The document discusses a new power-duration model introduced in WKO4 software. It provides more accurate modeling of the relationship between exercise power and duration than previous models by accounting for an athlete's functional reserve capacity and maximal power in addition to functional threshold power. Evaluation shows the WKO4 model has smaller errors and better predicts functional threshold power than other models. It is more sensitive to changes in an athlete's fitness over time.

1. The New Power-Duration Model in WKO4
November 19, 2013 | Andrew R. Coggan, Ph.D.

2. Importance of new power-duration model
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3. Performance Manager Chart in WKO4
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4. How do you evaluate mathematical models?
1. Statistical criteria
a. F test
b. Runs test
c. AIC
2. Residuals
3. Parameter estimates
a. Number
b. Independence
c. Precision
4. External validation
a. Distribution
b. Magnitude
c. Bias
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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5. Models of the power-duration relationship
CP1-10
CP3-30
AIS
Ward-Smith
CP 3-parameter
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
Pinot and Grappe
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6. Limitations of other models: residuals
CP1-10
CP3-30
AIS
Ward-Smith
CP 3-parameter
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
Pinot and Grappe
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7. Limitations of other models: validation
CP1-10
CP3-30
AIS
Ward-Smith
CP 3-parameter
Pinot and Grappe
(n/a)
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8. Conclusions
None of the presently-available models provide a
satisfactory description of the entire power-duration
relationship. A new model must therefore be
developed.
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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9. The new power-duration model in WKO4
Part III: Introduction of a superior approach
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10. Modeled vs. actual data: WKO4 model
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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11. Definitions of terms
• Pmax – the maximal power that can be generated for
a very short period of time. Units are W or W/kg.
• Functional reserve capacity (FRC) – the total amount
of work that can be done during continuous exercise
above FTP before fatigue occurs. Units are kJ or J/kg.
• Functional threshold power (FTP) – the highest
power that can be sustained in a quasi-steady-state
for a prolonged period of time. Units are W or W/kg
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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12. Intellectual property rights
• Registered trademarks are being pursued for the
following new terms – unauthorized use is expressly
prohibited:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Power-Duration Curve™
Power Duration Curve™
P-D curve™ / PD Curve™
Power-Duration History Chart™
Power Duration History Chart™
Functional Reserve Capacity™
FRC™
Dynamic Functional Reserve Capacity™
dFRC™
Rider Phenotyping™
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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13. Modeled vs. actual data: WKO4 model
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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14. Distribution of normalized residuals: WKO4 model
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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15. Normalized residuals vs. duration: WKO4 model
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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16. Independence of param. estimates: WKO4 model
Correlation matrix for WKO4 model
Pmax
Pmax
FRC
FRC
FTP
1.00
0.58
0.41
1.00
0.15
FTP
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
1.00
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17. CVs of model fit parameters
Pmax
FRC
FTP
6.8
±3.2%
4.7
±3.4%
1.2
±0.5%
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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18. Model fit parameters in WKO4
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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19. External validation: WKO4 model
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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20. External validation: WKO4 model
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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21. WKO4 vs. other models
“It ain’t braggin’ if you can back it up”
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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22. Limitations of other models: residuals
CP1-10
CP3-30
AIS
Ward-Smith
CP 3-parameter
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
Pinot and Grappe
22

23. Normalized residuals vs. duration: WKO4 model
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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24. Comparison of root mean squared errors
Model
RMSE
CP1-10
8.5±2.6%
CP3-30
12.3±4.5%
CP 3-parameter
1.1±0.4%
AIS
4.6±0.9%
Ward-Smith
2.5±0.6%
Pinot and Grappe
1.1±0.6%
WKO4 model
0.3±0.1%
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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25. Comparison of FTP prediction
Model
Slope
(unitless)
Intercept
(W)
S.E.E.
(W)
CV
(%)
CP1-10
0.87
24
±4.6
±1.5
CP3-30
0.89
33
±2.4
±0.8
CP 3-parameter
0.87
46
±4.8
±1.6
AIS
1.01
9
±20.5
±6.8
Ward-Smith
0.74
23
±8.6
±2.8
Pinot and Grappe
n/a
n/a
n/a
n/a
WKO4 model
0.93
21
±1.5
±0.5
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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26. Comparison of parameter estimates
Model
Pmax (W)
W’ or FRC (kJ)
CP or FTP (W)
CP1-10
∞
13.9±4.4
303±56
CP3-30
∞
19.2±6.1
285±52
CP 3-parameter
1219±309
22.4±8.1
277±53
AIS
∞
12.0±1.3
276±45
Ward-Smith
1145±318
n/a
360±64
Pinot and Grappe
1438±413
n/a
n/a
WKO4 model
1132±273
19.3±6.8
286±51
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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27. CP2-15 overestimates maximal steady-state
McLellan TM, Cheung KSY. A comparative evaluation of the
individual anaerobic threshold and the critical power. Med
Sci Sports Exerc 1992; 24:543-550.
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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28. CP1-10 overestimates maximal steady-state
Brickely G, Doust J, Williams CA. Physiological responses
during exercise to exhaustion at critical power. Eur J Appl
Physiol 2002; 88:146-151.
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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29. CP2-15 overestimates maximal steady-state
Pringle JSM, Jones AM. Maximal lactate steady
state, critical power and EMG during cycling. Eur J Appl
Physiol 2002; 88:214-226.
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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30. Comparison of parameter estimates
Model
Pmax (W)
W’ or FRC (kJ)
CP or FTP (W)
CP1-10
∞
13.9±4.4
303±56
CP3-30
∞
19.2±6.1
285±52
CP 3-parameter
1219±309
22.4±8.1
277±53
AIS
∞
12.0±1.3
276±45
Ward-Smith
1145±318
n/a
360±64
Pinot and Grappe
1438±413
n/a
n/a
WKO4 model
1132±273
19.3±6.8
286±51
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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31. FRC vs. W’
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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32. Pmax vs. 1 s power
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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33. Model is sensitive to changes across years
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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34. Model is sensitive to changes across years
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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35. Model is sensitive to changes w/in a year
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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36. Power-duration history chart in WKO4
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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37. Application of the model to running
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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38. Application of the model to swimming
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presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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39. Application of the model to skating
2013 WR in speed skating (men)
18
16
Average pace (m/s)
14
12
Functional reserve distance = 208 m
Functional threshold pace = 13.0 m/s
10
8
6
4
2
0
1
10
Time (s)
100
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
1000
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40. The new power-duration model in WKO4
• The most advanced mathematical model of the
exercise intensity-duration relationship ever
developed.
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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41. Next week: the final installment!
Current (i.e., WKO4) and possible future applications
of the new power-duration model will be presented
and discussed.
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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42. Stay Updated
Receive the latest updates on WKO4 and the science of
training.
Get Updates >
Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all intellectual property rights to this
presentation and the material it contains. These works are protected by copyright laws and treaties around the world. All such rights are reserved.
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