Study design

An experimental cohort study was carried out. Data were collected during incremental treadmill tests in the laboratories of the Department of Sports Medicine and Sports Nutrition of Ruhr University Bochum from 2015–2024 and were accessed on the 10^th of December 2024. The Ethics Committee of the Faculty of Sport Science at Ruhr University Bochum reviewed the study protocol (File number: EKS S 2025_04) and confirmed that no formal ethical approval was required for this type of secondary data analysis. All participants had provided written consent for the use of their performance diagnostic data for scientific purposes. All data were fully anonymized prior to analysis, and the authors had no access to information that could identify individual participants.

Participants

In total, data from 339 tests were collected, originating from 220 individual athletes. This included 11 elite male handball players (11 tests), 23 elite male field hockey players (23 tests), 100 elite female field hockey players (185 tests), and 86 elite male soccer players (120 tests). 81 athletes completed multiple measurements (2–6 tests) at different time points. Anthropometric data (height, weight) and age were collected before the running protocol. Handball players were tested in 2024, male field hockey players were tested in 2016, female hockey players were tested between 2016 and 2024, and soccer players were tested between 2015 and 2019. The handball player competed in the second-highest national league in Germany, the soccer players were active in the first and second divisions of the German Bundesliga, and the field hockey athletes competed at the highest competition level in Germany. All athletes trained and competed at a high-performance level and were categorized as elite based on their training volume and competitive status.

Instruments

The athletes performed one of three incremental treadmill tests (h/p/cosmos Saturn 250/100) to exhaustion. The specific protocol used was predetermined by the participating clubs or institutions as part of their internal fitness assessments. Therefore, athletes were not randomly assigned to protocols, and the choice of protocol often coincided with the type of sport. Each athlete completed only one protocol, with only two individuals participating in more than one. As such, protocol and sport were largely confounded, making it statistically infeasible to isolate the effect of protocol in the analysis. Protocol A started at 2.5 m/s, each step lasted 5 min and the increment was 0.5 m/s. Protocol B started at 2.0 m/s, each step lasted 5 min and the increment was 0.4 m/s. Finally, protocol C started at 2.22 m/s (8 km/h), each step lasted 3 min and the increment was 0.55 m/s (2 km/h). The treadmill was set at a 1% incline to better simulate the energy cost of running outdoors by compensating for the lack of air resistance [22]. For athletes with repeated measurement, the same protocol was used in all tests to ensure consistency withing subjects.

Oxygen uptake (V̇O₂, ml/min), CO₂ output (V̇CO₂, ml/min), respiratory exchange ratio (RER) and ventilation were measured breath-by-breath (MetaMax 3B-R2, Cortex Biophysik GmbH, Leipzig, Germany). The spirometer has previously been reported to have adequate validity and reliability for field testing [23,24]. The spirometer was calibrated using a 3-litre gas flow pump and a standard gas (oxygen, 15.00%; carbon dioxide, 5.09%) according to the manufacturer’s recommendations.

Data processing

Raw breath-by-breath data were processed using a moving average of 1 s. The energy cost per time frame was calculated using the approach of McArdle et al [25] by multiplying the oxygen uptake by the corresponding caloric equivalent determined by the respiratory exchange ratio. Steady-state conditions for each step were verified by ensuring that the percentage deviation in V̇O₂ over 30 seconds was less than 5%. A stage was only included if it was completed. Trials were also excluded if the subject was unable to run to maximal exertion due to injury or similar. Energy cost was then calculated in J/kg/m for each step to determine EC₀ in steady-state conditions for different running speeds. Net cost was calculated as the rate of energy expenditure above rest (assumed to be 3.5 ml/kg/min) [25] divided by speed [26].

Statistical analyses

All statistical analyses were performed with JASP (0.19.3).

