Data analysis

Model interpretation

While the evaluation metrics give a view of the model’s predictive performance, more advanced tools provide a look inside the model for associations between the predictors and target variables. Among these tools, the PDP library plots relative and absolute prediction distribution charts, along with the mean values and group sizes. The PDP plot shows the relative change in the model output for the different values of each predicting variable, with respect to a reference value (0), with prediction plots showing the range of outputs for each predictor using boxplots. Model feature relative importance was also computed. Pearson’s and Spearman’s correlations were displayed in correlation matrices to investigate the correlation between model variables.

All computations and analysis employed Jupyter Notebook (Google Colab) and Python, along with associated libraries (Pandas, NumPy, XG Boost, PDPbox, sklearn, Matplotlib, and sns).

Country rankings by number of race records and unique runners

Table 1 summarises the race records by the 69 countries of origin of the athletes and lists the countries by the number of recorded race results. Mean running speed is colour-coded, where darker colours correspond to faster running speeds. The United States of America (USA) accounted for about one-third of race records in terms of country of origin and country of the event, followed by Taiwan and some European countries, such as Germany, France, Italy, and Norway. other nations highlighted included those of the Anglosphere, such as Australia, the United Kingdom (UK), and South Africa. the fastest average running speeds were achieved by athletes from Lithuania, Israel, Russia, Hungary, Croatia, and Namibia (the latter had 14 records from four unique runners).

Event country ranking table

Table 2 summarises the events for the 55 different countries and lists the countries by the number of recorded race results. Mean running speed is colour-coded, where darker colours correspond to faster running speeds. the fastest running speeds were achieved in races held in Russia, the Netherlands, Israel, Slovakia, the Czech Republic, Croatia, and Hungary.

Correlation between model variables

To investigate a potential correlation between the country of origin of the athlete and the country where the races were held, we performed Pearson (Figure 1) and Spearman (Figure 2) correlations. Sex has a value of 0 for women and 1 for men. running speed showed a slight positive correlation with sex (hence faster speeds for 1’s). the age group consisted of sorted integers (18, 20, 25, 30, etc.) and the distribution followed an inverted U shape, so the correlations showed no simple linear pattern. An increasing Athlete_country_ID indicated only a minor representation in the sample for the country the ID represents, which was similar to the Event_country_ID. As such, care must be taken when interpreting the positive correlation (Pearson = 0.23 and Spearman = 0.31) between the country variables and running speed since a one-unit increase represents a 0.23 km/h (or 0.31 km/h by Spearman) increase in running speed. However, the unit increase in the country variable is meaningless as it only indicates a change of country. there were also positive correlations between sex and the country of origin and event. the highest correlation was between the countries of origin and countries of event, indicating that most runners competed in races in their country of origin.

Figure 1

Pearson’s correlations between model variables

Figure 2

Spearman’s correlations between model variables

XG Boost regression model

Evaluation metrics and feature relative importance

The model was trained and tested with all 103,334 records, with the accuracy (r² = 0.34) indicating a moderately weak effect of the predictor variables in the model output and suggesting that additional predictor variables should be added to improve its predictive power. The country of the event was considered the most important predictor of performance (based on data entropy reduction), with a score of 52%, followed by the athlete’s country, sex, and age group (Figure 3).

Figure 3

Optimal model feature relative importance

Partial dependence plots

Regarding sex, men were ~0.45 km/h faster than women (Figure 4). The PDP for the 30-34, 35-39 and 40-44 age groups was flat, indicating a broad range of ages positively contributing to the best running speed predictions (Figure 5). The results by athlete country peaked at ID 49 (Lithuania) (Figure 6), while the results by event country peaked at ID 21 (The Netherlands) (Figure 7).

Figure 4

Partial dependence plots for sex

Figure 5

Partial dependence plots for age group

Figure 6

Partial dependence plots for athlete’s country of origin

Figure 7

Partial dependency plots for the country where the race was held

Prediction distributions and target value diagrams

The mean difference between male and female predictions was ~0.6 km/h (middle chart). However, the median difference (top chart) was over 1.2 km/h, emphasising the performance gap between men and women (Figure 8). The fastest runners were recorded in the 40-44 and 45-49 age groups, obtaining the highest predictions (Figure 9). In the athlete country charts, distinctive peaks can be seen for Lithuania and Israel, with predictions well over the 9 km/h mark (Figure 10). In the event country charts, Israel, Latvia, Slovakia, Romania, Croatia, Czech Republic, Netherlands, Russia, and Hungary obtained prediction distributions over 8 km/h, pointing at a dominance of eastern European countries in fast 12-hour races. on the contrary, 12-hour races in Asian countries (Singapore, Philippines, Thailand) were among the slowest, as were those in the USA and Mexico (Figure 11).

