Approach

To assess our hypothesis, we procured data from the official ’Berlin Marathon’ website (www.bmw-berlin-marathon.com/) encompassing participants’ first and last names, gender, age, calendar year, and running times. It is worth noting that split times were not documented in the race records before 1999, and the year 2020 did not host a race due to the COVID-19 pandemic (www.bmw-berlin-marathon.com/).

The race

The Berlin Marathon occurs between the middle and concluding weeks of September in Berlin, with an elevation of 34 meters above sea level (www.bmw-berlin-marathon.com/). During this period, the city encounters an average temperature of approximately 15°C and an average humidity of about 75% (www.weather-atlas.com/en/germany/berlin-weather-september). The race route forms a sizeable loop through the historic city of Berlin, culminating at the iconic ’Brandenburger Tor.’ The course’s maximum elevation is 50 meters, with a maximum gain of 20 meters (www.bmw-berlin-marathon.com/). In detail, it climbs ~20 m with a slight uphill from 20–25 km and a bigger incline from 25–27 km then a downhill from 27–32 km. The start of the race is organized into time blocks ranging from 09:15 a.m. to 10:30 a.m., depending on the best time the starter states upon registration (www.bmw-berlin-marathon.com/).

Subjects

The athlete information was directly sourced from the official ’Berlin Marathon’ website (www.bmw-berlin-marathon.com/). We acquired the complete dataset encompassing all races from 1999 to 2019 in JSON format, which was subsequently transformed into Excel format utilizing a tailored Python script.

Weather data

We sourced all weather information for the race day from the ’Deutscher Wetterdienst’ website (https://opendata.dwd.de/climate_environment/CDC/observations_germany/climate/hourly/) specifically for the ’Alexanderplatz’ location, which is near the race venue. We accessed hourly data encompassing air temperature (°C), relative humidity (%), sunshine (duration in minutes), precipitation (mm), barometric pressure (mbar), cloud cover (duration in minutes), wind speed (km/h), and dew point (°C) commencing from 9:00 a.m. and spanning 8 consecutive hours. This duration accommodated all official finishers with race times of up to 8 hours. The data was provided with integer resolution (no decimal points). No information was available concerning any alterations, changes, or incidences of any type in the measuring instruments used during the analyzed timeframe.

Data processing

This study utilized two distinct datasets. The initial dataset encompassed comprehensive information about the ’Berlin Marathon’ participants from 1999 to 2019. This included partial and full race times, formatted as h:min:s, gender, age, and marathon year. Given the focus on assessing the impact of weather conditions on performance groups’ pacing, age data were excluded from the analysis. Nonetheless, gender-based variations were also explored. The second dataset documented weather conditions throughout each marathon held between 1999 and 2019. This encompassed hourly temperature measurements, atmospheric pressure, humidity, precipitation, wind speed, dew point, sunshine minutes, and cloud cover percentages for each hourly interval. These datasets were processed using a Google Colab notebook, utilizing Python 3.9 for statistical analysis, and creating results tables and visual charts. Race records underwent scrutiny to ensure data accuracy and coherence, with erroneous or incomplete entries excluded from the analysis.

Statistical analysis

The entire race record was classified into performance time groups based on individual runners’ race times. These groups were delineated as follows: under 2 hours 30 minutes, 2 hours 31 minutes to 3 hours, 3 hours 1 minute to 3 hours 30 minutes, 3 hours 31 minutes to 4 hours, 4 hours 1 minute to 4 hours 30 minutes, 4 hours 31 minutes to 5 hours, 5 hours 1 minute to 5 hours 30 minutes, 5 hours 31 minutes to 6 hours, and over 6 hours [22]. Importantly, each runner’s record was exclusively allocated to a single group.

