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. 2026 Apr 3;56(7):1637–1674. doi: 10.1007/s40279-026-02410-x

Table 4.

Summary of typical model critical speed (CS) and D′ bias, standard error ranges and the minimum data requirements to derive CS and D′ estimates

Model CS and D′ bias Typical standard error range Minimum data requirements
Distance-time

CS: likely comparable to inverse-time and 2-parameter hyperbolic models [13, 15, 21, 24, 27–31, 35–37, 116]. Likely greater than 3-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37]. Variable difference to exponential model [24, 29, 31, 35]

D′: likely comparable to inverse-time and 2-parameter hyperbolic models [13, 15, 21, 24, 27–31, 35–37, 116]. Likely lower than 3-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37].

CS: 1–2.8% [29–31, 34, 90]

D′: 5–28.2% [29, 30, 34, 39]

2 trials of different durations
Inverse-time

CS: likely comparable to distance-time and 2-parameter hyperbolic models [13, 15, 21, 24, 27–31, 35–37, 116]. Likely greater than 3-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37]. Variable difference to exponential model [24, 29, 31, 35]

D′: likely comparable to distance-time and 2-parameter hyperbolic models [13, 15, 21, 24, 27–31, 35–37, 116]. Likely lower than 3-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37].

CS: 2.3–3.8% [29–31, 34, 90]

D′: 7–20.5% [29, 30, 34, 39]

2 trials of different durations
2-parameter hyperbolic

CS: likely comparable to distance-time and inverse-time models [13, 15, 21, 24, 27–31, 35–37, 116]. Likely greater than 3-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37]. Variable difference to exponential model [24, 29, 31, 35]

D′: likely comparable to distance-time and inverse-time models [13, 15, 21, 24, 27–31, 35–37, 116]. Likely lower than 3-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37].

CS: 1.8–3% [29–31, 34, 90]

D′: 6–23.3% [29, 30, 34, 39]

2 trials of different durations
3-parameter hyperbolic

CS: Likely less than distance-time, inverse-time, and 2-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37]. Variability in difference to exponential model

D′: Likely greater than distance-time, inverse-time, and 2-parameter hyperbolic model [13, 23, 24, 29, 31, 33, 35, 37]

CS: 16.9–70.9% [29, 31, 90]

D′: > 100% [29]

2 trials of different durations
Exponential Variable difference to distance-time, inverse-time, and 2- and 3-parameter hyperbolic models [24, 29, 31, 35] CS: 7.7–9.6% [29, 31, 90] 2 trials of different durations
Stryd CP: comparable to work-time model. Less than inverse-time model. Greater than 3-parameter hyperbolic model [13] N/A CP can be generated after a few runs [91]

CP critical power, CS critical speed