Figure 8

Interpretability charts of the sex model

Figure 9

Model interpretability charts for the age group

Figure 10

Model interpretability charts for the athlete’s country of origin

Figure 11

Model interpretability charts for the country where the events were held

Event location was the most important predictor variable

The regression model found that the event location was the most important predictor, followed by the origin of the athlete, sex, and age. Whilst this result does not imply causality in any way, the information adds value to the scientific discussion on predictors of performance in the ultra-marathon. Most studies considered individual attributes as the most critical factors in running performance, which differs from the present findings. The importance of event location on running speed may be related to environmental characteristics that impair performance, including weather [17, 18]. For example, non-elite runners spend roughly five hours running a marathon, which harms performance and health. In this regard, statistics from 830,255 nonelite runners who completed the New York City Marathon between 1999 and 2019 showed that temperature and humidity slowed the pace of competitors of various ages but had more influence on those aged 20 to 59 [17]. Similar findings were obtained for runners who completed the Berlin Marathon, where increasing temperatures and decreasing humidity throughout the day were negatively related to running speed, with men being more affected than women [18].

Event locations, as a crucial predictor, may involve physiological factors such as altitude and climate. Countries like Russia and Israel, where top runners originated and achieved high running speeds, may offer environmental conditions that favour endurance, with altitude potentially affecting oxygen utilisation and cardiovascular adaptation. The variation in running speeds at different locations suggests that training environments also play a crucial role [19]. Factors such as access to varied terrains, advanced training facilities, and coaching expertise can influence an athlete’s physiological adaptation and overall preparedness for ultramarathon events [20].

Most 12-hour runners were from the USA, but the fastest were not

The USA accounted for about one-third of the 12- hour race records, both in terms of country of origin and country of event, followed by Taiwan and some European countries (e.g., Germany, France, Italy, and Norway), along with others from the Anglosphere (i.e., Australia, the United Kingdom, and South Africa). However, the fastest runners were from Lithuania, Israel, Russia, Hungary, and Croatia, confirming our hypothesis.

The higher frequency of runners from the USA is in agreement with previous literature. A macro-to-micro analysis of runners competing in 100-mile ultra-marathons showed the highest frequency of runners [21], as did a by Hoffman covering events held between 1977 and 2008 [22]. The high of runners from the USA was previously explained alongside the history of running in the USA and globally, as well as the increase in participation among women and older athletes [23, 24]. However, a higher participation rate does not equate to higher performance. For example, in 100-mile ultramarathons, the fastest runners in the top three, top 10, and top 100 for women were from Sweden, Hungary, and Russia, and Brazil, Russia and Lithuania for men [21]. The factors explaining that the fastest runners originated from Lithuania, Israel, Russia, Hungary, Croatia, and Namibia are unclear in the literature. However, these results can be related to the characteristics of the event. Our analyses revealed that the fastest running speeds were achieved in races held in Russia, the Netherlands, Israel, Slovakia, the Czech Republic, Croatia, and Hungary, which can increase runner participation in events in these countries. In addition, cultural, historical, and weather characteristics can benefit runners living near the place of competition. Identifying Lithuania, Israel, Russia, Hungary, Croatia, and Namibia as the origins of the fastest runners also raises questions about genetic predispositions, cultural influences, motivation, and training. Genetic factors impacting endurance, such as muscle fibre composition, as well as cultural attitudes toward long-distance running, could contribute to superior performance [25].

Exploring the idea that European ultra-marathoners are the fastest involves considering diverse terrains, cultural influences, and advanced training resources. The periodisation of ultra-marathon training is highly individualised and involves factors such as race specificity and athlete experience and goals [26]. Monitoring fatigue levels, adjusting training intensity, and incorporating adequate recovery are crucial aspects of successful ultra-marathon training [27]. Furthermore, mental preparation and nutrition planning play an integral role in ensuring that athletes are well-prepared for the mental and physical demands of ultramarathon races [28]. Therefore, training periodisation involves a structured approach to optimise physical and mental readiness for the unique challenges of ultramarathon distances [29].

