Joint coordination in recurve: Zhang 2024 study

Twenty-eight Chinese recurve archers across three administrative levels: eight international master athletes, that is the whole national squad preparing for Tokyo 2020, twelve of national first level and eight of national second level, from the provincial teams. Each shoots twelve valid arrows at thirty metres in an indoor facility, with eight infrared cameras at two hundred hertz and eighteen markers on the body plus three on the bow, for a total of 336 recorded shots.

The question is not how much a single joint moves but how the shoulder and the elbow of the drawing arm move relative to one another. The curve coupling the two angles, from raising the bow to the release, is decomposed by functional data analysis into three principal components that together explain 90.7 per cent of the variability between curves: the first accounts for 60 per cent, the second 19.2, the third 11.5.

Only the first component comes out related to level, with p reported as 0.03. According to the authors the international masters have a greater range of coupled movement in the first half of the draw and a smaller one in the second half and throughout the aiming, while the speeds of shoulder and elbow reach their peak together, in the early part of the draw, rather than at two separate moments. In the timings, the drawing phase lasts 2.1 ± 0.4 seconds in the masters, 2.2 ± 0.5 at first level and 2.5 ± 0.8 at second level, with a difference reported as p below 0.01; the duration of the aiming phase, 2.2 ± 1.3 against 2.4 ± 1.7 against 2.3 ± 1.6 seconds, does not separate the groups, and neither does the total duration.

The authors read this as the stronger archer coordinating shoulder and elbow synchronously rather than sequentially, because precision calls for synchrony and speed calls for sequence, and as anticipating the passage from the dynamic to the static. They connect it to an idea of Kisik Lee's, that the final part of the draw is a load transfer segment from the arms to the back, and argue that the stronger archers begin it earlier.

The loads of the first component, however, are -20.8 ± 130.2 in the masters, 2.9 ± 122.5 at first level and 26.2 ± 110.5 at second level: the standard deviations are four to five times the differences between the means.

The eight international masters are the entire Chinese national squad that trained between 2018 and 2020 for the Tokyo Games; the remaining twenty come from provincial teams. None had suffered an upper limb injury in the preceding six months. The three groups differ in other respects too: age 19.6 ± 3.8 against 17.4 ± 1.3 against 16.0 ± 1.3 years, draw weight 46.3 ± 4.8 against 42.1 ± 5.2 against 42.3 ± 4.2 pounds, years of practice 4.9 ± 2.0 against 3.5 ± 1.9 against 2.2 ± 0.8. Height and weight, on the other hand, are similar.

The article describes the participants as left-handed archers, specifying that they held the bow with the left arm and drew with the right. In the language of archery that is a right-handed archer, not a left-handed one; the fact of the matter is that they drew with the right arm, and this card reports it that way.

The usual indoor training facility, five minutes of warm-up in the same model of tight-fitting clothing for everyone, then eighteen reflective markers placed by a technician following Rab's upper limb model: vertex of the head, seventh cervical vertebra, sternum, sacrum, the two ear points, the two acromia, the two coracoid processes, the two radial styloids, the two ulnar styloids, the two third metacarpophalangeal heads and the two anterior superior iliac spines. Three further markers on the bow, above, below and in front. Eight infrared cameras at two hundred hertz for the kinematics, and a high-speed camera at one hundred hertz from the side to locate the instant of release.

Target at thirty metres. The coaches gave an immediate judgement on the quality of every shot, and a shot counts as valid when the quality of the movement meets the coach's criteria and the biomechanical parameters were captured in full: twelve valid shots per person, 336 in all. No score was recorded.

The cycle is split into two phases by three instants. The draw begins when the front of the bow reaches its highest point and ends at the bracing instant, defined as the first frame in which the lateral point of the right elbow moves less than half a millimetre forwards and backwards for at least five consecutive frames. The aiming phase runs from there to the release, that is to the moment the arrow leaves the string.

The three-dimensional angles are computed with Euler angles on a rigid body model. The sagittal plane angles of the shoulder and elbow on the drawing side are normalised to a length of one hundred; the series are fitted with one hundred and one fourth-order B-spline bases, with the smoothing parameter chosen as -1.5 by generalised cross validation. The functional principal components were kept where cumulative variance reaches 90 per cent and the eigenvalue exceeds 1, then rotated by the varimax method. One-way analysis of variance for the comparisons between levels, with a least significant difference post-hoc test and a threshold of 0.05, in SPSS 20.

The journal, Quality in Sport, is published by the Nicolaus Copernicus University in Toruń; on the article's front page the scientific disciplines assigned to it in the Polish ministerial evaluation are economics and finance, and management and quality sciences.

