Probabilistic Performance Profiling

A Model of the Power Duration Relation in Endurance Sports
  • Alexander AsterothEmail author
  • Melanie Ludwig
  • Kevin Bach
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1028)


A probabilistic model of maximal mean performance in endurance sports is presented. The joint distribution of three variables namely interval length, average power, and average heart rate is modeled using Gaussian processes. The model allows for prediction of maximal average performances even based on data from sub-maximal efforts.


Critical power Probabilistic model Gaussian processes Performance profiling 


  1. 1.
    Arts, F., Kuipers, H.: The relation between power output, oxygen uptake and heart rate in male athletes. Int. J. Sports Med. 15(05), 228–231 (1994)CrossRefGoogle Scholar
  2. 2.
    Bodner, M.E., Rhodes, E.C.: A review of the concept of the heart rate deflection point. Sports Med. 30(1), 31–46 (2000)CrossRefGoogle Scholar
  3. 3.
    Brickley, G., Doust, J., Williams, C.: Physiological responses during exercise to exhaustion at critical power. Eur. J. Appl. Physiol. 88(1–2), 146–151 (2002)Google Scholar
  4. 4.
    Brooke, J., Hamley, E.: The heart-rate–physical work curve analysis for the prediction of exhausting work ability. Med. Sci. Sports 4(1), 23–26 (1972)Google Scholar
  5. 5.
    Brooke, J., Hamley, E., Thomason, H.: Relationship of heart rate to physical work. J. Physiol. 197(1), 61P (1968)Google Scholar
  6. 6.
    Clingeleffer, A., Mc Naughton, L.R., Davoren, B.: The use of critical power as a determinant for establishing the onset of blood lactate accumulation. Eur. J. Appl. Physiol. Occup. Physiol. 68(2), 182–187 (1994)CrossRefGoogle Scholar
  7. 7.
    Ebert, T.R., Martin, D.T., McDonald, W., Victor, J., Plummer, J., Withers, R.T.: Power output during women’s World Cup road cycle racing. J. Appl. Physiol. 95, 8 (2005)Google Scholar
  8. 8.
    Ebert, T.R., Martin, D.T., Stephens, B., Withers, R.T.: Power output during a professional men’s road-cycling tour. Int. J. Sports Physiol. Perform. 1, 12 (2006)CrossRefGoogle Scholar
  9. 9.
    Hill, A.V.: Muscular Movement In Man: The Factors Governing Speed and Recovery from Fatigue. McGraw-Hill, New York (1927)Google Scholar
  10. 10.
    Housh, D.J., Housh, T.J., Bauge, S.M.: The accuracy of the critical power test for predicting time to exhaustion during cycle ergometry. Ergonomics 32(8), 997–1004 (1989)CrossRefGoogle Scholar
  11. 11.
    Karsten, B., Jobson, S.A., Hopker, J., Stevens, L., Beedie, C.: Validity and reliability of critical power field testing. Eur. J. Appl. Physiol. 115(1), 197–204 (2015)CrossRefGoogle Scholar
  12. 12.
    Monod, H., Scherrer, J.: The work capacity of a synergic muscular group. Ergonomics 8(3), 329–338 (1965)CrossRefGoogle Scholar
  13. 13.
    Moritani, T., Nagata, A., Devries, H.A., Muro, M.: Critical power as measure of physical work capacity and anaerobic threshold. Ergonomics 24(5), 339–350 (1981)CrossRefGoogle Scholar
  14. 14.
    Quod, M., Martin, D., Martin, J., Laursen, P.: The power profile predicts road cycling MMP. Int. J. Sports Med. 31(06), 397–401 (2010)CrossRefGoogle Scholar
  15. 15.
    Rasmussen, C.E.: Gaussian processes in machine learning. In: Summer School on Machine Learning, pp. 63–71. Springer, Berlin (2003)Google Scholar
  16. 16.
    Vogt, S., Schumacher, Y., Roecker, K., Dickhuth, H.H., Schoberer, U., Schmid, A., Heinrich, L.: Power output during the tour de France. Int. J. Sports Med. 28(9), 756–761 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alexander Asteroth
    • 1
    Email author
  • Melanie Ludwig
    • 1
  • Kevin Bach
    • 1
  1. 1.Bonn-Rhein-Sieg University o.A.S.Sankt AugustinGermany

Personalised recommendations