Subsequently, every record was assigned adjusted average weather values corresponding to their race duration on the event day. This approach enhanced the precision of weather condition representation for each runner’s race, leading to heightened resolution and accuracy. Additionally, utilizing the original data for split and total distance times, the average running speed (in km/h) and pace (in min/km) were calculated for each record. A comprehensive descriptive statistical analysis combined pace, race times, and weather data. This encompassed Pearson correlation analysis, calculation of statistical parameters for total and partial race times, and depiction of weather factors for each time group using boxplot charts. A multivariate Ordinary Least Squares (OLS) linear regression model was first built, and then a second, more sophisticated XG Boost regression model was implemented. The eight weather factors were used as predictors in all cases, and the race pace was the model output. Partial Dependence Plots (PDP) and Shape Additive Explanatory Values (SHAP) techniques were then used to interpret the XG Boost model predictions. Statistical values were presented in tables and charts detailing average (mean) and standard deviation (SD), as well as maximum (max) and minimum (min) values for each category. The ’N’ column denoted the sample count within each specific category. Assurance of Gaussian (normal) distribution for race times and paces was validated through histogram and probability density distribution plots, accompanied by statistical significance tests and computation of p-values. All analyses were carried out using the Python programming language (Python Software Foundation, https://www.python.org/), within a Google Colab notebook (https://colab.research.google.com/), and the Statistical Software for the Social Sciences (IBM SPSS v26. Chicago, Ill, USA).

Ethics approval

The institutional review board of St. Gallen, Switzerland (EKSG 01/06/2010) approved this study. Since the study focused on analyzing publicly accessible data, informed consent was exempt.

Impact of temperature on marathon performance

The well-established literature highlights a link between higher temperatures and declining performance among marathon runners [13, 27], with a pronounced effect in slower runners [8, 11]. According to thermodynamic principles, the body’s heat production correlates with its mass, while heat dissipation through processes like radiation, convection, and evaporation is influenced by its surface area [28]. As temperatures rise, the efficiency of heat dissipation through radiation, convection, and conduction diminishes, prompting the body to rely more on evaporative cooling. A study by Marino et al. revealed that runners with lower body mass generate and retain less heat than their heavier counterparts, a physiological characteristic that can impact performance even when maintaining similar running speeds [29]. However, it’s crucial to consider that reduced running speed might also stem from fatigue and depletion of myocellular energy stores [30].

Another plausible explanation for the more pronounced decline in performance among slower runners stems from the timing of marathon races, typically commencing early in the morning. Faster runners tend to benefit from cooler morning temperatures, while slower runners contend with warmer conditions as the day progresses [15], largely influenced by the duration of sunlight exposure [18]. Previous research has demonstrated a gradual reduction in marathon race speed with rising temperatures [14], and it has been established that overcast skies and limited sunlight do not correlate with faster marathon race times [5]. To enhance the experience for slower marathoners, it could be preferable for races to conclude before 09:00 a.m. or commence after 07:00 p.m. This scheduling approach would offer athletes progressively ameliorating weather circumstances characterized by diminished sun exposure, gradual temperature increases or declines (morning or evening), and minimal humidity increase [31].

While the negative correlation between running speed and temperature might appear intuitive, the observed outcome was shaped by the circumstance that faster runners (with higher running speeds) participated in the race during the early morning hours, around 09:00 a.m., when temperatures were still relatively cool. In contrast, runners with slower paces (completing the race in over 4 hours) faced warmer temperatures during the afternoon. This relationship has been accentuated by using adjusted averages in the dataset. The swifter runners encountered lower temperatures and elevated humidity levels, completing the course in under three hours. In contrast, leisure runners progressed at a slower pace, finishing the race later in the afternoon when temperatures were higher and humidity was lower.

Gender differences in pacing and performance

The effects of temperature on pacing were less pronounced in women than in men. This could be attributed to the more selective roster of women participating. The lower number of women compared to male counterparts highlights a natural selection bias, where the average participating woman is more experienced and dedicated more time to training, resulting in evener pacing and, subsequently, less loss of speed [32]. With the increasing popularity of marathons and an increasing number of women, this selection bias should disappear in the future [33].

Humidity and its effects on performance

Another significant discovery was the decline in humidity throughout the race, with a notable and positive correlation between running speed and humidity. This implies that as humidity diminished over the day, runners experienced a decrease in pace. The positive connection between running speed and humidity may find its rationale in the robust inverse correlation between temperature and relative humidity.

Humidity refers to the volume of water vapor present in the atmosphere. Elevated water vapor levels lead to higher humidity (www.weather.gov/lmk/humidity). The humidity level is also influenced by temperature. As temperatures rise, relative humidity decreases, whereas lower temperatures increase relative humidity (https://sciencing.com/temperature-ampamp-humidity-related-7245642.html). Within the context of physical activity in warm conditions, evaporation serves as a principal method for dissipating heat [34]. Humidity significantly affects heat dissipation through evaporation. Reduced relative humidity enhances sweating efficiency [35]. A lower presence of water vapor in the air allows sweat secretion to cool the body more effectively [35].

