Introduction

The popularity of the ultramarathon has increased tremendously over the last decades, with increasingly more organized events every year [1, 2]. An ultramarathon is currently defined as any running event taking longer than 6 hours [3]. Ultramarathon races are generally held as time-limited events (e.g., 24-hour races) or distance-limited events, such as the 100-km races [4].

The ability to predict running performance is of great interest for athletes and coaches, particularly in the ultramarathon. Indeed, it is helpful for prescribing speeds during tempo runs, determining the optimal pace strategy during the race, and even choosing splitting times [5–7].

Knechtle et al. proposed a simple equation to predict performance in 24-hour [8] and 100-km [9] races. These authors showed that performance in the 100-km race (Perf_100-km) is primarily related to training intensity and volume, as well as to the age of the runners, but less so to their anthropometric characteristics [9]. However, this study was based only on data from male ultramarathoners at the Biel ultramarathon in Switzerland, and the particular conditions of this race (start at 10:00 p.m., first weekend of June, no rain…) make it difficult to generalize these results to other races, especially in France where 100-km races are usually held in the daytime in September/October with generally lower temperatures. Indeed, temperature and thus season have been shown to influence marathon performance in [10–13].

The authors [9] were also able to obtain an important indicator: the personal best in the marathon. However, this record may have been achieved years earlier (or even decades) and, although it was associated with Perf_100-km from bivariate correlation analysis (p < 0.0001, r = 0.65), this potential predictive variable was excluded from stepwise multiple-regression analysis [9]. Indeed, an old record may sometimes no longer be representative of a runner’s current marathon performance potential and thus of 100-km performance. Therefore, a recent marathon performance (within the last 9 months) may be more appropriate.

The aim of the current study was to identify the predictive variables of Perf_100-km and develop an equation for predicting performance, using individual data, a recent marathon performance, and the environmental conditions at the start of the 100-km race.

Materials and methods

Results

The characteristics of the 56 runners are presented in Table 1.

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Table 1. Characteristics of 56 athletes and their performances in marathon and 100-km.

https://doi.org/10.1371/journal.pone.0279662.t001

From the sample of 56 subjects, significant bivariate correlations were found between Perf_marathon (p < 0.001, r = 0.838, 95%IC between 0.817 and 0.931), wind speed (p < 0.001, r = -0.545, 95%IC between -0.508 and -0.041), barometric pressure (p < 0.001, r = 0.535, 95%IC between 0.195 and 0.615), age (p = 0.034, r = 0.246, 95%IC between 0.277 and 0.666), BMI (p = 0.034, r = 0.245, 95%IC between 0.330 and 0.697), PR_marathon (p = 0.065, r = 0.204, 95%IC between -0.253 and 0.272) and Perf_100-km. Therefore, only these variables were included in models, because they were significantly correlated to Perf_100-km with p < 0.10.

Nevertheless, the first stepwise multiple linear regression analysis entered only Perf_marathon, wind speed and PR_marathon as the independent variables to yield the prediction equation, considering that the other variables (i.e., barometric pressure, age and BMI) were redundant with each other. Therefore, to improve the quality of the model (from a larger sample size; n = 591), subjects with missing variables were re-injected into the statistical analysis.

For this new statistical analysis, the characteristics of these 591 runners and environmental conditions are presented in Tables 2 and 3, respectively.

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Table 2. Characteristics of 591 athletes and their performances in marathon and 100-km.

https://doi.org/10.1371/journal.pone.0279662.t002

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Table 3. Characteristics and environmental conditions during the 100-km races.

https://doi.org/10.1371/journal.pone.0279662.t003

From the sample of 591 subjects, significant bivariate correlations were found between Perf_marathon (p < 0.001, r = 0.696, 95% IC between 0.672 and 0.751), wind speed (p < 0.001, r = -0.394, 95%IC between -0.460 and -0.324), PR_marathon (p = 0.001, r = 0.127, 95%IC between 0.054 and 0.212) and Perf_100-km.

The proposed prediction equation (i.e., model 1) is: (model 1) with Perf_100-km and Perf_marathon in minutes, wind speed in m.s^-1 and PR_marathon = 1 when PR_marathon was performed or 0 when no PR_marathon has been performed.

Very low multicollinearity was found (because VIF < 5) for the independent variables (VIF < 1.069). The increase in r² from adding the second (i.e., wind speed) and third predictors (i.e., PR_marathon) to the prediction equation was significant with F(1,588) = 76.225 (p < 0.001) and F(1,587) = 7.222 (p = 0.007), respectively. Moreover, Fisher’s test revealed a p < 0.001. The performance estimated by the prediction equation (including the three independent variables: Perf_marathon, wind speed and PR_marathon) was significantly correlated with the actual Perf_100-km (r = 0.741 and r² = 0.549). The standardized β coefficients and p values on Student’s t-test were 0.639 (p < 0.001), -0.241 (p < 0.001), and 0.075 (p = 0.007) for Perf_marathon, wind speed and PR_marathon, respectively. No autocorrelation in the residuals was noted. The 95%CI between actual and predicted Perf_100-km was between 0.719 and 0.788. The SEE for the prediction equation was 97 min, i.e., 13.2%.

The second multiple linear regression analysis (excluding environmental conditions) entered Perf_marathon and PR_marathon as the independent variables and yielded the following prediction equation (i.e., model 2): (model 2) with Perf_100-km and Perf_marathon in minutes and PR_marathon = 1 when PR_marathon was performed or 0 when no PR_marathon has been performed.

