All procedures used in the study met the ethical standards of the Swiss Academy of Medical Sciences 26 and were approved by the Institutional Review Board of Kanton St. Gallen, Switzerland, with a waiver of the requirement for informed consent of the participants given the fact that the study involved the analysis of publicly available data.

The data set for this study was obtained from the website of the FINA 15 . All athletes who ever finished a 5 km, 10 km and 25 km FINA World Cup open-water swim race between 2000 and 2012 were included. To determine the changes over time in peak swimming speed and in the sex difference in swimming speed, race times of the annual top and the annual top ten women and men were analysed. To increase the comparability between different race distances, all race times were converted to swimming speed (km/h) using the equation [swimming speed (km/h)] = [race distance (km)]/[race time (h)]. When less than the needed amount of athletes was available in a certain year for a certain distance, that year was excluded from analysis. To estimate the power density of the swimmers, the time differences between the last and the first finisher as well as between tenth and the first finisher were analysed and expressed as a percentage of the winner performance for both women and men.

In order to increase the reliability of the data analyses, each set of data was tested for normal distribution and for homogeneity of variances prior to statistical analyses. Normal distribution was tested using a D’Agostino and Pearson omnibus normality test and homogeneity of variances was tested using a Levene’s test. Trends in participation were analysed using regression analysis with ’straight line‘ and ’exponential growth equation‘ model where for each set of data (e.g. each sex) both models where compared using Akaike’s Information Criteria (AICc) to decide which model showed the highest probability of correctness. Single and multi-level regression analyses were used to investigate changes across years in swimming speed and age of the athletes. A hierarchical regression model was used to avoid the impact of a cluster-effect on results in case one athlete finished more than once in the annual top or the annual top ten. Furthermore, regression analyses of swimming speed were corrected for age of the athletes to prevent a misinterpretation of an ‘age-effect’ as a ‘time-effect’. Since it is assumed that the change in sex difference in endurance performance is non-linear 27 , we additionally calculated the non-linear regression model fitting the data best. We compared the best-fit non-linear models to the linear models using AIC and F-test in order to show which model would be the most appropriate to explain the trend of the data. Statistical analyses were performed using IBM SPSS Statistics (Version 21, IBM SPSS, Chicago, IL, USA), CurveExpert Professional (Version 2.0.3, Hyams D.G.) and GraphPad Prism (Version 6.01, GraphPad Software, La Jolla, CA, USA). Significance was accepted at p < 0.05 (two-sided for t-tests). Data in the text and figures are given as mean ± standard deviation (SD).

Table 1 presents the numbers of both finishes and finishers. Most swimmers competed in 5 km, followed by 10 km and 25 km. Between 2000 and 2012, on average 38 ± 16 women and 43 ± 17 men competed in a 5 km, 45 ± 29 women and 57 ± 35 men in a 10 km, and 19 ± 7 women and 25 ± 9 men in a 25 km FINA World Cup event. The number of finishers in 5 km increased significantly for men (r² = 0.36, p < 0.05) but not for women and overall finishers (p > 0.05) (Figure 1A). In 10 km, the number of finishers increased significantly for both women (r² = 65, p = 0.0014) and men (r² = 0.72, p = 0.0004) (Figure 1B). In 25 km, the overall number of finisher was unchanged (p > 0.05) (Figure 1C). Table 2 presents the numbers of finishes regarding the origin of the competitors. When all three race distances were considered, most of the finishes were achieved by competitors originating from Russia, followed by swimmers originating from Italy and Germany.

