Follow-through and archery score: Hah 2008 study

Eight archers from the team of a Seoul university shot at 70 metres under Olympic Round conditions, filmed by seven infrared cameras, and the authors looked for which variable of the follow-through, that is, of the stretch from release to the end of the movement, went together with the score of the arrow.

Two variables had nothing to do with it. The vertical displacement of the bow, measured with a marker on the pressure button and summarised for each archer as a coefficient of variation (from 0.05 to 0.14, mean 0.08), bears no statistical relation to the mean score, which ran from 8.58 to 9.50 points per arrow. Nor did the angular excursion of the drawing shoulder: grouping arrows by score, that angle lay between 30.24 and 31.80 degrees, in other words much the same.

What changed was the speed at which that angle was covered. The mean angular velocity of the shoulder fell from 158.12 degrees per second in the 7-point arrows to 141.54 in the 8s, 118.98 in the 9s and 121.44 in the 10s, with an overall mean of 135.02 degrees per second and a standard deviation of 18.42. The regression line on these four values is y = -0.0637x + 17.074, with an R squared of 0.874 and an F of 13.919; the authors take it as significant at the 10 per cent level, and the higher scores clustered around 120 degrees per second. The graphs of velocity over time show something else: the lower the score, the larger the peak in angular velocity during the follow-through, while in the 9s and 10s the pattern is almost identical and free of peaks.

The archers were eight men from the archery team of a Seoul university, with at least eight years of practice (from 8 to 14, mean 11), averaging twenty years of age, 77 kilograms and 177 centimetres. Each shot four ends of three arrows, twelve arrows apiece, at 70 metres on a 122 centimetre face, after a warm-up of their own choosing. Equipment was not standardised: each archer used their own bow and arrows, because the movement is sensitive to changes of kit.

Filming used seven Qualisys ProReflex MCU-240 infrared cameras at 200 frames per second, with fourteen markers on shoulders, elbows, wrists, hips and hands, plus one on the pressure button of the bow to track its vertical displacement. The reference frame was set with an L-frame in front of the right foot and calibrated with a two-marker wand. The data were processed with the Qualisys software and filtered with a fourth-order Butterworth low-pass at 30 hertz, keeping five frames of margin either side of the stretch analysed.

One phase only was analysed, bounded by two events: release, defined as the instant when the string starts to leave the fingers while the shoulder rotates, and the end of the follow-through. Within that phase the authors measured two things, the vertical displacement of the bow in the sagittal plane and the angle between the trunk and the right upper arm in the horizontal plane, from which they derive the angular excursion and angular velocity of the shoulder. The score of the individual arrow is the link with performance; the regressions were computed on the means of the four score groups.

The regression that carries the whole study rests on four points, the means of the 7, 8, 9 and 10 groups, not on the 96 arrows filmed: with four values an R squared of 0.874 comes easily, and no confidence intervals are reported. Nor is the relation cleanly linear, since the mean velocity of the 10s (121.44 degrees per second) is higher than that of the 9s (118.98). There is also an inconsistency between figures: the cloud of individual arrows is densest between 90 and 110 degrees per second, where about 36 per cent of the shots sit, while every score-group mean lies above 118.

On significance, the text and the abstract print "p = 0.65" while claiming the 10 per cent level, which is contradictory: with those degrees of freedom the coherent value is about 0.065, and that is what this record reads. The arrow count does not add up in the paper either, which writes "8 archers by 12 shots = 72" where the shots are 96, the number of data points then used in the scatter plots.

The authors state four limits: they did not take individual physique, psychological and physiological factors into account; the sample is too small to generalise; during the experiment a westerly wind was blowing at 3.3 metres per second on average, enough to move arrows by itself; and the shoulder angles were measured in the horizontal plane only, so whatever the shoulder does in the other planes is missing. It should be added that the group is small and homogeneous, eight men from the same team, and that the closing reading (an archer at this level should slow the follow-through down, a world-class archer should speed it up) comes from a comparison with an earlier study by the same authors on a single athlete, measured over a different range of velocities. The text is in Korean, with the abstract and tables in English.

The study looks at the part of the shot usually considered already over, and finds that in that part it is not position that separates the good arrows but speed. In eight experienced archers the bow moved vertically in much the same way every time and the shoulder covered much the same arc, about 31 degrees, in the 7-point arrows as in the 10s: what changed was how quickly the shoulder went away after release, and how much of a peak its movement had.

For someone who shoots, this is a different way of watching their own video. In an archer whose technique is already stable, the difference between a good arrow and a less good one may not show up in the positions: it shows up as a snatch, an acceleration of the shoulder that the other shots do not have. The authors read that snatch as the sign of a release made with the arm and the fingers instead of with back tension, that is, as the effect of an imbalance between push and pull.

As for the number, 120 degrees per second is not a measurement to chase: it comes from four means, on eight archers from the same team, with wind, and the regression is significant only if one accepts the 10 per cent level. The registry keeps this study as an association on archers, not as a training target, and its sturdiest contribution is a negative one: the vertical displacement of the bow after release, in experienced archers, did not explain the scores.