Pacing Strategy of 800 m and 1500 m Freestyle Swimming Finals in the World Championships According to the Performance in Males and Females of Different Age Groups

strategy refers to the distribution of effort and speed throughout the race to achieve optimal performance. This study aims to understand whether the choice of pacing strategy in swimming depends on the length of competitions and how sex, age, and performance level in uence this strategy. Participants were the nalists of the 800 m and 1500 m freestyle events at the elite and junior world championships in 2022–2023. Race outcomes and pacing parameters were compared between the two distances and across different groups of swimmers. Swimmers in both distances did not break world records. Pacing strategy generally followed a U-shape with signi cant differences in the frequency and duration of speed changes between the two distances. The 800 m exhibited more frequent changes in acceleration, while the 1500 m events generally followed a more consistent time-series pattern. There were differences in pacing strategies between males and females and between junior and elite swimmers. Swimmers closer to world records

a U-shape with signi cant differences in the frequency and duration of speed changes between the two distances. The 800 m exhibited more frequent changes in acceleration, while the 1500 m events generally followed a more consistent time-series pattern. There were differences in pacing strategies between males and females and between junior and elite swimmers. Swimmers closer to world records showed more consistent pacing patterns compared to those farther from records. This study suggests that pacing strategies are in uenced by race distance, sex, age, and performance level. The research highlights the complex interplay between physiological and psychological factors that shape a swimmer's decision-making during a race. Keywords: energy cost; endurance; training; technique; tactic; fatigue; performance; time series; mathematical modelling; sex difference 1. Introduction The successful execution of the race strategy at the major competitions of the season represents the nal challenge after months of training and preparation. To perform to the best of their abilities while remaining healthy, engaged, and injury-free, athletes must be mentored and coached in proper energy management through an appropriate pacing strategy, whether during training or competitions. Given the highly resistive properties of water, pacing strategy in swimming is a crucial aspect of performance, and it can signi cantly impact training and race outcomes [1–9]. Events of different lengths support various pacing strategies [3,10]. An “all-out” sprint strategy may be advantageous for sprints lasting less than 60 s, whereas athletes' longer- duration endurance performances may be enhanced by distributing energy resources more evenly, with minimal speed variation from lap to lap and an end spurt [5,6,11]. In open water swimming, it has been reported that swimmers competing in the shortest event had a minimal gap between them, and the leaders had begun the race in the head group [12]. Successful swimmers in the longer events adopted a more cautious strategy in the rst Appl. Sci.2023,13, 10515.

Appl. Sci.2023,13, 10515 2 of 16 half of the race by positioning themselves in the middle group [12]. Differences among events makes them an invaluable source for furthering our understanding of the pacing behaviours used by men and women, by the successful and unsuccessful, and by young and elite athletes [10]. It is important to note that reports of ~2.1% per decade improvements in swimming ability have been made [13]. However, the long-distance pool swimming race splits showed improvements, but not consistently. The percentage changes in the rst, second, penultimate, and last splits did not coincide with the percentage changes in race time, indicating that the gain in race time was primarily attained in the middle of the race. The slight decrease in lap-to-lap variability, which indicated that swimmers had gradually developed smoother pacing pro les, was the other notable change in pacing parameters [14]. It is therefore evident that the study of pacing strategy must be continuously updated in light of the evolution of sports performance [10]. Evidence suggests that the overall pacing strategy is adjusted during prolonged exer- cise to prevent early exhaustion brought on by a malfunction of one or more physiological systems. Therefore, it is asserted that pacing strategies are indicators of the physiological regulation that underlies them and that pacing strategies are in uenced by adjustments in muscle activation that are anticipatory in nature, based on afferent data from a vari- ety of physiological systems [15–17]. Due to the low mechanical ef ciency of swimming, the correct administration of the available energy is also highly dependent on technical abilities [18]. However, in competition, the athlete's surroundings constantly and simulta- neously present various external stimuli, requiring decision-making regarding where and when to allocate their accessible energy resources. These calls for action can appear and disappear over time and prompt an athlete to decide whether to maintain their current speed, slow down, or speed up [19]. It could be assumed that swimmers would be more or less exposed to those external stimuli depending on the length of the race. At least 90% of the energy used during

