## 4 Discussion  
This study attempts to shorten the 3 min all-out test (3 MT) while maintaining the accuracy of critical power (CP) and anaerobic work capacity (W\({}^{\prime}\)) estimates. By applying exponential functions to shorter time duration samples, we aimed to determine whether athletes could achieve reliable results without enduring the full 3 min test. The Critical Power Model (CPM) parameters (CP and W\({}^{\prime}\)) calculated at each 15 s time interval were subsequently compared to the parameters derived from the 3 min all-out test (\(CP_{3 MT}\) and \(W^{\prime}_{3 MT}\)). The findings of this study demonstrate that reducing the test duration by 33% for MONO (down to 120 s) and 50% for BI (down to 90 s) still provides accurate estimates of CP and W\({}^{\prime}\), with only a 5% difference from the traditional 3 MT. This suggests that a shorter, more manageable test can be used for fitness monitoring, addressing one of the major drawbacks of the standard 3 MT: its mentally and physically exhaustive nature. The results presented suggest that an all-out test duration of 120 s for MONO function and 90 s for BI function fitting provide accurate estimates of both \(W^{\prime}_{3 MT}\) (MONO \(p=0.23\) and BI \(p=0.10\), respectively) and \(CP_{3 MT}\) (MONO \(p=0.24\) and BI \(p=0.11\), respectively). \(W^{\prime}\) and CP did not show differences from the 3 MT parameters at time intervals extending beyond 120 s for MONO \(W^{\prime}_{135}\) and \(CP_{105}\) and 90 s for BI \(W^{\prime}_{90}\) and \(CP_{90}\), respectively. At durations shorter than 105 s for MONO and 75 s for BI, the power output still exhibited the rapidly decreasing pattern characteristic of the first phase of an all-out test. Capturing this fast-decline behavior at such short time intervals, however, resulted in lower CP estimates. As the time duration increased, the exponential functions could capture the second phase of the slower power decline, thereby offering more accurate and reliable estimates. The results from the present study, as well as findings from previous studies [7; 11], indicate that it is not essential for athletes to complete the full 3 min duration required by the traditional 3 MT in order to derive valid values for W\({}^{\prime}\) and CP. The test duration can be significantly shortened by up to 50%, with the resulting parameter estimates differing by only 5% from the original 3 MT values. Bland-Altman plots (Figure 4 and 5) further demonstrated an unbiased relationship in CP and W\({}^{\prime}\) estimates between the traditional 3 MT and the shortened exponential function-based approach. The Critical Power Model has historically been only loosely associated with the underlying metabolic processes [18]. The response letter by [PERSON] (2019) highlights some of the difficulties in ascribing the W\({}^{\prime}\) solely to metabolic depletion. We do not address the possible mechanisms accounting for the rapid decline in power output toward an asymptote [19]. Our shortened-duration approach, which utilizes an exponential function, provides an empirical description of the power-duration relationship. Nevertheless, this approach is in agreement with prior findings that W\({}^{\prime}\) can be entirely depleted within 90 s [8]. However, there is some evidence that a power reserve may be present for some athletes [20; 21]. Research on W\({}^{\prime}\) measurement has highlighted substantial variability and lower reliability, particularly with protocols that deviate from standard procedures. The 3 min all-out test (3 MT) shows variability in estimating W\({}^{\prime}\) and CP (critical power), with issues such as high intra-individual variability and error margins that impact subject-level reliability. For instance, subject-specific measures show significant variation, with the coefficient of variance for W\({}^{\prime}\) ranging from 4.83% to 17.32%, reflecting an inherent difficulty in producing consistent W\({}^{\prime}\) values across trials [22].