Different linear mixed models were applied and compared to analyse the relationship between EC₀ and its different hypothesised predictors (V̇O_2max, velocity, type of sport). EC0 was the dependent variable, while V̇O2max, speed, and type of sport were defined as fixed effect variables. Repeated measurements per athlete were accounted for by including “Subject ID” as a random-effects grouping factor. Sex differences were only analyzed for field hockey players due to absence of female athletes in soccer and handball. To model the relationship between EC₀ and its predictors, we used a two-level linear mixed-effects model. At Level 1 (within subjects), EC₀ for each test occasion i and subject j was predicted by sport, running velocity, and individual V̇O₂max:

At Level 2 (between subjects), intercepts and slopes were allowed to vary across individuals to account for inter-individual differences in the strength of these associations:

Here, the γ terms represent fixed effects across the population, while the u terms reflect subject-specific deviations. The residual error term εᵢⱼ was assumed to be normally distributed with constant variance.

To compare model fit, we used several statistical criteria. The Akaike information criterion (AIC) and the Bayesian information criterion (BIC) were employed to balance model fit with parsimony, while deviance and log-likelihood provided complementary measures of absolute fit. AIC was the primary criterion guiding model selection due to its balance between goodness of fit and generalizability. Among the tested models were simpler specifications (e.g., velocity only), pairwise combinations of predictors (e.g., sport + velocity), and more complex models including body mass. The final model including sport, velocity, and V̇O2max yielded the best performance across all fit criteria and was there therefore retained. Based on theoretical considerations and visual inspection of the data, we tested for non-linear effects of running velocity by including a quadratic term (velocity²) as an additional fixed effect. We also compared the estimated means with the 95% confidence intervals of our models. To assess the influence of using a fixed resting metabolic rate, a sensitivity analysis using gross EC₀ was conducted (i.e., without subtracting 3.5 ml/min/kg). This model used the same fixed and random structure as the main model. Model comparisons are reported in the supplement (S1 Table).

Energy cost of constant speed running

The estimated total mean values of the term for constant speed running (EC₀) differed between the types of sport studied and their respective athletes. It was considerably lower than in other studies with similar types of athletes. Although there are no studies evaluating a constant speed running term for field hockey and handball players, they could be considered as ‘physically active’ comparable to Buglione et al. (2013) [26].

Soccer players in our study had an energy cost of 3.79 J/kg/m for constant speed running, which is lower compared to the literature (4.53 J/kg/m, [27], 4.64 J/kg/m, [3], 4.42 J/kg/m, [26], 4.19 J/kg/m, [17], 4.66 J/kg/m, [28], 4.19 J/kg/m, [29]) and more similar to the originally proposed value for EC₀ for experienced mountain runners (3.6 J/kg/m, [12]). Several methodological differences may explain this discrepancy. Firstly, whereas previous studies mainly included amateur or sub-elite soccer players [27,29] or no soccer players at all [3], our study focused exclusively on elite players, who may exhibit superior running economy due to advanced physiological adaptation and technical efficiency [30,31]. Second, unlike studies conducted on artificial turf [27] or natural grass [28,29], we conducted our assessments on a calibrated treadmill, which minimizes surface-related energy losses and provides more consistent running conditions. The absence of external factors such as surface friction and ground compliance may have contributed to the lower energy cost observed in our study. Running on natural grass or artificial turf introduces variability in friction, which can increase muscular effort during propulsion and braking [32]. In addition, differences in ground compliance (i.e. surface stiffness and energy absorption) affect running mechanics, with softer surfaces requiring greater muscular compensation to maintain speed [33]. In contrast, treadmill running provides a consistent, relatively stiff surface with minimal frictional resistance, potentially reducing energy expenditure [21,34]. Thirdly, differences in footwear and running kinematics may have played a role. In contrast to field studies [27–29] where players wore soccer cleats or special cleats for artificial turf, treadmill running is typically performed in running shoes, which may improve running economy due to better cushioning and energy return [35,36]. In addition, research has shown that treadmill running may alter gait mechanics, for example by helping to bring the supporting leg back under the body during the support phase, which may affect the metabolic cost [37]. Finally, environmental factors also need to be considered. In contrast to outdoor studies where temperature, humidity, and wind resistance may influence energy expenditure [38], our study was conducted in a controlled indoor environment, minimizing external physical stressors. Given that heat and humidity can increase cardiovascular stress and energy expenditure [39], conducting our study in a standardized laboratory may have further contributed to the lower metabolic cost observed.

