Body measures and archery score: Musa 2018 study

A chapter from a book on the use of machine learning in sport. The authors measure height, weight, arm span and the circumferences of the abdomen, hip, thigh and calf in a group of archers, together with the score of six arrows shot after four practice arrows. They then apply a clustering algorithm, k-means with two clusters fixed in advance, which splits the archers into high and low potential, and test six variants of support vector machine to see how well a classifier recognises the two clusters.

The high potential cluster has higher values for the score and for every anthropometric measure except calf circumference. The linear variant of the classifier achieves the highest accuracy, 88 per cent, with a sensitivity of 100 per cent and a specificity of 60; the worst, with a fine Gaussian kernel, assigns every archer to the high potential cluster and has a specificity of zero. From this comes the chapter's conclusion: a bigger body goes with better shooting, and promising archers could be identified from their physical characteristics.

The chapter reports no correlation, no p value and no absolute value of any measurement, despite the word correlation in its title: the results are box plots and a table of classifier metrics.

The anthropometric measurements follow the ISAK protocol: height with a wall-mounted stadiometer, weight with an electronic scale, arm span and the circumferences of the calf, hip, thigh and abdomen with a tape measure. The score was collected before the anthropometric measurements: ten arrows in all, the first four as practice and the last six recorded. The shooting distance, the size of the target face, the type of bow and the conditions are not stated.

Clustering used k-means with two clusters decided in advance, minimising within-cluster variance with a Euclidean distance function, in Orange 3.11. The classifiers are six support vector machines with different kernels, linear, quadratic, cubic and three Gaussian variants, evaluated with fivefold cross-validation in MATLAB, reporting accuracy, sensitivity, specificity, precision, error and the Matthews correlation coefficient.

The flaw lies in the design of the analysis. The shooting score was used as one of the variables from which the algorithm forms the two clusters, so finding that the high potential cluster shoots better is not a result: it is the definition of the cluster. The classifier is then trained to recognise labels the algorithm built from those same variables, so the 88 per cent accuracy measures the internal consistency of that clustering, not any ability to predict the shooting of a new archer. The specificity of 60 per cent, with the kernel the authors chose, means that two archers in five from the low potential cluster ended up in the high one.

The chapter does not say how many people were measured. The metrics in the table are consistent with 50 archers, 35 in the high potential cluster and 15 in the other, but that is an inference from the numbers rather than a stated figure. Age, sex, level, discipline and years of practice are missing too, along with the values of the anthropometric measurements: there is no way to know whether the comparison is between adults and adolescents, between men and women or between different standards, and a difference in body size between two such groups could arise from any of those.

The closing part of the discussion rests on other papers rather than on these data: that larger people sway less in a static position, and that an endomorphic build goes with higher scores, are claims taken from earlier studies, one of them on the physical profile of basketball players. A book chapter does not go through a journal's peer review. The copyright page carries the year 2019, while the volume is registered under 2018.

The conclusion the chapter puts on its cover, that bigger people shoot better, does not hold up against the analysis that produced it, because the score sits inside the clustering that defines the two groups. For an archer there is nothing to take away about height, arm span or abdominal circumference.

The work stays in the registry for another reason: it is an example of how machine learning models are used to talk about talent in archery. An algorithm that splits a group in two, with the score among the variables, and a classifier that learns that split will always produce a high number, and that number says nothing about an archer who was not in the sample. It is the kind of claim to read closely when it arrives in the form of talent identification.