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# The New Power Duration Model in WKO4 - Part 2

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Mathematical modeling of the power duration relationship while cycling, Part 2 - Limitations of current models

Mathematical modeling of the power duration relationship while cycling, Part 2 - Limitations of current models

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• Intercept not different from 0, but slope significantly different from 1
• What RaceDay does and what GoldenCheetah used to do, ‘til Dan Connelly broke it
• Slope significantly different from 1; intercept significantly different from 0
• W’ higher and CP lower than when using 2 parameter model
• Throw it in the garbage bin!
• Slope significantly different from 1; intercept significantly different from 0
• Throw it in the garbage bin!
• Intercept and slope not significantly different from 0 and 1, respectively, but note wide scatter/low R2.
• Intercept and slope significantly different from 0 and 1, respectively. Also note the rescaling.
• IJSM 2011 – editor Greg Atkinson
• Throw it in the garbage bin!

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• 1. The New Power-Duration Model in WKO4 November 12, 2013 | Andrew R. Coggan, Ph.D.
• 2. Importance of new power-duration 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. 2
• 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 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. 3
• 4. Modeled vs. actual data: CP1-10 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. 4
• 5. Normalized residuals vs. duration: CP1-10 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
• 6. Independence of parameter estimates Correlation matrix for parameters of CP1-10 model W’ W’ CP 1.00 0.07 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. 1.00 6
• 7. External validation: CP1-10 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
• 8. The new power-duration model in WKO4 Part II: Limitations of current models 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. 8
• 9. Models to be discussed 1. 2. 3. 4. 5. CP3-30 Morton 3 parameter AIS Ward-Smith 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. 9
• 10. Modeled vs. actual data: 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. 10
• 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. 11
• 12. Independence of parameter estimates Correlation matrix for parameters of CP3-30 model W’ W’ CP 1.00 0.13 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. 1.00 12
• 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. 13
• 14. Modeled vs. actual data: 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. 14
• 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. 15
• 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 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. 1.00 16
• 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. 17
• 18. Modeled vs. actual data: 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. 18
• 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. 19
• 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 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. 1.00 20
• 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. 21
• 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. 22
• 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. 23
• 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. 1.00 24
• 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. 25
• 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. 26
• 27. Modeled vs. actual data: 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. 27
• 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. 28
• 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. 1.00 29
• 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. 30
• 31. 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. 31