The higher running economy of soccer and field hockey players compared to handball players is likely due to their sport-specific endurance training adaptations. Soccer and field hockey players commonly engage in high-intensity interval training (HIIT) and small-sided games (SSG), both of which improve maximal aerobic speed (MAS), running economy, and velocity at lactate threshold, while having little effect on neuromuscular performance [40]. These methods optimize their energy efficiency during sustained running, contributing to their lower energy cost per metre compared to handball players. In contrast, handball players perform more frequent accelerations, decelerations and multidirectional movements which are likely to result in a less economical style when tested at constant speeds. In addition, handball players engage in more strength and power training to improve handball-specific performance, resulting in greater muscle mass and higher energy expenditure during forward running [41].

V̇O_2max is widely recognized as a key indicator of aerobic capacity, but it does not necessarily determine running economy. V̇O_2max reflects the maximum amount of oxygen an individual can use during intense exercise. Running economy, on the other hand, represents the oxygen cost of maintaining a given running speed. Our data show a positive association between EC₀ and V̇O_2max which is consistent with previous research suggesting that higher aerobic capacity may be accompanied by reduced metabolic running economy [42–44]. Athletes with a higher V̇O_2max have a lower mean running economy (higher EC₀) during an incremental treadmill test to exhaustion (Fig 3). This is at least in part due to their higher fatty acid oxidation (lower RER) at all running speeds (Fig 6), which in turn reduces metabolic running economy [45]. A reduction in (metabolic) running economy has also been shown after a period of training that resulted in an increase in V̇O_2max [42]_. On the other hand, previous studies reported that the subgroup of athletes with the highest maximal speed during the incremental treadmill tests, which are probably those with the highest values of V̇O_2max, had the lowest EC₀ values (highest running economy) compared to the athletes with lower maximal running speed. This may be due to better biomechanical adaptations in the high V̇O_2max group [18].

In the subgroup of field hockey players, we were able to show that sex has an effect on EC₀, with the female field hockey players having a slightly higher EC₀ value compared to the male group of players. This is in line with previous research, showing that male athletes generally have better running economy than female athletes at absolute running speeds, i.e., they consume less oxygen per unit of body weight at the same speed [46,47]. However, when running intensity is matched relative to individual capacity, and oxygen consumption is expressed in ml/km/kg in experienced runners, these differences disappear [47,48]. The latter one is in contrast to our findings, as the small difference in the mean EC₀ of 0.11 J/kg/m between female and male hockey players actually increased to an estimated mean of 0.31 J/kg/m when individual V̇O_2max was included in the model. This suggests that the lower running economy in female field hockey players may be due to biomechanical rather than metabolic factors. This difference between the group-level mean EC₀ (3.95 J/kg/m) and the sex-specific model estimates (3.94 for female and 3.63 for male players) can be explained by the model structure. In the group-level model, sex was not included as a predictor, resulting in an averaged estimate across all hockey players. In contrast, the sex-specific model accounted for individual differences in both V̇O₂max and velocity, which were systematically higher in the male subgroup. Since both predictors were positively associated with EC₀ in our data, their inclusion in the model led to lower predicted EC₀ values for male players and slightly higher values for females. This reflects physiological variation rather than an artifact of model inconsistency.

