Analysis of the 10-day ultra-marathon using a predictive XG boost model

Abstract

Objective

Ultra-marathon running races are held as distance-limited or time-limited events, ranging from 6 h to 10 days. Only a few runners compete in 10-day events, and so far, we have little knowledge about the athletes’ origins, performance, and event characteristics. The aim of the present study was to investigate the origin and performance of these runners and the fastest race locations. A machine learning model based on the XG Boost algorithm was built to predict running speed from the athlete´s age, gender, country of origin, country where the race takes place, the type of race and the kind of running surface. The model explainability tools were then used to investigate how each independent variable would influence the predicted running speed.

Results

The model rated the origin of the athlete as the most important predictor, followed by age group, running on dirt path, gender, running on asphalt, and event location. Running on dirt path led to a significant reduction of running speed, while running on asphalt showed faster running speeds compared to other surfaces. Most athletes came from USA, followed by Russia, Germany, Ukraine, the Czech Republic, and Slovakia. Most of the runners competed in USA. The fastest 10-day runners were from Finland and Israel. The fastest 10-day races were held in Greece.

Conclusions

Most 10-day runners originated from USA, but the fastest runners originate from Finland and Israel. The fastest race courses were in Greece. Running on dirt paths leads to a significant reduction in running speed while running on asphalt leads to faster running speeds.

Introduction

Multi-day races are running events typically held as time-limited races where athletes should complete as much distance as possible. Ultra-marathons are held from 6 h to several days, with 10-day events generally considered the longest competition duration [1,2,3,4]. A 10-day race is mainly held on flat asphalt roads or tracks where athletes have to run as many kilometers within these 10 days. Considering the difficulty level of a 10-day event, the number of participants is reduced compared to ultra-marathons of shorter duration [1,2,3,4].

The low number of ultramarathoners competing in the longest time-limited race format is associated with fewer published papers investigating these races. Only a few studies investigated the age of peak performance [1, 2] and the sex difference in performance [3]. Regarding the age of peak performance, a study reported a value of 44.6 years [4] while another study reported for the ten fastest women ever a value of 37 ± 4 years and for men of 48 ± 6 years [2].

Considering the origin of ultra-marathoners, we have knowledge about short events, such as 6-h [5] and 12-h races [6] where runners originated from Europe. A study showed that the fastest 100-mile ultra-marathoners come mostly from Eastern European countries such as Lithuania, Latvia, Ukraine, Finland, Russia, Hungary, Slovakia, and Israel [7]. A recent study investigating 72-h ultra-marathons reported that the fastest runners originated from Ireland, Japan, and Ukraine [8].

The objectives of the study were to investigate the origin of the fastest 10-day runners and to determine the countries where the fastest 10-day events were held. We hypothesized that the fastest 10-day runners originate from Europe.

Method

Ethical approval

This study was approved by the Institutional Review Board of Kanton St. Gallen, Switzerland (EKSG 01/06/2010).

Data set and data preparation

Data download

Race data was downloaded from the website of DUV (Deutsche Ultramarathon Vereinigung) (https://statistik.d-u-v.org). Each race record included the athlete´s first and last name, age group, gender, country of origin, race location and year, race performance in distance (km) and average running speed (km/h). We added the type of the race (road or track running) and the running surface (gravel, paving, grass, concrete, asphalt, and combinations).

Country rankings by number of race records and unique runners

The data set is aggregated by the values in the athlete country column and then sorted by number of records to rank the athletes’ countries by number of race records. To rank the countries holding the events by the number of race records, the data set is aggregated by the values in the event country column and then sorted by number of records. Running speed descriptive statistics and unique runners are calculated for each country. The mean running speed is color-coded, with darker colors corresponding to higher values (faster running speeds). The first column in the ranking tables is the index to interpret the PDP charts (Partial dependence plots).

