## 1 Introduction  
Being an easily accessible physical activity, running has reached a notable degree of popularity in recent times [1, 2]. It serves not only as a means of maintaining good health and fitness but also as a platform for competition organized in major and minor road, cross-country, and trail races, comprising both amateur and elite levels. In order to achieve better performances and thus faster running times, many amateur runners have adopted structured training plans, which are widely available in the present era. The advancement of research in areas such as gait analysis, running technology, and diagnostics has led to the development of a plethora of tools designed to enhance running performance [3; 4; 5]. In addition to the self-evident approach of enhancing performance by (specific individualized) physical training, improving running economy represents a key method to faster racing, as better RE leads to faster race times at the same physical fitness level. Running economy (RE) is defined as the energy demand of human running locomotion and can be approximated in terms of the steady-state oxygen consumption (\(\dot{\text{VO}}_{2}\); \(\text{mL}\cdot\text{kg}^{-1}\cdot\text{min}^{-1}\)) at a given submaximal running speed [6]. Energy cost of transport (ECT; \(\text{kcal}\cdot\text{kg}^{-1}\cdot\text{km}^{-1}\)) and metabolic power (\(\text{W}\cdot\text{kg}^{-1}\)) are also used as more accurate measures of RE, capturing differences in energy yield per volume of oxygen due to varying substrate (i.e., carbohydrates and fat) utilization [7]. Along with maximal oxygen uptake (\(\dot{\text{VO}}_{2_{\text{max}}}\)) and fractional utilization of \(\dot{\text{VO}}_{2_{\text{max}}}\) at ventilatory thresholds, RE is one of the primary determinants of endurance running performance [8; 9; 10] and has been shown to be a strong predictor of 10 km race performance [11]. As such, effective strategies for improving RE are of high interest to all runners aiming to improve their race times and to further stakeholders of competitive sport, including coaches, sport scientists, and sport equipment manufacturers. Several interventions targeting physiological changes have been demonstrated to be effective in improving RE, such as different types of cardiovascular and resistance training, stretching, and nutritional interventions [12]. Following the release of Nike's first carbon-fiber-enhanced running shoe Vaporfly 4% in 2017, an increased focus has been placed on RE improvements elicited through optimized material properties of running footwear, giving rise to a novel category of running shoes commonly referred to as carbon-plate running shoes (CPRSs) and recently recoined by some authors to 'advanced footwear technology' (AFT) [13]. While the longitudinal bending stiffness (LBS) of CPRSs is increased through carbon-fiber-based stiffening elements (\"plates\") embedded in their midsoles, many of those running shoes nowadays also provide an increased cushioning because of their lightweight and resilient novel foams. The more general term AFT aims to explicitly account for the combination of both biomechanical concepts of increased stiffness and cushioning. The exact mechanisms of AFT leading to RE and performance benefits are still a topic of current debate [14; 15; 16], with suggested mechanisms comprising an altered gear ratio at the ankle joint through increased LBS [17; 18], a higher degree of energy storage and return in the midsole foam [19], a reduction in negative work through stiffening of the metatarsophalangeal joint [20], a \"teeter-totter\" effect, i.e., supporting leverage between toe and heel parts of the shoe, resulting in a higher force acting on the heel during push-off [14], and better suited gastrocnemius muscle fiber contraction speeds for optimal power production and increased energy return via the Achilles tendon [21].