The p-values do not survive a comparison with the table they should come from, and this can be checked by hand. The loads of the first component are -20.8 ± 130.2 across eight masters, 2.9 ± 122.5 across twelve first-level archers and 26.2 ± 110.5 across eight second-level ones. An analysis of variance on those twenty-eight archers, with those means and those standard deviations, gives F equal to 0.30 on 2 and 25 degrees of freedom, that is p of about 0.74: no difference. The reported value, 0.03, is reproduced almost exactly, 0.029, only by treating the 336 shots as 336 independent observations, that is F equal to 3.59 on 2 and 333 degrees of freedom. But one archer's twelve shots are not twelve archers: counting them that way inflates the amount of information twelvefold and lowers the threshold in proportion. The same holds for the duration of the draw, where means of 2.1, 2.2 and 2.5 seconds with those standard deviations give F equal to 1.06 and p of about 0.36 across the twenty-eight archers, while the article's p below 0.01 is obtained only across the 336 shots.

The unit of analysis, then, is the thing to know before citing this study: at the level of the participants, which is the level at which the question is posed, neither of the two main results holds. What remains is the description, which is a different matter and stands on its own: the shoulder-elbow coupling curves of the masters have a recognisable shape, and the functional decomposition shows it well.

Level, moreover, is not separated from anything else. The three groups differ by three and a half years in age between the first and the third, by four pounds in draw weight, by more than double in years of practice. A difference in coordination between a nineteen-year-old drawing forty-six pounds for five years and a sixteen-year-old drawing forty-two for two may come from the age, the draw weight or the years, and none of these three was controlled for.

The shots were chosen by the coaches. A shot enters the data when the quality of the movement meets the coach's criteria: the selection therefore runs through the technical judgement of whoever coaches that group, not through a criterion common to all, and the discarded shot is precisely the one where the coordination was different. Since the outcome of the study is the shape of the coordination, filtering on the quality of the shape works directly on the outcome.

No score was collected. The levels are federal classifications, not measures of performance, so the study says that those ranked higher coordinate differently, not that such coordination produces a score. At thirty metres, in training, the scores were there and were not recorded.

The three components are described in the results in almost identical words. The first speaks of a smaller range in the first half of the draw, larger in the second and throughout the aiming; the third of a smaller range in the first half, larger in the second and smaller in the aiming; the second of a larger range in the first half, smaller in the second and smaller in the aiming. They differ by a single word, and what really tells them apart are the figures, which are also the only evidence for the interpretation given: a load vector superimposed on a coupling curve is not a number anyone can check.

Finally the editorial context. Quality in Sport is a regional venue, already marked as such in the registry, and on the article's front page the disciplines assigned to it in the Polish ministerial evaluation are economics, finance and management sciences: it is not a biomechanics journal. Twenty-eight days separate receipt from publication, with revision on 19 December and publication on the 20th.

The sample, it should be said, shares its data with the same authors' other article on shooting consistency, so in the registry the two count once.

The description this study gives of the movement is interesting and worth knowing, provided it is kept separate from the p-values, which do not hold.

The description is this: in the international masters the shoulder and the elbow of the drawing arm reach their peak speed together, in the early part of the draw, and in the second half the coupled movement reduces; in the other two groups the speed has two peaks, one in the first half and one in the second. Put in the terms of a shooting hall: the stronger archer carries with the whole arm from the start and slows down in the final part, instead of arriving at the face with a second push. The authors read that slowing as the handover from the arms to the back, and set it alongside Kisik Lee's idea that the last part of the draw is a load transfer segment. That is a reasonable pairing of a curve with a teaching, not a test of that teaching.

What this study does not allow anyone to say covers everything else. The differences between the three levels, across the twenty-eight archers who are the right unit, are not statistically distinguishable: the loads of the first component have standard deviations four to five times larger than the distances between the means, and an analysis of variance on those numbers gives p of about 0.74. The very value of 0.03 the article reports is obtained only by counting each archer's twelve shots as twelve archers. So the shape of the masters' coordination can be described; saying that it separates the levels cannot.

Nor does the duration of the draw separate them: the masters' 2.1 seconds against the second level's 2.5 are inside the noise, with the same counting problem. It is worth noting that on this point the authors reach a cautious conclusion that is useful anyway: that the quick rhythm of the stronger archers is a consequence of their capacity to anticipate rather than something to insist on in training. That sentence remains a sensible hypothesis.

And there is no score: the three levels are federal categories, the shots were selected by the coaches on the quality of the movement, and the value of the arrows was not recorded. The registry keeps this work as a description of the coordination between shoulder and elbow in high-level archers, with a note that the comparisons between levels do not hold at the correct unit of analysis, and not as evidence that synchronous coordination produces a score.