XG boost regression model

The algorithm used is the XG Boost (eXtreme Gradient Boosting), trained with the full sample. The 10-day sample used to build, evaluate, and interpret the XG Boost regression model consists of 958 race records from 452 unique runners from 46 countries who participated in races held in 6 countries between 1991 and 2022. The following variables are used as predictors, or inputs to the model: Athlete_gender_ID, Age_group_ID, Athlete_country_ID, Event_country_ID. The binary indicators of running surface (RS): RS_asphalt, RS_concrete, RS_dirt_path, RS_grass, RS_gravel, RS_paving, RS_track. The predicted variable, or algorithm output is the Race (running) speed (km/h) variable. A holdout evaluation strategy was used to train and evaluate the model, iteratively training and evaluating different instances with different test splits and different numbers of estimators/learn rates. Two evaluation metrics, MAE (mean absolute error) and r², are calculated with the model SHAP-based (SHapley Additive exPlanations) relative features importances. PDP and prediction distribution plots are computed and compared to the full sample descriptive charts. The optimal model parameters and accuracy scores were: 200 estimators (learners or trees); learning rate of 0.5; r² score of 0.65 (in-sample test); and MAE of 0.37 km/h.

Numerical encoding of categorical variables

Before the XG Boost model could be trained, the predictor values had to be converted (encoded) into numerical data. The Athlete gender variable is encoded as female = 0 and male = 1. The Age group variable is numerically encoded in 5-year groups. The Athlete country and Event country variables are encoded based on their position in the rankings’ tables. The run surface variable is one-hot encoded, giving place to a set of 7 new binary variables that indicate if the race takes place in that surface (1) or otherwise (0).

Baseline model with OLS MLR

Here we build a Multivariable Linear Predictor (MLR) based on Ordinary Least Squares (OLS) to predict the average race speed from the available predictors.

Model training and evaluation strategy

A holdout evaluation strategy is used to tune the model by iteratively training and evaluating different models with different test splits and different numbers of estimators/learn rates. The results of the simulation achieved the best r² scores of 0.648.

Optimal model evaluation metrics and features importance

The model is finally rebuilt with n_estimators = 200 and learn_rate = 0.5 and trained and tested over the full sample, obtaining an accuracy value of R² = 0.65, which indicates the model can explain 65% of the variability of the target (race speed) within this dataset. All computation and analysis were performed using a Jupyter notebook (Google Colab) and Python and associated libraries (pandas, numpy, xgboost, pdpbox, sklearn, matplotlib, and sns).

Results

Table 1 summarizes the race records by the countries of origin of the athletes. Most athletes came from USA, Russia, Germany, Ukraine, the Czech Republic, and Slovakia. The fastest runners were from Finland.

Table 1 Athlete country ranking

Table 2 summarizes the events. Most of the runners competed in USA. The fastest running speeds were achieved in Greece.

Table 2 Event country ranking

Multivariable linear predictor (MLR) based on ordinary least squares (OLS)

The model obtains r² = 0.210 where all predictors are statistically significant except Gender_ID, RS_concrete, and Event_country_ID. The simple MLR model can only model linear relationships, so that is how even the coefficients do not align with the most sophisticated ML (XG Boost + SHAP + PDP) analysis.

SHAP aggregated values chart for XG Boost model

Athlete_country_ID is the most important feature. This variable is encoded according to the country position in the ranking. Age_group_ID makes for a more interpretable chart, with red dots (higher ages) on the left side, hence reducing running speed. Similarly, Gender_ID has only two values. The SHAP chart shows low values (blue dots, female race records) accumulate on the left, meaning a reduction of the race speed. RD_dirt_path and RS_asphalt are both among the top features by importance, and with a separation of the dots. In the first case, red dots (presence of this running surface in the race) see a reduction of running speed. The interpretation for the asphalt flag is right the opposite (Fig. 1).

Fig. 1

SHAP aggregated values chart for XG Boost model

Model:	OLS	Adj. R-squared:	0.203
Dependent variable:	Running speed (km/h)	AIC:	2377.4291
		BIC:	2426.0775
No. Observations:	958	Log-Likelihood:	− 1178.7
Df model:	9	F-statistic:	28.04
Df residuals:	948	Prob (F-statistic):	2.27e-43
R-squared:	0.210	Scale:	0.69309

