The New Power Duration Model in WKO4 - Part 2

The New Power-Duration Model in WKO4November 12, 2013 | Andrew R. Coggan, Ph.D.

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. 2

Importance of new power-duration model

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How do you evaluate mathematical models?

1. Statistical criteriaa. F testb. Runs testc. AIC

2. Residualsa. Distributionb. Magnitudec. Bias

3. Parameter estimatesa. Numberb. Independencec. Precision

4. External validation

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Modeled vs. actual data: CP1-10

𝑃 (𝑡 )=𝐶𝑃+𝑊 ′ /𝑡

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. 5

Normalized residuals vs. duration: CP1-10

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Independence of parameter estimates

W’ CP

W’ 1.00 0.07

CP 1.00

Correlation matrix for parameters of CP1-10 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. 7

External validation: CP1-10

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The new power-duration model in WKO4

Part II: Limitations of current models

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Models to be discussed

1. CP3-30

2. Morton 3 parameter3. AIS4. Ward-Smith5. Pinot and Grappe

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. 10

Modeled vs. actual data: CP3-30

𝑃 (𝑡 )=𝐶𝑃+𝑊 ′ /𝑡

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. 11

Normalized residuals vs. duration: CP3-30

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. 12

Independence of parameter estimates

W’ CP

W’ 1.00 0.13

CP 1.00

Correlation matrix for parameters of CP3-30 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. 13

External validation: CP3-30

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. 14

Modeled vs. actual data: 3-parameter CP

𝑃 (𝑡 )=𝐶𝑃+𝑊 ′∗( 1𝑡−

𝑊 ′

𝐶𝑃−𝑃𝑚𝑎𝑥)

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. 15

Normalized residuals vs. duration: 3-parameter CP

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. 16

Independence of param. estimates: 3-parameter CP

Correlation matrix for 3-parameter CP modelW’ Pmax

CP 1.00 -0.06 0.31

W’ 1.00 0.69

Pmax 1.00

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. 17

External validation: 3-parameter CP

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. 18

Modeled vs. actual data: AIS model

𝑃 (𝑡 )=𝐶𝑃+𝑊 ′1𝑡

+(𝑊 ′2𝑡𝑎𝑢

−𝐶𝑃 )(1−𝑒−𝑊

′ 1𝑡𝑎𝑢 )(

𝑡𝑎𝑢𝑡

)

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. 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. 20

Independence of parameter estimates: AIS model

Correlation matrix for 3-parameter CP modelCP W’ 1 W’ 2 tau

CP 1.00 0.58 0.80 -0.36

W’ 1 1.00 0.48 -0.15

W’ 2 1.00 -0.27

tau 1.00

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. 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. 22

Modeled vs. actual data: 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. 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. 24

Independence of param. estimates: Ward-Smith

Correlation matrix for Ward-Smith modelPmax CP tau

Pmax 1.00 0.67 -0.07

CP 1.00 -0.27

tau 1.00

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. 25

External validation: Ward-Smith 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. 26

“Record power profile” of Pinot and Grappe

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. 27

Modeled vs. actual data: P&G

𝑃 (𝑡)=𝑃𝑚𝑎𝑥∗𝑡𝑏

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. 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. 29

Independence of parameter estimates: P&G

Pmax b

Pmax 1.00 -0.82

b 1.00

Correlation matrix for parameters of Pinot and Grappe 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. 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. 31

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