The New Power-Duration Model in WKO4 November 19, 2013 | Andrew R. Coggan, Ph.D.
Feb 22, 2016
The New Power-Duration Model in WKO4November 19, 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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Performance Manager Chart in WKO4
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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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Models of the power-duration relationship
CP1-10 CP3-30 CP 3-parameter
AIS Ward-Smith
π (π‘ )=πΆπ+π β² /π‘ π (π‘ )=πΆπ+π β²β(1π‘ β
π β²
πΆπβππππ₯ )
)
π (π‘ )=πΆπ+π β² /π‘
π (π‘ )=πΆπ+π β²1π‘ +(
π β²2π‘ππ’ βπΆπ )(1βπ
βπβ² 1
π‘ππ’ )(π‘ππ’π‘ )
Pinot and Grappeπ (π‘ )=ππππ₯βπ‘π
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Limitations of other models: residuals
CP1-10 CP3-30 CP 3-parameter
AIS Ward-Smith Pinot and Grappe
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Limitations of other models: validation
CP1-10 CP3-30 CP 3-parameter
AIS Ward-Smith Pinot and Grappe
(n/a)
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Conclusions
None of the presently-available models provide a satisfactory description of the entire power-duration relationship. A new model must therefore be developed.
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The new power-duration model in WKO4
Part III: Introduction of a superior approach
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Modeled vs. actual data: WKO4 model
π (π‘ )= π (ππππ₯ ,πΉπ πΆ ,πΉππ ,β¦)
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Definitions of terms
β’ Pmax β the maximal power that can be generated for a very short period of time. Units are W or W/kg.
β’ Functional reserve capacity (FRC) β the total amount of work that can be done during continuous exercise above FTP before fatigue occurs. Units are kJ or J/kg.
β’ Functional threshold power (FTP) β 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. 12
Intellectual property rights
β’ Registered trademarks are being pursued for the following new terms β unauthorized use is expressly prohibited:
1. Power-Duration Curveβ’2. Power Duration Curveβ’3. P-D curveβ’ / PD Curveβ’4. Power-Duration History Chartβ’5. Power Duration History Chartβ’6. Functional Reserve Capacityβ’7. FRCβ’8. Dynamic Functional Reserve Capacityβ’9. dFRCβ’10. Rider Phenotypingβ’
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Modeled vs. actual data: WKO4 model
π (π‘ )= π (ππππ₯ ,πΉπ πΆ ,πΉππ ,β¦)
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Distribution of normalized residuals: WKO4 model
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Normalized residuals vs. duration: WKO4 model
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Independence of param. estimates: WKO4 model
Correlation matrix for WKO4 modelPmax FRC FTP
Pmax 1.00 0.58 0.41
FRC 1.00 0.15
FTP 1.00
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CVs of model fit parameters
Pmax FRC FTP6.8
Β±3.2%4.7
Β±3.4%1.2
Β±0.5%
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Model fit parameters in WKO4
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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
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. 21
WKO4 vs. other models
βIt ainβt bragginβ if you can back it upβ
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Limitations of other models: residuals
CP1-10 CP3-30 CP 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. 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. 24
Comparison of root mean squared errors
Model RMSE
CP1-10 8.5Β±2.6%
CP3-30 12.3Β±4.5%
CP 3-parameter 1.1Β±0.4%
AIS 4.6Β±0.9%
Ward-Smith 2.5Β±0.6%
Pinot and Grappe 1.1Β±0.6%
WKO4 model 0.3Β±0.1%
Ζ=βπ£πππππππ+ππππ
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Comparison of FTP prediction
Model Slope(unitless)
Intercept (W)
S.E.E.(W)
CV(%)
CP1-10 0.87 24 Β±4.6 Β±1.5
CP3-30 0.89 33 Β±2.4 Β±0.8
CP 3-parameter 0.87 46 Β±4.8 Β±1.6
AIS 1.01 9 Β±20.5 Β±6.8
Ward-Smith 0.74 23 Β±8.6 Β±2.8
Pinot and Grappe n/a n/a n/a n/a
WKO4 model 0.93 21 Β±1.5 Β±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. 26
Comparison of parameter estimates
Model Pmax (W) Wβ or FRC (kJ) CP or FTP (W)CP1-10 β 13.9Β±4.4 303Β±56CP3-30 β 19.2Β±6.1 285Β±52
CP 3-parameter 1219Β±309 22.4Β±8.1 277Β±53AIS β 12.0Β±1.3 276Β±45
Ward-Smith 1145Β±318 n/a 360Β±64Pinot and Grappe 1438Β±413 n/a n/a
WKO4 model 1132Β±273 19.3Β±6.8 286Β±51
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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. 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. 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. 30
Comparison of parameter estimates
Model Pmax (W) Wβ or FRC (kJ) CP or FTP (W)CP1-10 β 13.9Β±4.4 303Β±56CP3-30 β 19.2Β±6.1 285Β±52
CP 3-parameter 1219Β±309 22.4Β±8.1 277Β±53AIS β 12.0Β±1.3 276Β±45
Ward-Smith 1145Β±318 n/a 360Β±64Pinot and Grappe 1438Β±413 n/a n/a
WKO4 model 1132Β±273 19.3Β±6.8 286Β±51
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FRC vs. Wβ
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Pmax vs. 1 s power
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Model is sensitive to changes across years
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Model is sensitive to changes across years
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Model is sensitive to changes w/in a year
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Power-duration history chart in WKO4
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Application of the model to running
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Application of the model to swimming
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Application of the model to skating
10 100 10000
2
4
6
8
10
12
14
16
18 2013 WR in speed skating (men)
Time (s)
Aver
age
pace
(m/s
) Functional reserve distance = 208 mFunctional threshold pace = 13.0 m/sAverage prediction error = 3.3%
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The new power-duration model in WKO4
β’ The most advanced mathematical model of the exercise intensity-duration relationship ever developed.
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Next week: the final installment!
Current (i.e., WKO4) and possible future applications of the new power-duration model will be presented and discussed.