	Coef	Std.Err	t	P >|t|	[0.025	0.975]
const	2.5113	0.1128	22.2574	0.0000	2.2898	2.7327
Gender_ID	0.0853	0.0569	1.4989	0.1342	− 0.0264	0.1969
Age_group_ID	− 0.0127	0.0023	− 5.5512	0.0000	− 0.0172	− 0.0082
Athlete_country_ID	0.0086	0.0034	2.5458	0.0111	0.0020	0.0152
Event_country_ID	0.0294	0.0348	0.8469	0.3973	− 0.0388	0.0977
RS_asphalt	1.2674	0.0735	17.2548	0.0000	1.1233	1.4116
RS_concrete	− 0.1584	0.2299	− 0.6892	0.4909	− 0.6096	0.2927
RS_dirt_path	− 1.0230	0.0975	− 10.4971	0.0000	− 1.2143	-0.8318
RS_grass	0.5096	0.1748	2.9147	0.0036	0.1665	0.8527
RS_gravel	0.4702	0.1743	2.6977	0.0071	0.1282	0.8123
RS_paving	0.3118	0.1206	2.5844	0.0099	0.0750	0.5486
RS_track	0.4225	0.1606	2.6311	0.0086	0.1074	0.7376

Partial dependence plots (PDP)

The model output is ~ 0.2 km/h higher for males than females (Fig. 2). The highest model output is given to runners in age group 45–49 years (Fig. 3). The results by athlete country reached their peak at ID 30 (Finland), followed by Israel (ID 34) (Fig. 4). The event country PDP is flat, with a 0.1–0.2 km/h difference between the average model output. This is in line with the low importance rating of the feature (Fig. 5). Figures 6, 7, 8, 9, 10, 11, 12 present the PDP for the running surfaces. Running on asphalt is faster than running on any other surface.

Fig. 2

Partial dependence plots (PDP) for gender

Fig. 3

Partial dependence plots (PDP) for age group

Fig. 4

Partial dependence plots (PDP) for country of origin of the athlete

Fig. 5

Partial dependence plots (PDP) for the country where the race was held

Fig. 6

Partial dependence plots (PDP) for running surface asphalt

Fig. 7

Partial dependence plots (PDP) for running surface concrete

Fig. 8

Partial dependence plots (PDP) for running surface dirth path

Fig. 9

Partial dependence plots (PDP) for running surface grass

Fig. 10

Partial dependence plots (PDP) for running surface gravel

Fig. 11

Partial dependence plots (PDP) for running surface paving

Fig. 12

Partial dependence plots (PDP) for running surface track

Prediction distributions and target plots

The difference between the predictions of men and women is ~ 0.11 km/h (Fig. 13). The 45–49-year age group leads (Fig. 14). Finland and Israel are the fastest countries of origin (Fig. 15) and Greece holding the fastest races (Fig. 16). Figures 17, 18, 19, 20, 21, 22, 23 show the prediction distributions and target plots for running surfaces. Running on asphalt is faster than running on any other surface.

Fig. 13

Prediction distributions and gender-target plots

Fig. 14

Prediction distributions and target plots for the age group

Fig. 15

Prediction distributions and target plots for the athlete´s country of origin

Fig. 16

Prediction distributions and target plots for the country where the events took place

Fig. 17

Prediction distributions and target plots for running surface asphalt

Fig. 18

Prediction distributions and target plots for running surface concrete

Fig. 19

Prediction distributions and target plots for running surface dirt path

Fig. 20

Prediction distributions and target plots for running surface grass

Fig. 21

Prediction distributions and target plots for running surface gravel

Fig. 22

Prediction distributions and target plots for running surface paving

Fig. 23

Prediction distributions and target plots for running surface track

Discussion

Origin of the fastest 10-day runners

The model assigned the highest importance to the athlete's origin as the primary predictor. Age group emerged as the second most influential factor, followed by gender and the event's location. This order of importance suggests that the geographical background of the athlete plays a crucial role in shaping performance. Most athletes came from USA, followed by runners from Eastern Europe (Russia, Germany, Ukraine, the Czech Republic, and Slovakia). The high number of US-American athletes is explained by the ‘Sri Chinmoy 10 Day Race’ held since 1996, accumulating a participant count exceeding 700 finishers over the years. (https://us.srichinmoyraces.org/events/6-10-day-race). This enduring history of the event highlights the consistent participation of athletes from the USA. Some of the abovementioned countries had a tradition of high-level ultra-marathon runners where Russian runners dominate the ‘Comrades Marathon’ [9].