resources. These calls for action can appear and disappear over time and prompt an athlete to decide whether to maintain their current speed, slow down, or speed up [19]. It could be assumed that swimmers would be more or less exposed to those external stimuli depending on the length of the race. At least 90% of the energy used during the 800 and 1500 m freestyle competitions is thought to come from aerobic metabolism [18,20]. Indeed, numerous swimmers actually compete in both distances due to their similar energy requirements. Although few studies have compared their race tactics, it appears plausible that they adopted similar pacing strategies, so a parallel analysis of the two events may be instructive [7,8,21]. Studying the pace strategy in events with similar energetic resources but different durations may aid in understanding how much pacing decision-making is in uenced by external factors [19,22,23]. World records are an excellent paradigm of study because they led to the most optimal and outstanding performances in history. The study of world-class athletes' performance can provide a near-absolute standard of what athletes can achieve at their peak [24]. Simulat- ing their competition strategy in training and minor races could provide useful indications to develop the swimmer's individual best pacing strategy for future events [25–31]. It has been highlighted that most studies on swimming pacing strategy have been conducted on 200 and 400 m events, while there is limited research on long-distanceswimming [6] . Among long-distance pool swimming studies, some have analysed males and females 800 and1500 m freestyle competitions, but none of them discussed the differences in pacing strategy between sexes nor between distances [7,21]. There is therefore a very strong rationale for updating the study of pacing strategy to provide the most actual individualised spectrum of the best pacing strategy. To this purpose, the analysis of real-world top-level competitions needs to be differentiated by sex, age, and competition level. The direct comparison of the pacing strategy adopted in the longest world championship swimming events could help understanding the mechanism underpinning swimmers' tactical choices. The aim of this study was to determine

most actual individualised spectrum of the best pacing strategy. To this purpose, the analysis of real-world top-level competitions needs to be differentiated by sex, age, and competition level. The direct comparison of the pacing strategy adopted in the longest world championship swimming events could help understanding the mechanism underpinning swimmers' tactical choices. The aim of this study was to determine whether choosing a swimming pacing strategy depends on the length of the competition and to conduct an updated parallel analysis of two endurance swimming events supported by similar energy resources but of different durations. To this purpose, the pacing strategies of all the elite and junior 2022–2023 world championships nalists in the 800 and 1500 m freestyle competitions have been compared.

Appl. Sci.2023,13, 10515 3 of 16 To gain deeper insight into the speci city of a swimmer's tactics, the analysis was also differentiated by sex, age, and performance level. 2. Materials and Methods All procedures were conducted according to the Helsinki Declaration. This study has received approval and authorization from the Foro Italico Ethics Committee of the University of Rome, with the designation CAR 155/2023. As only information that was readily accessible to the public was used, informed consent from athletes was judged unnecessary. The competition information for the long-course 800 and 1500 metre freestyle swimming world championships for men and women was collected from the website https://www.worldaquatics.com/swimming, which was accessed from 1 August to 20 August 2023. All data were collected, then anonymously analysed in the past. Athletes' topic identi cation numbers, the competition's name, distance, overall nishing position (ranking), split times (split) every 50 m, and the completion time were all included in each competition report. Procedures and methods of the present work have been previously described [9]. A total of 96 results relative to 48 male and 48 female nalists of the 800 and1500 m freestyle at long-course elite and junior world championships held in 2022 and 2023 were studied. The results of the 19th FINA World Championships Budapest (Budapest, Hun- gary), 8th FINA World Junior Swimming Championships Lima (Lima, Peru), and World Aquatics Championships Fukuoka (Fukuoka, Japan) were analysed. Elite swimmers' age was 23.2 3.4 years; juniors' age was 16.4 1.4 years. 2.1. Data Analysis To examine the ascending and descending trends of the time series as well as to assess the randomness of split uctuations over the median period, a mathematical analysis was used. The goal of the time series analysis is to determine whether the split times should be viewed as a true time series or as random samples. If a statistical test conducted on the data does not result in the rejection of randomness, then the analysis of data indexed by time is mathematically useless. The null hypothesis that a sequence is a random sample was tested using a typical statistical test of

