The document discusses limitations of current mathematical models for describing the power-duration relationship and evaluating athletic performance. It analyzes several existing models, including the CP, 3-parameter CP, AIS, Ward-Smith, and Pinot and Grappe models, finding that none provide a satisfactory description across the entire power-duration range. It concludes that a new model needs to be developed to better capture the power-duration relationship.

1. The New Power-Duration Model in WKO4
November 12, 2013 | Andrew R. Coggan, Ph.D.

2. Importance of new power-duration model
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3. 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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4. Modeled vs. actual data: CP1-10
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5. Normalized residuals vs. duration: CP1-10
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6. Independence of parameter estimates
Correlation matrix for parameters of CP1-10 model
W’
W’
CP
1.00
0.07
CP
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7. External validation: CP1-10
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8. The new power-duration model in WKO4
Part II: Limitations of current models
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9. Models to be discussed
1.
2.
3.
4.
5.
CP3-30
Morton 3 parameter
AIS
Ward-Smith
Pinot and Grappe
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10. Modeled vs. actual data: CP3-30
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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. Normalized residuals vs. duration: CP3-30
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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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12. Independence of parameter estimates
Correlation matrix for parameters of CP3-30 model
W’
W’
CP
1.00
0.13
CP
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13. External validation: CP3-30
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14. Modeled vs. actual data: 3-parameter CP
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15. Normalized residuals vs. duration: 3-parameter CP
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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: 3-parameter CP
Correlation matrix for 3-parameter CP model
W’
CP
W’
1.00
Pmax
-0.06
0.31
1.00
0.69
Pmax
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17. External validation: 3-parameter CP
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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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18. Modeled vs. actual data: AIS 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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19. Normalized residuals vs. duration: AIS 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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20. Independence of parameter estimates: AIS model
Correlation matrix for 3-parameter CP model
CP
CP
W’ 1
W’ 2
W’ 1
W’ 2
tau
1.00
0.58
0.80
-0.36
1.00
0.48
-0.15
1.00
-0.27
tau
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21. External validation: AIS 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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22. Modeled vs. actual data: Ward-Smith
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23. Normalized residuals vs. duration: Ward-Smith
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. Independence of param. estimates: Ward-Smith
Correlation matrix for Ward-Smith model
Pmax
Pmax
CP
CP
tau
1.00
0.67
-0.07
1.00
-0.27
tau
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. External validation: Ward-Smith 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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26. “Record power profile” of Pinot and Grappe
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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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27. Modeled vs. actual data: P&G
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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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28. Normalized residuals vs. duration: P&G
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. Independence of parameter estimates: P&G
Correlation matrix for parameters of Pinot and Grappe model
Pmax
Pmax
b
1.00
-0.82
b
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. 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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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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