Finland and Israel as dominating nations

The fastest runners were from Finland. One of them is Pekka (Asprihanal) Aalto, who had a personal best performance of 1340 km in 10 days (https://3100.srichinmoyraces.org/ashprihanal-aalto). Finland has a large ultra-marathon scene with the ‘Kauhajoki Ultra Running Festival’ (http://karhumaraton.fi/kurf). In contrast, Israel has short ultra-marathon such as the ‘Ultramarathon Sovev Emek’ as Israel’s longest ultra race (https://sovev-emek.org/), the ‘Spartanion’ (https://spartanion.com/) or the ‘Dead Sea Marathon Israel’ (https://deadsea.run/en/).

The fastest races

The fastest running speeds were achieved in Greece. In the ‘Athens International Ultramarathon Festival’ in Athens, Greece, many different race formats have been offered since 2005 (www.dayrunners.gr/). A 10-day split was recorded at ‘1000 Miles Athens Int. Ultramarathon Festival’. Why are most ultramarathon runners from Europe? We think it is possible to draw a parallel with the same factors with the Kenyan, Ethiopian, and Jamaican runners [10]. The prevalence of ultramarathoners originating from Europe can be attributed to several factors [11] such the tradition and history of long-distance running in European countries [12, 13]. The continent hosts numerous well-established races, providing ample opportunities for individuals to engage in ultrarunning [14]. Cultural and social factors, such as a strong emphasis on health and wellness, may also play a role [15, 16]. The European lifestyle, with its focus on outdoor activities and a holistic approach to well-being, aligns well with the demands and aspirations of ultramarathon enthusiasts [17].

Men were faster than women

Men ran 0.11 km/h faster than women which is well-known in ultra-running [18]. The gap decreases with increasing race distance/duration [18] and age [19]. Women could reduce the gap to men for most timed ultra-marathons and for those age groups where they had a high participation [3]. The physiological differences between men and women can contribute to the performance gap. Possible reasons are differences in muscle mass [20] and muscle strength [21], running stride [22], aerobic capacity [23, 24], metabolism [26, 26], hormonal metabolism [27,28,29], fatigue resistance [25], and training strategies [30, 31].

The age of peak running performance

The fastest running speeds were achieved in age group 45–49 years. The 10-day race format is the longest race format for time-limited ultra-marathons, and it has been shown that the age of maximum ultra-marathon performance increased with increasing race duration in time-limited races from 6 h to 10 days [4]. The observed phenomenon can be explained by a combination of different factors such as experience [32] and training [33], aerobic capacity [34, 35], muscle efficiency [36], running technique [37, 38], mental toughness [39, 40], experience [4], recovery [41], injury prevention [41], optimal body composition [42] and physiological adaptations [43,44,45].

The aspect of running surface

These races are all held on a flat terrain, some races are held across two different surfaces (asphalt and dirt path). Asphalt seems to be the fastest surface, where the other surfaces show a reduction in running speed. Little is known regarding the impact of running surface on running performance. Ferro-Sánchez et al. investigated the impact of different running surfaces (grass, synthetic track, and concrete) and found that greater impacts were produced on concrete compared to synthetic track and grass [46]. Tessutti et al. analyzed the influence of running on asphalt, concrete, natural grass, and rubber on in-shoe pressure patterns and found that running on natural grass attenuates in-shoe plantar pressures [47]. Wang et al. analyzed plantar load data during running on concrete, synthetic rubber, and grass surfaces and showed that different surfaces affected the plantar loads differently while running [48]. Ultra-marathoners would profit from selecting ultramarathon running races with asphalt considering a faster running speed.

Conclusion

Finland and Israel as countries producing the fastest runners in the 10-day format adds a valuable dimension to our understanding. The revelation that Greece hosts the fastest race courses contributes practical information to professionals, including athletes, coaches, and race directors, enabling them to set optimal performance goals based on the event country. Running on dirt path led to a reduction of running speed, while running on asphalt showed faster running speeds compared to other surfaces.