the split times should be viewed as a true time series or as random samples. If a statistical test conducted on the data does not result in the rejection of randomness, then the analysis of data indexed by time is mathematically useless. The null hypothesis that a sequence is a random sample was tested using a typical statistical test of randomness based on the number and the maximal length of monotonous phases by keeping track of turning points, phase lengths, difference- signs, rank correlation, records, and rank serial correlation [32]. A statistic, denoted by (nandt), serves as the foundation for the test, with critical values given by and de ned as follows. A series is considered a maximal sequence of consecutive measurements that is monotonous; then,nis the number of such series andtis the length of the longest one. If one of the inequalities u(n)> " 1 3 (2n 1) 1.96 r 16n 29 9 0 # ,t(n)<[3.3(log10n+1) ] where [x] denotes the integer part ofx, we reject randomness; in other words, we conclude that the sequencex1,. . .,xncan be considered as a true time series, not as a random sample. In our case,n= 16 andn= 30, so that the critical region is given by n> 4.204 ort< 5 for 800-m andn> 9.723 ort< 6 for 1500-m The number of consecutive splits held faster (shown with a “minus” sign) or slower (marked with a “plus” sign) than the median velocity was used to compute the length of split sequences for each nalist. The count of the number of or + sequences was used to determine how many split sequences there were. The longest sequence that had the same or + sign was determined to be the maximum length of split sequences. 2.2. Variables Analysed Race Time% Record Time—To assess the performance level of each athlete, we con- sidered their competition nish time as a percentage of their respective record time (Race

2.2. Variables Analysed Race Time% Record Time—To assess the performance level of each athlete, we con- sidered their competition nish time as a percentage of their respective record time (Race

Appl. Sci.2023,13, 10515 4 of 16 Time% Record Time) and divided in the performer's closest (100–105% of WR) and farthest from the record time (105–112% of WR). Coef cient of variation—The coef cient of variation in velocity along the race was calculated as a percentage of the standard deviation of the split times divided by the mean of the split times (CV%). Sequences Number% Splits Number—The count of the number of negative or positive ( or +) acceleration sequence as a percentage of the number of splits of each race. Maximal length of sequences% Splits Number—The longest sequence holding the same or + sign as a percentage of the number of splits of each race. Time series—When the sequence represented a true time series, it was given the value 1;when half of the sequence was a true time series, it was given the value 2; and if it was a random series, the value 3 (Time series 1—Half 2—Random 3). Normalised velocity—Each split time was expressed as percentage of the mean indi- vidual split times. To compare the split times between the two distances, the splits 2–29 of the 1500 m race were considered every 100 m, thus obtaining the same number of splits as the 800 m race (n = 16). All variables were compared between 800 and 1500 m races in all swimmers, and then separating males and females, elite and junior, medallists (placed from 1st to 3rd) and non-medallists (placed from 4th to last), 100–105% and 105–112% of world records. 2.3. Statistical Analysis For each category, descriptive data (mean and SD) and effect size (ES) are presented. The Shapiro–Wilk test was used to determine whether the data were normal. Depending on the distribution of the data, ANOVA, Mann–Whitney U, or Kruskal–Wallis for repeated measurements with post-hoc Bonferroni correction tests were used. IBM SPSS Statistics for Windows, version 26.0, was used to conduct statistical analyses (IBM Corp, Armonk, NY, USA). The threshold for signi cance was xed at 0.05. 3. Results As described in Table, none of the swimmers of the world championships analysed reached or improved the

Mann–Whitney U, or Kruskal–Wallis for repeated measurements with post-hoc Bonferroni correction tests were used. IBM SPSS Statistics for Windows, version 26.0, was used to conduct statistical analyses (IBM Corp, Armonk, NY, USA). The threshold for signi cance was xed at 0.05. 3. Results As described in Table, none of the swimmers of the world championships analysed reached or improved the respective world record. All nal times resulted within 101% and 112% of world records. Race times in percentage of respective word records presented no differences between the 800 and 1500 m competitions, except for males (p =0.00), elite(p =0.02), and 100-105% (p =0.02) swimmers that reached times closer to the respective world records in the 1500 m race. Table 1.Competitions times. Race Time% Record Time 1500 m 800 m Subjects n Mean SD Mean SD SE p All Athletes 96 105.2 2.8 105.5 2.1 0.1 0.07 Males 48 104.2 0.0 106.0 1.4 0.9 0.00 * Females 48 106.2 3.0 104.9 2.5 0.5 0.43 Elite 64 103.7 1.6 104.5 1.7 0.4 0.02 * Junior 32 108.2 2.3 107.5 1.3 0.4 0.90 Medallists 32 103.9 2.1 104.5 1.8 0.3 0.34 Non-medallists 64 105.9 2.9 106.0 2.1 0.0 0.15 100–105% of WR 48 103.1 1.1 103.6 1.1 0.4 0.02 * 105–112% of WR 48 107.7 2.1 107.1 1.2 0.4 0.76 p: differences between 1500 and 800 m freestyle results; *:p< 0.05.