RUS = Russia, ITA = Italy, GER = Germany, FRA = France, ESP = Spain, CZE = Czech Republic, USA = United States of America, AUS = Australia, GBR = Great Britain, HUN = Hungary, UKR = Ukraine, CAN = Canada, BRA = Brazil, NED = Netherlands, ECU = Ecuador, MEX = Mexico, BUL = Bulgaria, VEN = Venezuela, CRO = Croatia, GRE = Greece, SLO = Slovenia, ARG = Argentina, SUI = Switzerland, RSA = Republic of South Africa, CHN = China, POR = Portugal, EGY = Egypt, ISR = Israel, BEL = Belgium, HKG = Hong Kong, MKD = Macedonia, NZL = New Zealand, POL = Poland, AZE = Azerbaijan, SVK = Slovakia, GUA = Guatemala, JPN = Japan, CRC = Costa Rica, IRL = Ireland, SWE = Sweden, TUR = Turkey, SYR = Syria, KAZ = Kazakhstan, INA = Indonesia, AUT = Austria, CHI = Chile, BLR = Belarus, DOM = Dominican Republic, MNE = Montenegro, OMA = Oman, CYP = Cyprus, PUR = Puerto Rico, FAR = Faroe Islands, FIN = Finland, GUM = Guam, IND = India, MAS = Malaysia, PLE = Palestine, SRB = Serbia, TUN = Tunisia, UAE = United Arab Emirates, BAN = Bangladesh, COK = Cook Islands, CUB = Cuba, DEN = Denmark, KSA = Saudi Arabia, LBA = Libya, MAR = Morocco, ROU = Romania, THA = Thailand.

For the annual fastest, swimming speed remained stable across years in 5 km (5.50 ± 0.21 km/h for men and 5.08 ± 0.19 km/h for women) (Figure 2A), in 10 km (5.38 ± 0.21 km/h for men and 5.05 ± 0.26 km/h for women) (Figure 2B) and in 25 km (5.03 ± 0.32 km/h for men and 4.58 ± 0.27 km/h for women) (Figure 2C) also when corrected for multiple finishes and age of the athletes with multiple finishes (Table 3). Considering the annual ten fastest, swimming speed remained constant in 5 km in women (5.02 ± 0.19 km/h) but decreased significantly and linearly (Table 4) in men from 5.42 ± 0.03 km/h to 5.39 ± 0.02 km/h (Figure 2D) also when controlled for multiple finishes and age of the athletes with multiple finishes (Table 3). In 10 km, swimming speed increased significantly and linearly (Table 4) in women from 4.75 ± 0.01 km/h (2002) to 5.74 ± 0.01 km/h (2012) but remained stable in men at 5.36 ± 0.21 km/h (Figure 2E) also when controlled for multiple finishes and age of the athletes with multiple finishes (Table 3). In 25 km, swimming speed decreased significantly and linearly (Table 4) in women from 4.60 ± 0.06 km/h to 4.44 ± 0.08 km/h but remained unchanged at 4.93 ± 0.34 km/h in men (Figure 2F) also when controlled for multiple finishes and age of the athletes with multiple finishes (Table 3).

For the annual fastest, the sex difference in swimming speed remained unchanged in 5 km (7.6 ± 3.0%) (Figure 3A), in 10 km (6.1 ± 2.5%) (Figure 3B) and in 25 km (9.0 ± 3.7%) (Figure 3C) also when controlled for multiple finishes (Table 5). For the annual ten fastest, the sex difference remained stable in 5 km at 7.65 ± 0.59% (Figure 3D), decreased significantly and linearly (Table 6) in 10 km from 7.7 ± 0.7% (2002) to 1.2 ± 0.3% (2012) (Figure 3E) and increased significantly and linearly (Table 6) from 4.7 ± 1.4% to 9.6 ± 1.5% in 25 km (Figure 3F) also when corrected for multiple finishes (Table 5). For the annual ten fastest, the sex difference was stable at 7.6 ± 0.6% in 5 km, decreased significantly and linearly (Table 6) from 7.7 ± 0.7% (2002) to 1.2 ± 0.3% (2012) in 10 km and increased significantly and linearly from 4.7 ± 1.4% to 9.6 ± 1.5% in 25 km.

