Sideways string at release and score: Horsak 2011

The same archer and the same 56 shots as in an earlier paper by the authors, this time asking whether the string running off sideways after the release costs points. On the field it is taken for granted that it does. Here the relationship runs the other way: maximum lateral string deflection explains 18% of the variance in the scores, and with a positive sign, meaning that the arrows with more deflection are the ones that scored higher (F = 11.73; R = 0.426; R squared = 0.181; p = 0.001). Of the nine joint ranges across the three fingers, the only one that predicts deflection is that of the distal joint of the middle finger, and it predicts it poorly: an R squared of 0.109 with p = 0.014, negative in sign. One shot whose deflection lay more than three standard deviations from the mean was excluded.

The finger ranges confirm the picture from the other paper: 81 degrees in total for the index finger, 58 for the middle and 48 for the ring finger, with the knuckles almost still at between 6 and 9 degrees and most of the movement in the proximal and distal joints.

The new part is the calculation on variability. Splitting the shots into good (10 or the innermost ring, 12 arrows) and poor (8 or less, 18 arrows), aligning the middle finger's curves on the minimum of the proximal joint and measuring how far each curve departs from its group's mean, the difference appears in the metacarpophalangeal joint (t = -2.98; p = 0.006) and not in the other two (p = 0.122 and p = 0.545). The authors conclude that minimising lateral deflection is not the central problem for an expert archer, and that what counts is rather the ability to repeat the same movement. Among the possible explanations they put forward two things they did not measure: a compensation by the bow arm, which can correct a larger deflection, and small differences in stiffness between arrows.

The archer is from the Austrian B national team, aged 49, with six years of competitive recurve shooting, an indoor best of 1131 points out of 1200 and an outdoor best of 1233 out of 1400. He shot in three sessions, ten ends of three arrows each, at 18 metres on a 40 cm indoor triple face. Of the 90 shots filmed, 56 proved usable: in the others a marker was hidden from the cameras.

The system is a Vicon with eight infrared cameras, six at 1.3 and two at 4.0 megapixels, at 500 hertz, with the calculations performed on the raw data; accuracy, tested on two markers a known distance apart on a rigid object, stays within 0.2 mm. Twenty semicircular 9 mm markers were placed on the drawing hand and forearm, on the wrist, the metacarpal area and the joints of the index, middle and ring fingers, leaving out the thumb and little finger; flexion and extension angles are computed by the method of Cheng and Pearcy from a reference frame built on the hand. A 4 mm cylindrical marker was fixed to the string 7 cm below the nocking point.

The start and end of the movement were set from the velocity of the drawing wrist, when it drops to 0.1 metres per second at full draw and again in the follow-through. Lateral deflection is computed as follows: for every frame between the string leaving the fingers and the arrow leaving the string, the position of the marker on the string is projected onto the horizontal plane and its distance from the line joining the two end positions is measured; maximum deflection is the largest of those values. The analyses are stepwise multiple regressions, first to explain deflection from the nine joint ranges, then to explain the score. The same data, for the finger part, had already been presented at a conference in 2009.

One archer and 56 arrows, with the score of each arrow as the outcome: inside that score sits everything else in the shot, from aiming to tuning, and 18% of variance explained means that 82% lies elsewhere. A regression on one person does not transfer to other archers, and the stepwise selection of one predictor out of nine, on 56 observations, is a procedure that readily picks up chance; the link with the distal joint of the middle finger is called weak by the authors themselves.

The most concrete figure is missing: lateral deflection is never reported in millimetres, neither as a mean nor as a range. There is no telling whether the result is about two millimetres or two centimetres, and the regression is left without units. The analysis of variability finds its difference only in the joint that moves least, the metacarpophalangeal one, where a given departure counts for far more than in the others, and the two groups are of 12 and 18 arrows.

The authors flag what they take to be the main limitation themselves: there are no data on the orientation of the arrow relative to the target and to the bow along its flight, so the step from the string to the point of impact is left uncovered. And the two explanations they offer for the unexpected result, compensation by the bow arm and differences in stiffness between arrows, are not measured: they remain hypotheses. It should be added that the shooting took place in a laboratory, indoors, with twenty markers glued to the string hand, which is not the condition of a competition.

The idea that the string should leave the fingers as nearly as possible in the plane of the bow, with the least sideways movement, is among the most repeated when the release is taught. In this archer the arrows with more deflection scored slightly higher, not lower. That does not make deflection a virtue: 18% of variance in a single person is a thread, and the authors themselves think the bow arm or the arrow may lie behind it. What the result does is remove support for the opposite claim.

Read alongside the high-speed filming by Park and Logan, where only four of sixteen elite archers had the nock leaving the string on the bow's centre line, the picture that emerges is that the sideways movement of the string is normal and varies a great deal between archers, rather than a fault to be driven to zero.

The second pointer concerns variability. In the good arrows the movement of the middle finger repeated itself more closely than in the poor ones, and the measured difference sits in the knuckle, that is in the joint that moves least of all and is therefore also the easiest to keep still. It remains a measurement on one archer and on thirty arrows in all, and it says nothing about how that similarity is achieved.