Appl. Sci.2023,13, 10515 5 of 16 As shown in Table, sequence numbers were signi cantly higher in the 800 m com- petitions for all the swimmer groups. The maximal length of sequences of the same sign ( or +)were longer in the 800 m competitions, but the difference reached a signi cant level only when all swimmers were analysed as a whole (p =0.01) and for the junior(p =0.00), medallists (p =0.04), and 105–112% (p =0.04) groups. Table 2.Splits sequences. Sequences Number (%) Maximal Length of Sequences (%) 1500-m 800-m 1500-m 800-m Subjects n Mean SD Mean SD SE p Mean SD Mean SD SE p All Athletes 96 31.3 11.0 34.6 12.8 0.3 0.00 * 32.6 9.5 37.6 9.9 0.5 0.01 * Males 48 33.1 0.2 37.2 13.4 0.3 0.00 * 28.5 11.5 35.7 10.0 0.7 0.09 Females 48 29.4 10.5 32.0 12.0 0.2 0.00 * 36.7 7.3 39.6 9.7 0.3 0.07 Elite 64 31.7 10.8 34.0 13.1 0.2 0.00 * 32.3 9.4 37.3 10.8 0.5 0.32 Junior 32 30.4 11.7 35.9 12.6 0.4 0.00 * 33.1 10.1 38.3 8.2 0.5 0.00 * Medallists 32 31.7 8.9 37.9 13.6 0.5 0.00 * 31.3 8.7 35.2 10.2 0.4 0.04 * Non-medal. 64 31.0 33.0 33.0 12.3 0.2 0.00 * 33.2 10.0 38.9 9.8 0.6 0.12 100–105% 48 32.4 33.2 33.2 13.0 0.1 0.00 * 30.6 9.0 38.1 9.8 0.7 0.20 105–112% 48 29.8 12.8 35.8 12.8 0.5 0.00 * 34.8 9.8 37.3 10.2 0.2 0.04 * p: differences between 1500 and 800 m freestyle results; *:p< 0.05. As displayed in Table, the time-series analysis revealed that the 1500 m competitions presented a signi cantly higher occurrence of “true” time series with respect to the 800 m competitions when all swimmers' results were taken as a whole (p =0.01) and for the male (p =0.04) and the elite (p =0.02) groups. The coef cient of variation in velocity along the race (CV%) was not signi cantly greater in the 800 m competitions for all groups. Table 3.Variability of splits times along races. Time Series 1—Half 2—Random 3 CV% 1500-m 800-m 1500-m

results were taken as a whole (p =0.01) and for the male (p =0.04) and the elite (p =0.02) groups. The coef cient of variation in velocity along the race (CV%) was not signi cantly greater in the 800 m competitions for all groups. Table 3.Variability of splits times along races. Time Series 1—Half 2—Random 3 CV% 1500-m 800-m 1500-m 800-m Subjects n Mean SD Mean SD SE p Mean SD Mean SD SE p All Athletes 96 1.0 0.1 1.3 0.7 0.5 0.01 * 2.9 0.5 2.9 0.6 0.1 0.60 Males 48 1.0 2.2 1.4 0.8 0.6 0.04 * 2.9 0.5 2.9 0.6 0.0 0.94 Females 48 1.0 0.0 1.2 0.6 0.4 0.15 2.8 0.5 2.9 0.6 0.3 0.56 Elite 64 1.0 0.2 1.4 0.8 0.6 0.02* 2.8 0.5 2.8 0.5 0.0 0.98 Junior 32 1.0 0.0 1.1 0.5 0.4 0.78 2.9 0.6 3.1 0.6 0.3 0.40 Medallists 32 1.0 0.0 1.5 0.9 0.7 0.24 2.8 0.4 2.8 0.5 0.0 0.96 Non-medallists 64 1.0 0.2 1.2 0.5 0.4 0.16 2.9 0.6 3.0 0.6 0.2 0.55 100–105% of WR 48 1.0 0.2 1.3 0.7 0.5 0.20 2.9 0.4 2.9 0.4 0.1 0.91 105–112% of WR 48 1.0 0.0 1.3 0.7 0.6 0.77 2.8 0.6 3.0 0.7 0.2 0.47 p: differences between 1500 and 800 m freestyle results; *:p< 0.05. Figure the 1500 m with respect to the 800 m competitions resulted signi cantly faster from the 5th to the 12th split (p =0.00). The 1500 m velocity remained close to the mean velocity (100%) from the 3rd to the 7th split and declined afterwards until the spurt of the two last

The study analyzes pacing strategies in elite and junior swimmers during 800 m and 1500 m freestyle events.