Prior research has indicated that heightened humidity levels can adversely impact athletic performance. Notably, moderate-intensity exercise in warm settings has shown a gradual decline in performance as relative humidity increases [36]. In controlled laboratory settings, investigations have highlighted reduced maximal aerobic capacity under elevated temperatures and varying humidity conditions [37]. The impact of humidity on marathon performance has also been explored in previous studies [9, 12]. Our findings confirm that a decrease in humidity was associated with a decrease in running performance. A comprehensive study examining the influence of weather conditions on 1,280,557 age group runners participating in the ’New York City Marathon’ between 1970 and 2019 showed that higher temperatures, lower humidity, and lower wind speed corresponded with decreased performance. Specifically, the detriments of elevated humidity were more pronounced among men aged 40–59 and women aged 25–65 [9]. Another study focusing on the effects of weather on marathon running performance in the ’Stockholm Marathon’ showed a significant and negative correlation between relative air humidity and the anomaly in marathon finishing times [38]. However, the authors attributed these effects of relative humidity to its negative correlation with air temperature [38]. Pragmatically, the rise in temperature and the race’s duration likely held more explanatory power in elucidating performance decline than the decrease in humidity.

Impact of other environmental factors

Given the absence of rainfall across all editions of the ’Berlin Marathon,’ we were precluded from examining potential correlations between rain and running speed. It is known that rain can hinder marathon performance [38]. For instance, in the ’Stockholm Marathon,’ there was a noteworthy and adverse correlation between rain and the anomaly in marathon finishing times [38]. Interestingly, contrasting these findings, the ’Boston Marathon’ witnessed record times accomplished under the influence of drizzle [12].

The wind speed displayed a slight negative correlation with humidity, pressure, and dew point while demonstrating a weak positive correlation with the time of day. A study of master runners participating in the ’New York City Marathon’ revealed a notable advantage associated with elevated wind speeds, particularly among men [9]. A study exploring the effects of wind assistance and resistance on a runner’s forward motion recorded a net negative effect of winds exceeding the velocity of a runner on an oval track [39]. The extra energy expended against the wind will not be compensated by an equal gain when running with the wind [39]. As observed in the ‘Berlin Marathon’, our models have shown that wind speed doesn’t lend itself as a detrimental predictor of the race pace. This could result from the urban landscape and mostly lower wind speeds throughout all marathon editions.

Cloud cover did not serve as a relevant predictor for performance. Recent findings have called into question the perceived importance of cloud cover for marathon running performance. Contrary to popular belief, neither cloud cover nor low sunshine are associated with faster marathon times. Data indicate that world records and the fastest marathon performances occur irrespective of cloud cover, and optimal temperatures for fast running are typically 10–15°C [40].

Although we collected weather data at hourly intervals and initiated our analysis at 09:00 a.m. utilizing time-adjusted averages based on performance groups, it is important to note that the race itself featured interval starts spanning from 09:15 a.m. to 10:30 a.m. This variation depended on individual best times, often associated with half or marathon times, that each runner indicated during registration. Notably, novice marathon participants commenced the race at 10:30 a.m. within the final starting block (Block H). These differences could potentially have impacted the outcomes of our analyses. Furthermore, the absence of accessible data concerning anthropometric attributes, such as body height and mass, prevented us from investigating the interplay between environmental factors, performance, and athletes’ physical characteristics. Additionally, we lacked information regarding these runners’ experience and training volume [41].

Limitations

A limitation of the study is that the correlation between running performance and temperature/humidity may be affected by the fact that slower runners tend to run for longer periods, particularly during later start times when the day is heating up and humidity levels are dropping. It is important to exercise caution when drawing causal relationships from this correlational data. As environmental temperature increases, relative humidity decreases but the total amount of water vapor in the air may not have changed (absolute humidity).

Relative humidity decreased with increasing marathon race times. This is likely a result of increasing temperatures during the day given the early start times and warming temperature as the day progresses and the longer the slower runners are exposed to this environmental process which is likely more of a correlational result. It is absolute humidity that determines sweat, evaporation and heat stress risk [42–44]. Furthermore, the course is not entirely flat and the analyses did not include changes in elevation as a potential influence on pacing of the athletes.