Are all goals equal?

Among the statistics frequently taken in any sport are goal-scoring stats. Whether goal kicking in rugby or shooting a goal in netball, goal-scoring players are given a percentage rating based on a hit or miss system.

However, a paper by two New Zealand sports scientists, Dr Kenneth Quarrie and Professor Will Hopkins, from AUT’s Sport Performance Research Institute, argues that goal scoring success is more than just hit or miss.

In a study examining IRB rugby matches, the pair point out that straight hit-miss measures do not account for factors such as the relative difficulty of kicking from different parts of the field, environmental effects or that some kickers are typically called upon for easier or more difficult kicks. When these factors are accounted for, player goal kicking rankings can change.

“There are … players for whom raw kicking percentage provides a distorted picture of their true ability. This is the case especially for those players who attempt either much more difficult or much easier kicks than is the norm,” write the researchers in their published paper.

The same could also be argued for netball, where the goal shoot will typically have the higher scoring percentage but takes most of their shots from directly under the post. Compare this to the goal attack, who is usually expected to either promote the ball to the goal shoot or, if circumstances dictate, take the more difficult shot from further out in the circle. Ranking the shooting statistics of the two players to determine their relative shooting abilities is likely to be similarly misleading.

In the rugby study, the pair developed a generalised linear mixed model to analyse 6,769 goal-kick attempts (2,967 conversions and 3,802 penalties) in 582 international rugby matches played from 2002 to 2011. The model adjusted for kick distance, kick angle, a rating of the importance of each kick (the likelihood that the outcome of the kick would affect the outcome of the match) and venue-related conditions, which can have a random effect on success.

“Wellington, New Zealand, is renowned as an exceptionally windy city, and the fact that the success rate at Westpac Stadium in Wellington was the lowest of any stadium [in the study] probably reflects that kickers find it difficult to adapt to the atmospheric conditions at the venue.”

The researchers reported that 72% of the 6,769 kick attempts were successful. “Forty-five percent of points scored during the matches resulted from goal kicks, and in 5.7% of the matches, the result of the match hinged on the outcome of a kick attempt. There was an extremely large decrease in success with increasing distance … and a small decrease with increasingly acute angle away from the mid-line of the goal posts.”

The pair concluded that their generalised linear mixed model with its random-effect solutions provides a better tool for ranking the performance of goal kickers in rugby. “This modelling approach could be applied to other performance indicators in rugby and in other sports in which discrete outcomes are measured repeatedly on players or teams.”

The research was published online ahead of print on 4 March 2014 in the international Journal of Science and Medicine in Sport.