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The New Power Duration Model in WKO4 - Part 1

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Mathematical modeling of the power duration relationship while cycling, Part 1 - A primer on modeling.

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The New Power Duration Model in WKO4 - Part 1

  1. 1. The New Power-Duration Model in WKO4 November 5, 2013 | Andrew R. Coggan, Ph.D.
  2. 2. The power-duration relationship Linear time scale Log time scale 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. 3. The new power-duration model in WKO4 • A heart-warming tale in which the mean maximal power chart and the power profiling table meet, fall in love, get married, and have a child that turns out to be somewhat of a child prodigy. 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. 4. 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. 4
  5. 5. Webinar series topics • • • • Part I: A primer on modeling Part II: Limitations of current models Part III: Introduction of a superior approach Part IV: Present and possible future applications 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. 6. The $64,000 question Why? 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. 6
  7. 7. The power-duration relationship Linear time scale Log time scale 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. 8. The $64,000 answer Because having a robust mathematical description of an individual’s power-duration relationship provides quantitative insight re. their unique abilities and paves the way for other analyses. 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. 9. 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. 9
  10. 10. Evolution of 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. 10
  11. 11. Uses for the power-duration model 1. Auto FTP 2. Pmax 3. FRC 4. dFRC 5. Phenotyping 6. Individual adaptations scores 7. Auto match finding 8. Identification of outliers 9. Optimal pacing strategy 10. Application to other sports 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. 12. The new power-duration model in WKO4 Part I: A primer on modeling 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
  13. 13. Some mathematical models Coggan AR, Ruby BC, Zderic TW. FASEB J 1999; 13: A1055 Herrero P, et al. J Nucl Med 2007; 48: 955-964. Herrero P, et al. J Nucl Med 2007; 48: 2046-2055. Coggan AR, et al. J Nucl Cardiol 2009; 16: 562-570. 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. 14. Caveats re. mathematical modeling • Mathematical models are theoretical constructs that may, or may not, have a basis in reality • All models are wrong, but some are useful • The usefulness of any model depends in part upon its domain of validity 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. 15. Example of a limited domain of validity Model structure Model validation Coggan AR, et al. J Nucl Cardiol 2009; 16: 562-570. 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. 16. 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. 16
  17. 17. Most important take-home message? R2 is not an adequate indicator of the goodness-of-fit of a multi-parameter, non-linear 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. 17
  18. 18. R2 as a measure of goodness-of-fit 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. 19. R2 as a measure of goodness-of-fit 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. 20. R2 as a measure of goodness-of-fit 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
  21. 21. 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. Magnitude b. Distribution 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. 21
  22. 22. What is a “normalized residual”? 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. 23. Residuals of linear fit 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. 24. 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. Magnitude b. Distribution 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. 24
  25. 25. The critical power 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. 26. Distribution of normalized residuals 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. 27. Normalized residuals vs. duration 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. 28. Independence of parameter estimates Correlation matrix for parameters of critical power 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 28
  29. 29. External validation 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
  30. 30. Model vs. reality 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. 31. Distribution of normalized residuals 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
  32. 32. Normalized residuals vs. duration 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. 32
  33. 33. Limitations of the critical power model “The critical power concept is not without its limitations...in particular, it tends to greatly overestimate the maximal power that can be generated for only a few seconds, and it predicts that there should be a power output below which fatigue will never occur. In addition, the exact values obtained for W' and critical power depend in part on the testing protocol, e.g., the exact combination of powers and durations used to define the curve...” - Yours truly, post to the wattage list on 2/11/2002 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. 33
  34. 34. Summary • Modeling the power-duration relationship provides many potential benefits • Such benefits, however, will only be realizable with a sufficiently robust model • Standard criteria and approaches (which do not include R2) exist for evaluating mathematical models • The classic critical power model fails to adequately describe the entire power-duration relationship 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. 34
  35. 35. 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. 35

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