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

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.