The power density in swimming speed of the 1st to the 10th finisher showed no changes in 5 km (Figure 4A), 10 km (Figure 4B), and 25 km (Figure 4C), also when corrected for multiple finishes and age of the athletes with multiple finishes (Table 7). Also for the 1st to the last finisher, no changes in power density were found in 5 km (Figure 4D), 10 km (Figure 4E), and 25 km (Figure 4F), also when corrected for multiple finishes and age of the athletes with multiple finishes (Table 7). The power density from the 1st to the 10th finisher was similar in 5 km (-1.95 ± 2.10% for women and -1.83 ± 1.44% for men), 10 km (-0.83 ± 1.52% for women and -0.55 ± 0.62% for men) and 25 km (-3.31 ± 3.27% for women and -3.76 ± 2.97% for men). For the 1st to the last finisher, the power density was lower in women (-18.13 ± 6.54%) compared to men (-24.21 ± 12.0%) in 5 km, higher in women (-22.21 ± 8.12%) compared to men (-17.51 ± 4.60%) in 10 km and lower in women (-13.77 ± 6.01%) compared to men (-16.22 ± 6.51%) in 25 km.

For the annual fastest in 5 km, the age of the peak swimming speed decreased in women (Figure 5A) from 28 years to 22 years whereas it remained unchanged in men at 26.7 ± 3.6 years (Table 8). In 10 km (Figure 5B), the age of the fastest women decreased from 29 years (2002) to 19 years (Table 8). For the fastest men, however, it increased from 20 years (2002) to 28 years. In 25 km, the age of the fastest women and men (Figure 5C) remained unchanged at 26.7 ± 4.0 and 27.9 ± 3.8 years, respectively (Table 8). For the annual ten fastest, the age of peak swimming speed remained unchanged for women and men in 5 km (Figure 5D) at 22.4 ± 1.2 and 24.8 ± 0.9 years (Table 8). In 10 km, the age of the fastest women remained unchanged at 23.4 ± 0.9 years (Figure 5E) but increased in men from 24.2 ± 2.6 to 28.4 ± 4.8 years (Table 8). In 25 km (Figure 5F), the age of the fastest women and men remained unchanged at 23.7 ± 0.9 and 27.2 ± 1.1 years, respectively (Table 8).

The numbers of participants increased for men in 5 km and for both sexes in 10 km whereas the numbers of participants were constant in all other distances. Most swimmers competed and finished in 5 km, followed by 10 km and 25 km. As FINA World Cup races are organized on a professional base, i.e. allowing only a reserved number of participants 15 and a great increase in the numbers of participants were not to be expected. From each sex, the five fastest finishers of last year’s World Cup races and the five fastest Olympians can enter each year a series of races. Nevertheless, an increasing number of races each year provides for more possible participants. Furthermore, the number of open-water ultra-distance swimming events is small compared to indoor pool swimming 15 .

An interesting finding was that swimming speeds remained stable across years for the annual fastest swimmers in 5 km, 10 km and 25 km. As the sex difference in swimming speed was constant in the annual fastest finishers, neither a trend of increase nor decrease in swimming speed was found nor it seems as performance in the best long-distance swimmers competing from 5 km to 25 km has plateaued. A possible explanation may by the short period of time investigated of 13 years, as other authors found an increase in swimming speed in long-distance swimming over longer periods 5 6 7 28 . For example, Nevill et al. reported an increase for swimming speeds in pool swimmers competing across all distances during the 60’s and 70’s when investigating data from 1956–2006, while swimming speeds plateaued in the last thirty years 28 . Therefore, swimming speed in long-distance may level off as short- and middle-distance swimming did 35 years ago.

The best models to describe the changes in sex differences in swimming speed were linear in both the annual fastest and the annual ten fastest competitors. It has been stated that linear models cannot keep up with the gender gap in sport and non-linear models would be better 27 . Our findings, however, cannot support this theory. For the annual fastest swimmers, the sex differences remained unchanged in 5 km, in 10 km and in 25 km.

Performance in all endurance sports depends on the athlete’s ability to produce a high energy output constantly on an economical level. Both physiological and anthropometric differences between sexes seem to influence the sex difference in performance. Maximum oxygen uptake (VO₂max) was reported as the most significant predictor variable for endurance performance 29 . While elite male athletes reach a VO₂max of up to 85 ml · min^-1 · kg^-1 30 , women’s VO₂max is lower with a maximum of 70 ml · min^-1 · kg^-1 31 . VO₂max is mainly dependent from the heart’s performance and the lung capacity 32 . The maximal cardiac output in elite male athletes is higher than in elite female athletes 33 . The same was reported for lung capacity 34 . VO₂max directly depends from both maximal cardiac output and lung capacity and is therefore larger in men than in women 32 . Therefore, men have generally more physiological potential to perform at a higher level than women.