What drives an individual to choose a sports discipline that exposes and pushes the limits of human physical and psychological limits? Understanding the motivations behind participating in ultra-marathons involves delving into the interconnected aspects of an athlete’s biology, psychology, and social influences [30]. Biopsychosocial factors collectively contribute to shaping the mindset and drive of these extraordinary individuals [31]. Biologically, exploring the physiological adaptations that occur in ultra-marathon runners is fascinating. Endurance training induces changes in cardiovascular efficiency, muscle strength, and metabolic pathways, allowing athletes to maintain prolonged efforts [32]. Additionally, genetic predispositions may play a role in an individual’s aptitude for ultra-marathon distances [33]. From a psychological perspective, delving into the mindset of ultra-marathoners unveils a complex interplay of mental resilience, motivation, and goal setting [34]. These athletes often have an intrinsic motivation to challenge themselves, seeking personal growth and accomplishment [35]. The ability to endure prolonged physical exertion also requires a robust mental framework, including coping strategies for pain, fatigue, and the psychological toll of long-distance running [36]. Social factors contribute significantly to the appeal of ultra-marathons, with community and camaraderie within the ultra-running world fostering a supportive environment [37]. Athletes often find inspiration and encouragement from their peers, creating a shared identity among those who embrace the challenges of ultra-marathon distances [38]. Social networks, events, and online communities further contribute to the diffusion of ultra-running culture [39]. Examining the biopsychosocial profile of ultramarathon athletes provides valuable insights for sports science and understanding human motivation, resilience, and the pursuit of extraordinary challenges [40]. It showcases the intricate interplay between biological predispositions, psychological factors, and social influences that collectively shape the mindset of those who choose to venture into the realm of ultra-marathons [41].

Correlations between country of origin and country of event

We found a strong correlation between the country of origin of the athlete and the country of the event, indicating that athletes prefer to compete in their home country. We also found a correlation between the country of the event and running speed, indicating that countries with substantial participation had lots of average or poor performers, which brought the average performance down. In contrast, the overall quality of runners was higher in countries with a lower number of participants. We also found a positive correlation between sex and country and both the athlete/event country variables, which suggests that as participation reduced, the men-to-women ratio seemed to increase.

Sex differences in performance and the age of peak running performance

Men were, on average, 0.5 km/h faster than women. Performance differences between sexes are well established in the scientific literature [42, 43]. the observed sex disparity in running speeds is consistent with established physiological differences between men and women. Men typically exhibit greater muscle mass, higher aerobic capacity, and different fat metabolism patterns, contributing to their overall faster running speeds in ultra-marathons [44]. Studying the evolution of women’s performance compared to men’s in ultramarathon races holds significant interest for several reasons since it comprehensively explores sex-specific physiological adaptations and capabilities in response to extreme and prolonged physical exertion [45].

Understanding how women’s performance in ultramarathons has evolved compared to men’s provides valuable insights into the progress, challenges, and potential advancements in female endurance sports [46]. This research can help break down sex-related stereotypes and promote equal opportunities and recognition in ultra-marathon competitions [47]. Future studies need to investigate the trend in sex differences over time to estimate whether women can close the gap with men in the future.

Understanding sex differences is instrumental for coaches, athletes, and sports scientists in tailoring training programs that optimise the performance of both male and female ultra-marathon runners [48]. Additionally, highlighting the achievements of women in ultra-marathons can inspire a broader cultural shift, encouraging more women to participate in these challenging events and fostering inclusivity within the sporting community [49]. In essence, studying the evolution of women’s performance compared to men’s in ultra-marathons not only contributes to the scientific understanding of athletic capabilities but also promotes sex equality, encourages participation, and enhances overall awareness of the diverse achievements in endurance sports [50].

Athletes in the 40-44 and 45-49 age groups were fastest. The concentration of participants and top performers in these age groups indicates potential advantages associated with these age ranges. Factors such as accumulated training, previous experience, enhanced endurance capabilities, and optimised pacing strategies may contribute to the superior performance observed in these age groups [51].