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The New Power-Duration Model in WKO4
November 19, 2013 | Andrew R. Coggan, Ph.D.
Importance of new power-duration model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(...
Performance Manager Chart in WKO4

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) an...
How do you evaluate mathematical models?
1. Statistical criteria
a. F test
b. Runs test
c. AIC

2. Residuals

3. Parameter...
Models of the power-duration relationship
CP1-10

CP3-30

AIS

Ward-Smith

CP 3-parameter

Andrew R. Coggan, Ph.D., Peaks ...
Limitations of other models: residuals
CP1-10

CP3-30

AIS

Ward-Smith

CP 3-parameter

Andrew R. Coggan, Ph.D., Peaks Coa...
Limitations of other models: validation
CP1-10

CP3-30

AIS

Ward-Smith

CP 3-parameter

Pinot and Grappe

(n/a)

Andrew R...
Conclusions
None of the presently-available models provide a
satisfactory description of the entire power-duration
relatio...
The new power-duration model in WKO4

Part III: Introduction of a superior approach

Andrew R. Coggan, Ph.D., Peaks Coachi...
Modeled vs. actual data: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) ...
Definitions of terms
• Pmax – the maximal power that can be generated for
a very short period of time. Units are W or W/kg...
Intellectual property rights
• Registered trademarks are being pursued for the
following new terms – unauthorized use is e...
Modeled vs. actual data: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) ...
Distribution of normalized residuals: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are ...
Normalized residuals vs. duration: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the...
Independence of param. estimates: WKO4 model

Correlation matrix for WKO4 model
Pmax
Pmax
FRC

FRC

FTP

1.00

0.58

0.41
...
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 Grou...
Model fit parameters in WKO4

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or ...
External validation: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/...
External validation: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/...
WKO4 vs. other models
“It ain’t braggin’ if you can back it up”

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or Tra...
Limitations of other models: residuals
CP1-10

CP3-30

AIS

Ward-Smith

CP 3-parameter

Andrew R. Coggan, Ph.D., Peaks Coa...
Normalized residuals vs. duration: WKO4 model

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the...
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...
Comparison of FTP prediction
Model

Slope
(unitless)

Intercept
(W)

S.E.E.
(W)

CV
(%)

CP1-10

0.87

24

±4.6

±1.5

CP3...
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

∞

...
CP2-15 overestimates maximal steady-state
McLellan TM, Cheung KSY. A comparative evaluation of the
individual anaerobic th...
CP1-10 overestimates maximal steady-state
Brickely G, Doust J, Williams CA. Physiological responses
during exercise to exh...
CP2-15 overestimates maximal steady-state
Pringle JSM, Jones AM. Maximal lactate steady
state, critical power and EMG duri...
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

∞

...
FRC vs. W’

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s) of all...
Pmax vs. 1 s power

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) and/or licensee(s...
Model is sensitive to changes across years

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the ow...
Model is sensitive to changes across years

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the ow...
Model is sensitive to changes w/in a year

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the own...
Power-duration history chart in WKO4

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s)...
Application of the model to running

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s) ...
Application of the model to swimming

Andrew R. Coggan, Ph.D., Peaks Coaching Group, and/or TrainingPeaks are the owner(s)...
Application of the model to skating
2013 WR in speed skating (men)

18

16

Average pace (m/s)

14
12

Functional reserve ...
The new power-duration model in WKO4
• The most advanced mathematical model of the
exercise intensity-duration relationshi...
Next week: the final installment!
Current (i.e., WKO4) and possible future applications
of the new power-duration model wi...
Stay Updated
Receive the latest updates on WKO4 and the science of
training.
Get Updates >

Andrew R. Coggan, Ph.D., Peaks...
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The New Power Duration Model in WKO4 - part 3

[Updated 11/22] Introduction of a Superior Approach. Dr. Andy Coggan presents criteria from weeks 1&2 to evaluate a new model and demonstrate how it overcomes many of the previous limitations - Webinar 3/4

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The New Power Duration Model in WKO4 - part 3

  1. 1. The New Power-Duration Model in WKO4 November 19, 2013 | Andrew R. Coggan, Ph.D.
  2. 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. 3. Performance Manager 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. 3
  4. 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 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. Models of the power-duration relationship 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 5
  6. 6. 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 6
  7. 7. Limitations of other models: validation CP1-10 CP3-30 AIS Ward-Smith CP 3-parameter Pinot and Grappe (n/a) 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. 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. 8
  9. 9. The new power-duration model in WKO4 Part III: Introduction of a superior approach 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. 10. Modeled vs. actual data: 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. 10
  11. 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. 11
  12. 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. 12
  13. 13. Modeled vs. actual data: 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. 13
  14. 14. Distribution of normalized residuals: 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. 14
  15. 15. 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. 15
  16. 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 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. 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. 17
  18. 18. Model fit parameters 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. 18
  19. 19. 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. 19
  20. 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. 20
  21. 21. WKO4 vs. other models “It ain’t braggin’ if you can back it up” 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. 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. 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. 23
  24. 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. 24
  25. 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. 25
  26. 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. 26
  27. 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. 27
  28. 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. 28
  29. 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. 29
  30. 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. 30
  31. 31. FRC vs. W’ 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. Pmax vs. 1 s power 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. Model is sensitive to changes across years 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. Model is sensitive to changes across years 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. Model is sensitive to changes w/in a year 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
  36. 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. 36
  37. 37. Application of the model to running 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. 37
  38. 38. Application of the model to swimming 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. 38
  39. 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 39
  40. 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. 40
  41. 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. 41
  42. 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. 42

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