Background: Beyond the difference in marathon performance when comparing female and male runners, we tested the hypothesis that running strategy does not different according to sex. The goal of the present study is to compare the running strategy between the best female and male marathon performances achieved in the last two years. Methods: Two aspects of the races were analyzed: (i) average speed relative to runner critical speed (CS) with its coefficient of variation and (ii) asymmetry and global tendency of race speed (i.e., the race’s Kendall $\mathsf{\tau })$ . Results: The females’ best marathons were run at 97.6% ± 3% of CS for the new record (Brigid Kosgei, 2019) and at 96.1% ± 4.4% for the previous record (Paula Radcliffe, 2003). The best male performances (Eliud Kipchoge, 2018 and 2019) were achieved at a lower fraction of CS (94.7% ± 1.7% and 94.1% ± 2.3% in 2018 and 2019, respectively). Eliud Kipchoge (EK) achieved a significant negative split race considering the positive Kendall’s $\mathsf{\tau }$ of pacing (i.e., time over 1 km) ( $\mathsf{\tau }$ = 0.30; p = 0.007). Furthermore, EK ran more of the average distance below average speed (54% and 55% in 2018 and 2019, respectively), while female runners ran only at 46% below their average speed. Conclusions: The best female and male marathon performances were run differently considering speed time course (i.e., tendency and asymmetry), and fractional use of CS. In addition, this study shows a robust running strategy (or signature) used by EK in two different marathons. Improvement in marathon performance might depend on negative split and asymmetry for female runners, and on higher fractional utilization of CS for male runners.

A marathon was recently run in less than 2 h by a man who ran the three fastest marathons ever recorded in a span of three years—Eliud Kipchoge—in the Tokyo Olympic games. Here, we demonstrate that the best marathons were run according to a pace distribution that is statistically not constant and with negative asymmetry. The concept of mirror race enables us to show that the sign of asymmetry is not due to sampling fluctuations. We show that marathon performance depends on pacing oscillations between extreme values, and that even the best marathons ever run differ and can be improved upon. The utilization of extreme values and oscillations allows for recovery and optimization of the complementary aerobic and anaerobic metabolisms. Our findings suggest new ways to approach the pacing for optimizing endurance performance.

In this study, we obtain the size distribution of voids as a three-parameter redshift-independent log-normal void probability function (VPF) directly from the Cosmic Void Catalog (CVC). Although many statistical models of void distributions are based on the counts in randomly placed cells, the log-normal VPF that we obtain here is independent of the shape of the voids due to the parameter-free void finder of the CVC. We use three void populations drawn from the CVC generated by the Halo Occupation Distribution (HOD) Mocks, which are tuned to three mock SDSS samples to investigate the void distribution statistically and to investigate the effects of the environments on the size distribution. As a result, it is shown that void size distributions obtained from the HOD Mock samples are satisfied by the three-parameter log-normal distribution. In addition, we find that there may be a relation between the hierarchical formation, skewness, and kurtosis of the log-normal distribution for each catalog. We also show that the shape of the three-parameter distribution from the samples is strikingly similar to the galaxy log-normal mass distribution obtained from numerical studies. This similarity between void size and galaxy mass distributions may possibly indicate evidence of nonlinear mechanisms affecting both voids and galaxies, such as large-scale accretion and tidal effects. Considering the fact that in this study, all voids are generated by galaxy mocks and show hierarchical structures in different levels, it may be possible that the same nonlinear mechanisms of mass distribution affect the void size distribution.

The study of pace strategy in different environments could help to understand its dependence on athletes’ energetic limits or on sport-specific factors. The aim of this study was to analyse the pacing strategy of finalists 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 significant 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-significantly 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 first 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 influence of specific environment and sport type on the pacing strategy of world level competitions seems to be supported.

A new group of marathon participants with minimal prior experience encounters the phenomenon known as “hitting the wall,” characterized by a notable decline in velocity accompanied by the heightened perception of fatigue (rate of perceived exertion, RPE). Previous research has suggested that successfully completing a marathon requires self-pacing according to RPE rather than attempting to maintain a constant speed or heart rate. However, it remains unclear how runners can self-pace their races based on the signals received from their physiological and mechanical running parameters. This study aims to investigate the relationship between the amount of information conveyed in a message or signal, RPE, and performance. It is hypothesized that a reduction in physiological or mechanical information (quantified by Shannon Entropy) affects performance. The entropy of heart rate, speed, and stride length was calculated for each kilometer of the race. The results showed that stride length had the highest entropy among the variables, and a reduction in its entropy to less than 50% of its maximum value (H = 3.3) was strongly associated with the distance (between 22 and 40) at which participants reported “hard exertion” (as indicated by an RPE of 15) and their performance (p < 0.001). These findings suggest that integrating stride length’s Entropy feedback into new cardioGPS watches could improve marathon runners’ performance.

Although the marathon race has been democratized, it remains complex due to the famous “hitting the wall” phenomenon after the 25th km. To characterize this “wall” from a physiological and Rate of Perceived Exertion (RPE) perspective in recreational marathon runners, we report first continuous breath-by-breath gas exchange measurements during an actual marathon race. In order to test the hypothesis that RPE could be a candidate for controlling the marathon pace, this study examined the relationship between RPE and the physiological variables time course throughout a marathon. Only the respiratory frequency and heart rate increased progressively during the race in all the runners, while the oxygen uptake and ventilatory rate followed different kinetics according the individuals. However, the indexation of the physiological parameters and speed by RPE showed the same decreased tendency for all the runners. In conclusion, these results suggest that running a marathon must be self-paced with the RPE.