IBM Corp, Armonk, NY, United States). Level of signi cance was set atp< 0.05. 3. Results 3.1. Descriptive Statistics Table the Shapiro–Wilk test results. The distributions were signi cantly non-normal * for 19 of the 26 variables. Table 1.Descriptive statistics; mean and standard deviation (St. Dev.). Variables Discipline Mean St. Dev. Total Time s 1500 m Swimming 892.2 13.1 5000 m Running 785.0 9.9 Average Time of splits s 1500 m Swimming 29.7 0.6 5000 m Running 15.9 0.3 Median time of splits s 1500 m Swimming 15.9 0.5 5000 m Running 24.6 1.3 Sequences of splits n 1500 m Swimming 13.3 14.8 5000 m Running 13.0 4.6 Maximal length of split's sequences n 1500 m Swimming 10.9 13.0 5000 m Running 15.2 4.4 Splits faster than median speed n 1500 m Swimming 14.9 0.3 in the whole competition 5000 m Running 24.4 1.9 Splits faster than median speed n 1500 m Swimming 9.0 3.1 in the rst half 5000 m Running 13.0 3.8 Splits faster than median speed n 1500 m Swimming 5.9 3.1 in the second half 5000 m Running 11.5 4.3 Percentage of splits faster than median speed % 1500 m Swimming 49.6 1.0 in the whole competition 5000 m Running 48.9 3.9 Percentage of splits faster than median speed % 1500 m Swimming 30.0 10.3 in the rst half 5000 m Running 25.9 7.5 Percentage of splits faster than median speed % 1500 m Swimming 19.6 10.4 in the second half 5000 m Running 22.9 8.7 3.2. Time Series All athletes' competition split times analysis results were negative for randomness, through both median and the ascendent and descendent, meaning that their speed varia- tions can be considered true time series. 3.3. Split

25.9 7.5 Percentage of splits faster than median speed % 1500 m Swimming 19.6 10.4 in the second half 5000 m Running 22.9 8.7 3.2. Time Series All athletes' competition split times analysis results were negative for randomness, through both median and the ascendent and descendent, meaning that their speed varia- tions can be considered true time series. 3.3. Split Speed Variations by Athlete's Ranking Figure average. As expected, the faster rst split and the spurt of the last split are evident. The speed variations of each split with respect to the average along the rest of the competition shows that the medallist swimmers maintained a signi cantly slower pace from split 1 to 13, and a signi cantly faster pace from split 20 to 29, with respect to non-medallist swimmers, who started at a faster pace but then rose above the average speed in the second half.

Appl. Sci.2023,13, 6455 5 of 13Appl. Sci. 2023, 13, x FOR PEER REVIEW 5 of 13 3.2. Time Series All athletes’ competition split times analysis results were negative for randomness, through both median and the ascendent and descendent, meaning that their speed varia- tions can be considered true time series. 3.3. Split Speed Variations by Athlete’s Ranking Figure 1 and Table 2 depict the swimmers’ speed variation of each split around the average. As expected, the faster first split and the spurt of the last split are evident. The speed variations of each split with respect to the average along the rest of the competition shows that the medallist swimmers maintained a significantly slower pace from split 1 to 13, and a significantly faster pace from split 20 to 29, with respect to non-medallist swim- mers, who started at a faster pace but then rose above the average speed in the second half. Figure 1. Pacing strategy of swimming competition. Speed difference among each split and the average speed of swimming competition. Mann–Whitney U significance values for the differences between medallists and non-medallists; * = p < 0.05. Variation of the speed of each split around the average, for medallists, from 1° to 3°; non-medallists, from 4° to 8° placement in the 1500 m swim- ming finals. Table 2. Differences between medallist and non-medallist swimmers. Splits Mann–Whitney U Effect Size Split 1 0.01 * 0.2 Split 2 0.01 * 1.1 Split 3 0.11 0.6 Split 4 0.04 * 0.9 Split 5 0.03 * 0.7 Split 6 0.22 0.5 Split 7 0.04 * 0.7 Split 8 0.02 * 0.7 Split 9 0.33 0.8 Split 10 0.02 * 0.8 Figure 1. Pacing strategy of swimming competition. Speed difference among each split and the average speed of swimming competition. Mann–Whitney U signi cance values for the differences between medallists and non-medallists; * =p< 0.05. Variation of the speed of each split around the average, for medallists, from 1 to 3 ; non-medallists, from 4 to 8 placement in the 1500 m swimming nals. Table 2.Differences between medallist and non-medallist swimmers. Splits Mann–Whitney U

This research compares pacing strategies in swimming and running competitions.