With VIF = 1.001 for both Perf_marathon and PR_marathon, very low multicollinearity was found for the independent variables. The increase in r² from adding PR_marathon to the prediction equation was significant with F(2,588) = 12.335 (p < 0.001). The performance estimated by the prediction equation (including Perf_marathon and PR_marathon) was significantly correlated with the actual Perf_100-km (r = 0.703 and r² = 0.494). The standardized β coefficients and p values on Student’s t-test were 0.692 (p < 0.001) and 0.103 (p < 0.001) for Perf_marathon and PR_marathon, respectively. The analyse of the residuals indicated no autocorrelation. The 95%CI between actual and predicted Perf_100-km was between 0.680 and 0.758. The SEE for this second prediction equation was 103 min, i.e., 14.0%.

Discussion

The current study aimed to identify the predictive variables of Perf_100-km in order to develop a prediction equation. The results showed significant bivariate correlations between Perf_100-km and individual data (i.e., age and BMI), recent performance and attaining (or not) of personal record during the marathon (i.e., Perf_marathon and PR_marathon), and certain environmental conditions at the start of the 100-km race (i.e., wind speed and barometric pressure). However, only Perf_marathon, PR_marathon and/or wind speed during the 100-km race were included in the prediction equations.

Age and BMI were significantly correlated with Perf_100-km in the bivariate correlation analysis, but these variables were removed from the multiple linear regression analyses because they were also significantly correlated with Perf_marathon (p < 0.001 and r = 0.433 for age, and p = 0.015 and r = 0.290 for BMI) and were thus predictive variables already included in prediction equations. This outcome is not surprising because Knechtle and colleagues showed that when the personal best Perf_marathon is included in the prediction equation, the addition of individual variables (e.g., BMI) does not improve the accuracy of the predicted time [9, 14, 15]. Moreover, age and BMI are known to be correlated with Perf_marathon [16].

In the present study, the barometric pressure during the 100-km races was negatively correlated with the wind, with a very high correlation coefficient (p < 0.001 and r = -0.998). Thus, when wind speed was entered into the stepwise multiple linear regression analysis, barometric pressure in the prediction equation was no longer related to Perf_100-km (i.e., model 1). Recent studies have confirmed the influence of wind speed on Perf_marathon [12, 13]. The current results confirm this for 100-km races; yet it would have been interesting to know the wind direction in order to determine whether it was a head wind, side wind or tail wind. In contrast to these studies [12, 13], a decrease in performance was nevertheless not found in races in the rain. Notably, of the four 100-km races included, only one experienced rainfall, and it involved only three athletes.

The prediction equation including wind speed during the 100-km race provided slightly more accurate predictions (SEE = 13.2 vs 14.0% for models 1 and 2, respectively). However, to allow athletes and/or coaches to predict Perf_100-km more simply, model 2 (without wind speed) may be sufficient. Indeed, predicting Perf_100-km to help the athlete determine the optimal pace strategy during the race and/or choose splitting times can be simple using a single previous Perf_marathon (in the last 9 months), whereas forecasting environmental conditions (often changing and difficult to forecast far in advance), such as wind speed, can be more complicated (for a low gain; i.e., improvement of 0.8% in accuracy). In the literature, about 10% accuracy is generally accepted as tolerable for predicting running performance [5], especially in amateur athletes who want to perform a 100 km for the first time.

It should be noted that, in the future, the accuracy of predictions might be improved by removing the limitations of the present study. For example, one limitation was the self-declaration of body height and weight and thus the calculation of athletes’ BMI. Height and weight were not measured in this study, but self-reported. Thus, the runners may have under- or overestimated these parameters. Nevertheless, it should be noted that runners are known to self-report their anthropometric data accurately [17]. Also, to avoid the possible influence of physical fitness between the marathon and the 100-km race, the two performances had to be performed within a time interval of 9 months. Yet, this time interval may not be negligible, thus allowing for significant changes in physical fitness. Similarly, although environmental conditions during the 100-km races were collected, this information was not available for the marathons. Therefore, it cannot be ruled out that some runners performed in different environmental conditions in the marathon and the 100-km race (e.g., marathon at 30°C in June vs 100-km at 15°C in September). Last but not least, running performance can be affected by a multitude of potential factors as physiological (e.g., maximal oxygen uptake, running economy, anaerobic threshold…), psychological (e.g., motivation, stress) and environmental (e.g., race profile: uphill, downhill…) variables. These variables have not been collected during the current study. However, a potential perceptive could be to include several of these variables to attempt to develop other models more accurate. However, despite these potential limitations (i.e., physical fitness, environmental conditions and psychological states between the marathon and the 100-km race), the proposed equations had an acceptable level of accuracy in amateur athletes. Nevertheless, a future study should confirm the validity of the 2 models presented in this study fom new sample of athletes.

Conclusion

Perf_100-km was significantly correlated with individual data (i.e., age and BMI), recent performance and the attaining (or not) of personal record during the marathon (i.e., Perf_marathon and PR_marathon), and certain environmental conditions at the start of the 100-km race (i.e., wind speed and barometric pressure). However, only Perf_marathon, PR_marathon and wind speed during the 100-km race proved useful to predict Perf_100-km. Moreover, for simplicity, model 2 including only Perf_marathon and PR_marathon (in the 9 months prior to a 100-km race) seems to be sufficient to predict Perf_100-km with an acceptable level of accuracy (SEE = 14.0%), especially in amateur athletes who want to perform a 100 km for the first time.

Acknowledgments

The author is grateful to the French Athletics Feredation (Fédération Française d’Athlétisme) for data diffusion.