The sex difference in performance was often discussed in other sports disciplines such as running 35 36 , cycling 37 , swimming 5 6 7 , or the combination of the three in triathlon 4 38 . The probably most controversial discussed publication dates back to 1992, when Whipp and Ward 35 used linear statistical models to prove their point of women outrunning men in marathon running. A series of publications followed, discussing the subject intensely 27 36 39 40 . So far, in neither of the mentioned sports, women were ever able to outperform men with very rare single exceptions such as the initially mentioned Diana Nyad swimming from Cuba to Florida 23 . In triathlons from the classical Olympic distance (i.e. 1.5 km swimming, 40 km cycling and 10 km running) 41 to Deca Iron ultra-triathlons (i.e. 38 km swimming, 1,800 km cycling, 422 km running) 22 , the authors found sex differences of performance that seemed to increase with increasing duration or distance of the triathlon event.

Swimming speed results in single open-water long-distance performances of Diana Nyad and Christoph Wandratsch are hard to compare as water temperatures and weather cannot be influenced but have an influence on performance 7 42 . Effects of water temperature and different means to avoid undercooling or overheating have been discussed differently 43 . Both undercooling 43 and overheating 44 threaten performance after prolonged exposure. However, specific anthropometric characteristics such as body fat seemed to influence performance in long-distance swimming. A high body fat percentage was favourable of withstanding the cold of the water 45 46 . To avoid large differences between different races, the highest as well as the lowest temperature in long-distance swimming are defined by FINA. Above 31°C and below 16°C there are no races at all, between 16°C and 26°C swimmers may use wetsuits 15 .

In the annual ten fastest, women became faster in 10 km but slower in 25 km whereas men showed no changes in performance. These changes in female performances led to a linear decrease in sex difference in 10 km and a linear increase in sex difference in 25 km. In the annual fastest, however, no changes occurred in both swimming speeds and sex differences in swimming speeds. Therefore, women could not generally reduce the gender gap in ultra-distance swimming performance, especially in the longer race distances.

In contrast to the annual fastest swimmers, the annual ten fastest women became faster in 10 km between 2000 and 2012. Maybe the 10 km race is an ideal race for women. A recent study investigating the performance in 10 km open-water swimming including World Cup races, European Championships, World Championships and Olympic Games from 2008 to 2012 showed an unchanged swimming speed for women but performance impaired in men 9 . A possible explanation may be drafting as the 10 km could be the optimal distance (i.e. swimming speed and duration of the race) to draft a whole race. In 5 km, the sex difference in muscle strength may allow men to outpace women whereas 25 km may be too long to simply rely on drafting for women. However, other unknown factors may be present in 10 km. As our results are in line with findings for recreational athletes 5 6 7 it seems rather unlikely that women will outperform men in the future in longer swim distances. This assumption will be supported by the unchanged power density in swimming speed for both women and men.

The sex difference in performance between female and male endurance and ultra-endurance athletes might be partially explained by differences in anthropometric characteristics between women and men such as differences in skeletal muscle mass and body fat. Knechtle et al. 22 argued that the increase in sex difference with increasing race distance in ultra-races such as an ultra-triathlon was most probably due to the lower skeletal muscle mass in women. It has been shown that male ultra-endurance athletes had a higher skeletal muscle mass than female ultra-endurance athletes 47 48 49 50 51 . For example, male Ironman triathletes with 41 kg skeletal muscle mass had a 46% higher skeletal muscle mass compared to female Ironman triathletes with 28 kg skeletal muscle mass 48 . Considering ultra-runners, male ultra-runners with 38 kg skeletal muscle mass 49 had a 38% higher muscle mass compared to female ultra-runners with 27.4 kg 50 . For ultra-swimmers 51 , the sex difference in skeletal muscle mass was considerably higher compared to runners 49 50 . Male open-water ultra-swimmers with 42 kg of skeletal muscle mass had 45% more skeletal muscle mass compared to female open-water ultra-swimmers with 29 kg of skeletal muscle mass 51 . These differences in skeletal muscle mass between female and male ultra-endurance athletes might explain the increase in sex difference with increasing race length in open-water ultra-distance swimmers.

