*4.1. Model Performance and Physiological Properties*

Performance measurements show precise prediction abilities which were fairly replicable between the training and test sets (see Figures 2 and 3). The obtained R<sup>2</sup> explained approximately 60% to 70% of the differences, while errors were moderate-to-low, under 1 km·h−<sup>1</sup> for most cases. With additional internal validation, they were both still located in the upper sensitivity range. Thus, the model accuracy was only minorly reduced. In previous publications, such as that by Petek et al. for VO2peak [36], similar results were observed. However, usually, previous researchers have not carried out an initial selection of the most suitable variables, and so far, studies have been based on previously established parameters, only changing their proportions. Our study showed that VO2 at RCP and maximal VO2 were the most important parameters responsible for the prediction of middleto long-distance running velocity (a lower impact of VO2 at AT was noted). This confirms previous findings by Thompson et al. and Lanferdini et al. [16,37] that the VO2 can be described as the universal and comparable performance measure, and that it is strongly related to running speed. Moreover, according to the physiological relationship between exercise performance and [La−]b at AT, at RCP, and maximal VO2, they also significantly influence the predicted velocities (but in the varied order compared with VO2, with more impact from sub-maximal levels at AT or RCP than maximal [La−]b values). This is confirmed in studies by Tanaka and Matsuura [12] and Schabort et al. [19], as growing [La<sup>−</sup>]b and training intensity were positively correlated in both. Thus, of greater improtance seems to be the ability to rapidly utilize and prevent excess growth in [La−]b by EA than working at maximal value for a prolonged time. Our study confirmed the previous findings by Farrell et al. [38] on this point. Another important variable was pulmonary ventilation. The majority of the influence was created by VERCP, and only for Vmax, was there a significant impact of VEmax. The higher it was, the better running velocity was observed. Thus, it can be concluded that the higher oxygen (O2) supply and better carbon dioxide (CO2) utilization yielded an improvement in running performance. This is a well-documented concept that was stated by Sjodin and Svedenhag in the 1980s [32]. Our insights on both VO2 and VE also confirmed that performance at RCP is strongly correlated with other running and general exercise indices [15]. When it comes to somatic parameters, they also showed a relevant effect on velocity. Higher BMI [19] and increasing age [39] were associated with lower endurance performance. On the other hand, BC, described as a percentage of BF and FFM, showed some effect on the predicted velocity, despite their impact on males being not enough to be included in the modeling for this gender. It is worth mentioning that the influence of BF was more noticeable in females, perhaps because they naturally have a higher level of BF [40]. HR was one of the variables with the lowest impact on velocity (see Figure 3). Moreover, we emphasize that HR, which shows high inter-individual variability and is difficult to precisely estimate for EA [21], was not included in any of our equations. To summarize, the degree of the relationships between the variables is interesting. It is very promising to assess how precisely we can estimate VAT, VRCP, and Vmax based on the above-mentioned parameters.

#### *4.2. Clinical Considerations*

Our results also have important clinical applications for patients from the general and athletic populations. The development of sports cardiology has resulted in a higher number of EA patients, including former cardiac patients or those suspected of having exertional cardiac abnormalities. TE CPET is often performed to some level of submaximal intensity or until refused. However, those who are less experienced may quit earlier, before reaching their optimal diagnostic intensity level, because they are not mentally adapted to perform such demanding activities [31,41]. The calculation (MET × running velocity) is used by medical professionals to provide personalized recommendations for cardiac rehabilitations [31]. Selection of the most important variables and additional comparison of those directly achieved with the predicted velocity verify whether an optimal level of intensity was achieved.

#### *4.3. Practical Applications*

The characteristics of selected variables and prediction models could be used in the preparation of exercise recommendations for both professional and recreational EA as patients in clinical settings [7]. The highest accuracy of the observed repeatable values would be for EA, mainly for running activities (i.e., during long-distance running or football), due to the characteristics similar to those in the derivation cohort [36]. Thanks to the use of VAT, VRCP, and Vmax prediction models, there would be no need to run the full CPET protocol and measure all parameters, but only the most significant and contributing ones [19]. This is a matter of importance, as CPET is often impossible to perform according to the full protocol due to the limited availability of specialized clinics and equipment or the high cost of the procedure [42]. This model can also be used to verify/assess whether the athlete obtains sufficient running speed on the basis of the directly measured parameters. Of course, it currently would not be the gold standard or method of choice. Thus, results should be generalized carefully. However, they could be used as a valuable supplement to direct measurements in the present. We encourage other researchers to test our velocity prediction models and evaluate the proportion of the obtained variables using different populations to assess to what extent the results can be extrapolated and transferred.

#### *4.4. Limitations*

A possible limitation is that participants underwent CPET in different phases of the day (circadian rhythm), month (menstrual cycle for female athletes), or season [43,44]. Moreover, we did not evaluate the training volume of the EA. The participants received dietary and preparation tips, but we cannot be sure that they were rigorously implemented; thus, some BIA results for BC should be analyzed with caution. Some data in [La<sup>−</sup>]b were missed (not all participants decided on the [La<sup>−</sup>]b test because it was an optional variable in the clinic's CPET portfolio) and RF imputation was applied. RF is recognized as the best method for filling data gaps, and our imputation did not cause a significant negative effect on the [La−]b data precision. The models still showed high prediction abilities at the building and validation (i.e., out-of-bag error) stages. A comparison of both datasets (first set only with directly measured [La−]b and second only with imputed [La−]b) did not show significant differences between them (*p* = 0.4) [26]. Volunteers individually declared the intensity level on the Borg scale, and the evaluation could differ between participants. The above limitations result from the specifics of the study, which is population-based, and not a controlled trial. In order to minimize their importance, the above-described internal validation was applied, which revealed the high data precision and replicability of the derived equations.

#### *4.5. Future Directions*

We advise that future prediction models used to estimate running velocities should be applied in cohorts with comparable characteristics to those from which they were primarily created (similar to other prediction models used in sports diagnostics) [36]. It is especially important in narrow and specified populations, including well-trained EA or cardiology patients [36]. We underline that there is a significant necessity for more accurately adjusted contributing factors and the development of new, advanced machine-learning prediction algorithms using unified TRIPOD recommendations [18]. This will enable the subsequent choice of the appropriate protocol to use in medical diagnostic and training prescriptions, depending on the participant's disease type or fitness level [7]. We recommend assessing our methods in an external environment, such as the 3000 m distance run, to cover all evaluation sites [45,46]. It is worth mentioning that, as stated by Figueiredo et al., the critical speed showed a better predictive value for the 5 km running results regarding a steady run than the peak velocity. Although our research focuses mostly on CPET performed in the clinical settings on the mechanical treadmill, we recommend further studies which will investigate the effect of critical speed compared to peak velocity [47].