In general, running at higher velocities requires more energy per unit of time [49], but the energy cost per distance covered can be similar or even lower compared to running at slower speeds. Our data show that the energy cost of constant speed running increases at lower speeds, but the rate of increase decelerates beyond approximately 3.5 m/s, resulting in an almost plateau-like curve at higher velocities (Fig 4). This pattern appeared largely linear across the tested speed range, with no substantial deviation observed at lower velocities. Accordingly, we considered a linear model specification for EC₀ to be appropriate and statistically justified. This is consistent with some previous studies investigating the relationship between running economy and speed [50–52], but also differs from one study [48] which showed a curvilinear U-shape with a nadir reflecting the most economical speed at 13 km/h (3.6 m/s). This study used highly trained endurance athletes specialized in long-distance running. Studies of EC₀ in team sports have not investigated the influence of different velocities on EC₀, they have all used a protocol consisting of constant speed running at one speed rather than constant speed running at different velocities [26–28].

Practical relevance

The variation in the energy cost of running at constant speed across different sports and V̇O₂_max groups highlights the importance of using more than a single fixed value in the metabolic power approach. Instead, the selection of sport-specific EC₀ values is crucial, and an even more accurate approach would take into account individual differences in V̇O₂_max. Given that athletes with a higher V̇O₂_max tend to have a higher EC₀, incorporating both sport type and individual physiological characteristics may improve the accuracy of metabolic power estimation. The metabolic power approach has been applied to several team sports, including soccer [3,9], handball [53,54], rugby league [10], Australian football [11] and field hockey [8]. However, sport-specific EC₀ values have only been established for soccer [17,26]. The inclusion of a sport-specific EC₀ is essential to refine and advance the metabolic power approach in each individual team sport, allowing for a more accurate assessment of energy expenditure. When individual EC₀ values are available, athlete monitoring can become even more precise and tailored to individual needs. Inaccuracies in the EC₀ value can systematically affect the estimation of metabolic power and thus the cumulative metabolic work derived from tracking data. Even moderate deviations in the EC₀ may result in substantial over- or underestimation of physical load, particularly in high-intensity intermittent sports [26]. This further underlines the value of using individualized or at least sport-specific EC₀ values in applied athlete monitoring.

Methodological considerations

Since each athlete completed only one of the three treadmill protocols, it was not possible to assess the isolated effect of protocol design (e.g., initial speed or stage duration) on the energy cost of running. As a result, potential protocol-related influences could not be disentangled from group characteristics such as sport type. In addition, our results need to be validated in a sport-specific context, taking into account factors such as running shoes and surface type, both of which may influence energy cost. Moreover, resting metabolic rate was not individually measured but assumed to be 3.5 ml/kg/min for all athletes. While this is a commonly accepted value in literature, individual variations in resting metabolic rate, especially in athletes with different body compositions and fitness levels, may introduce some degree of systematic bias. To evaluate the robustness of this assumption, we conducted a supplementary analysis using gross EC0. This model yielded nearly identical model fit and fixed-effect estimates, supporting the stability of our findings regardless of how resting V̇O₂ is treated. Nonetheless, we chose to retain net EC₀ in the main text to ensure comparability with previous studies, which have typically reported net energy cost values. Due to time constraints during routine performance diagnostics, a direct measurement of resting metabolic rate was not feasible. Furthermore, as data were collected over several years, minor variation due to equipment servicing or calibration cannot be ruled out. Additionally, one of the protocols included test stages starting at 2.0 m/s, which approaches the typical walk–run transition. All athletes were instructed to run throughout the test. These stages were retained in the model, and due to its non-linear structure, potential effects at lower speeds were appropriately accounted for.

Perspective

This research is helping to improve the accuracy of the metabolic power approach, but there is still much work to be done. These values need to be compared with those obtained in sport-specific contexts and settings. Ideally, a single assessment per athlete at the beginning of each season would be sufficient to provide an individualized value. For a more comprehensive monitoring of energy expenditure during match play, it is essential to consider not only the energy cost of locomotion – calculated using the metabolic power approach – but also the additional demands of sport-specific actions. Future research should focus on the integration of these movement patterns to provide a more complete assessment of the total energy expenditure of an athlete’s in a competitive setting.