The age of peak swimming speed in these elite open-water ultra-swimmers was at ~22-28 years depending upon the race distance. These swimmers were therefore considerably younger compared to recreational swimmers investigated by Eichenberger et al. 6 7 where the age of peak swimming speed was at ~30-39 years in recreational 12-hour pool swimmers 6 and recreational 26.4 km open-water swimmers 7 . In pool swimming, elite athletes were younger than open-water ultra-swimmers as reported by Berthelot et al. 52 with ~21 years for elite pool-swimmers competing in 50 m to 1,500 m freestyle. However, Berthelot et al. 52 reported differences in the age of peak swimming speed regarding the length of a race. The peak performance in 1,500 m freestyle was achieved at a younger age of ~18 years compared to the 50 m freestyle at ~23 years, respectively 52 . In elite freestyle swimmers competing at national level, the age of peak swimming speed was at ~19-25 years when all distances were considered 21 . In 50 m freestyle, women were fastest at the age of ~20 years and men at the age of ~23 years. Considering the longest pool distance, women were fastest in 1,500 m freestyle at the age of ~18 years and men at the age of ~20 years 21 .

Considering the results of the present study it seems likely that the age of peak swimming speed decreased from ~20-23 years in of 50 m to ~18-20 years in 1,500 m to increase again to ~23-27 years in 25 km events. Recent investigations 53 54 addressed a potential association of the age of peak performance with the length of an event. In ultra-marathon running, Rüst et al. 54 mentioned the possibility that older runners rather compete in ultra-marathons due to a deficit in physiological factors such as VO₂max compared to young athletes in their best age. It could be argued that the world’s elite swimmers at the age of ~20 years rather compete in short- and middle distance than in long-distance events. They may change to the ultra-distances after their career in the short distances.

Physiological and anthropometric differences might explain the differences in the age of peak performance between short- to middle-distance and long-distance swimming. Peak swimming speed in sprint swimming was highly associated to strength, power 55 and anaerobic capacity 56 . In longer race distances such as the 1,500 m freestyle, peak swimming speed was rather associated with VO₂max 56 , anaerobic threshold 57 and anthropometric characteristics such as body fat 58 59 60 .

The study is the first to analyse the sex difference of performance in professional open-water long-distance swimmers competing in the FINA World Cup races in 5 km, 10 km and 25 km. The strength of the study is that the statistical analysis excluded the influence of multiple finishes of the same athlete and bypassed a therefore a possible bias of results. Furthermore, both linear and non-linear analyses were performed to find the best model for each point of interest. The study is limited since variables such as physiological parameters 61 , anthropometric characteristics 62 , training data 62 , previous experience 63 , nutrition 64 65 and motivational 66 factors were not considered but may have influenced the results. Further studies need to investigate why swimming speeds in elite long-distance swimming plateaued from 2000–2012 and why the sex difference of performance in long-distance swimming was smaller than expected. Moreover, a systemic analysis of the sex difference of swimming speed across distances from 50 m to 25 km and more would give further insights in the sex difference for different race distances. Future studies might investigate from which country the fastest swimmers in 5 km, 10 km and 25 km originate.

For athletes and coaches, women showed no changes in swimming speed in the 5 km FINA races, increased swimming speed in the 10 km FINA races but decreased swimming speed in the 25 km FINA races. The fastest swimming speeds were attained at the age of ~22-28 years considering all distances from 5 km to 25 km. Elite women intending to improve in 25 km and to lower the gender gap in 25 km would most probably need to increase skeletal muscle mass and muscular strength to follow the fastest men.