Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Steve Rigdon, PhD

CiteScore 2018: 1.67

SCImago Journal Rank (SJR) 2018: 0.587
Source Normalized Impact per Paper (SNIP) 2018: 1.970

See all formats and pricing
More options …
Volume 11, Issue 4


Volume 1 (2005)

Fair compensation for gate and wind conditions in ski jumping – estimated from competition data using a mixed model

Magne Aldrin
  • Corresponding author
  • Norwegian Computing Center, P.O. Box 114 Blindern, Oslo 0314, Norway
  • University of Oslo – Department of Mathematics, P.O. Box 1053 Blindern, Oslo 0317, Norway
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-10-13 | DOI: https://doi.org/10.1515/jqas-2015-0022


Ski jumping is a Winter Olympic sport where the athletes try to fly as far as possible with the best possible style on a ski jumping hill. The best athletes may achieve distances around 100 m on the smallest hills and up to 251.5 m (the world record) on a flying hill. The length of a ski jump is affected by the gate from which the jumpers start, where higher gates give higher speed and therefore longer jumps. Wind conditions are also important, head winds tend to give longer jumps and tail winds tend to give shorter jumps. To ensure relatively fair conditions during competitions, a system including gate and wind compensations was introduced from January 2010. If the conditions change considerably during a round, the jury can change the gate number to avoid too long or too short jumps, and the athlete is then given a compensation (positive or negative). Furthermore, the athletes are given a compensation for the wind conditions during their jump. In this paper, the fairness of this compensation system is investigated by an analysis of the results from 80 ski jumping competitions for men arranged in the World Cup, World Championships and Olympics in the 2011/2012, 2012/2013 and 2013/2014 seasons. The analysis is based on a mixed model. I found that the present compensation for gate number is reasonably fair, but with a tendency for 10% over-compensation. On the other hand, I estimate that the present compensation factor for head winds should be increased by 48% (95% CI 40–57%) and for tail winds by 22% (95% CI 16–30%) to fully compensate for wind conditions.

This article offers supplementary material which is provided at the end of the article.

Keywords: model selection; regression; weather conditions


  • Akaike, H. 1974. “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control 19:716–723.CrossrefGoogle Scholar

  • Bates, D., M. Maechler, B. Bolker, and S. Walker. 2015a. “Fitting Linear Mixed-effects Models Using lme4.” Journal of Statistical Software, accepted for publication, arXiv:1406.5823 (http://arxiv.org/abs/1406.5823).

  • Bates, D., M. Maechler, B. Bolker, and S. Walker. 2015b. lme4: Linear Mixed-effects Models Using Eigen and S4. R Package Version 1.1-9 (http://cran.r-project.org/web/packages/lme4/lme4.pdf).

  • Claeskens, G. and N. Hjort. 2008. Model Selection and Model Averaging. Cambridge: Cambridge University Press.Google Scholar

  • Efron, B. and R. J. Tibshirani. 1997. An Introduction to the Bootstrap. New York: Chapman and Hall. 450 pp.Google Scholar

  • FIS. 2014. Home Page of the International Ski Federation (FIS),Oberhofen/Thunersee,Switzerland. Retrieved April 2014 (http://www.fis-ski.com).

  • Pawitan, Y. 2001. In All Likelihood – Statistical Modelling and Inference using Likelihood. Oxford, UK: Clarendon Press.Google Scholar

  • R Development Core Team. 2009. R: a Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0 (http://www.R-project.org).

  • Schwarz, G. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics 6:461–464.CrossrefGoogle Scholar

  • Virmavirta, M. and J. Kivekäs. 2012. “The Effect of Wind on Jumping Distance in Ski Jumping–Fairness Assessed.” Sports Biomechanics 11:358–369.Web of ScienceCrossrefGoogle Scholar

  • Zuur, A., E. Ieno, N. Walker, A. Saveliev, and G. Smith. 2009. Mixed Effects Models and Extensions in Ecology with R. 1st ed. New York: Springer, 574 p., doi: 10.1007/978-0-387-87458-6.Google Scholar

About the article

Corresponding author: Magne Aldrin, Norwegian Computing Center, P.O. Box 114 Blindern, Oslo 0314, Norway; and University of Oslo – Department of Mathematics, P.O. Box 1053 Blindern, Oslo 0317, Norway, e-mail:

Published Online: 2015-10-13

Published in Print: 2015-12-01

Citation Information: Journal of Quantitative Analysis in Sports, Volume 11, Issue 4, Pages 231–245, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2015-0022.

Export Citation

©2015 by De Gruyter.Get Permission

Supplementary Article Materials

Comments (0)

Please log in or register to comment.
Log in