Control of the draw in archers: Azadjou 2023 study

Fourteen archers from the Polish national team and fourteen people who had never drawn a bow, seven men and seven women in each group, were filmed by nine cameras at 100 frames per second while performing a bow draw. For three points on the body, the bow hand, the drawing hand and the centre of mass, three quantities were computed: how wide a region of states the movement passes through, how far the movement tends to continue in the direction it has already taken, and how regular the signal is.

The first quantity, the volume of the convex hull of the phase portrait, gives 7.0 against 8.3 for the bow hand, 7.3 against 8.0 for the drawing hand and 6.3 against 11.2 for the centre of mass, with the professionals lower every time. The body of a national-team archer, during the draw, therefore passes through a narrower range of positions, velocities and accelerations, and the difference is nearly double at the centre of mass while at the hands it is about a sixth.

The second quantity, the Hurst exponent, gives 0.71 against 0.79 at the bow hand, 0.85 against 0.86 at the drawing hand and 0.82 against 0.86 at the centre of mass. All the values sit above 0.5, so every movement continues in the direction it has taken, but the professionals less than the beginners; the authors read this as more frequent and smaller corrections.

The third, sample entropy, gives 0.024 against 0.023 at the bow hand, 0.020 against 0.014 at the drawing hand and 0.035 against 0.025 at the centre of mass: the professionals' signals are less regular. Eight of the nine comparisons come out at p below 0.01; the one that does not is the bow hand's entropy. The professionals completed the movement in 4.2 seconds at most, the beginners in up to 9.7.

The recordings were made with nine Vicon cameras at 100 frames per second and 34 markers placed according to the full-body Plug-In-Gait scheme. The centre of mass is computed as the centroid of all body segments; each hand's position comes from a marker on the back of the hand, just below the head of the second metacarpal. The target was 5 metres away. The professionals performed two successful shots, the beginners one (two if the first was unusable) and never released: for safety they stopped at the aiming phase and let down, so the part compared is set-up, draw and aim.

The professionals drew between 36 and 40 pounds, the beginners 30, the limit the consulting coaches recommended for someone starting out. Before the recordings the beginners did no more than watch a professional archer perform the movement in silence, with no instruction, and for each person only the first attempt without occluded markers was analysed.

The signal processing is the decisive part. The three-dimensional trajectory of each body point was reduced to a single dimension by principal component analysis, in which the first component explains between 56.5 and 76.1% of the variance. The signals were resampled to 1,000 points, normalised on the maximum value and mean-centred, with every other signal reversed and a low-pass filter applied to avoid jumps; then the fourteen signals in each group were joined end to end into a single 14,000-point signal per group. On that single signal the phase portrait was reconstructed with an embedding dimension of three, and the convex hull volume, the Hurst exponent by rescaled range analysis and the sample entropy were computed. Significance comes from resampling: a thousand sets drawn from each group's single signal, then compared with t-tests.

The professionals had 11.1 years of practice plus or minus 7.9, the beginners none; age was 23.7 plus or minus 9.9 against 23.5 plus or minus 1.3, with height and mass practically identical between the groups.

There is no per-archer measurement. Each group is a single signal, obtained by joining the fourteen draws end to end, and the p-values come from resampling that signal a thousand times, not from twenty-eight independent people. The statistical comparison sets two curves against each other, not two populations, and the authors say so: comparing individual participants was not their aim. Anyone reading these numbers as a difference between two groups of archers is reading something the design did not measure.

The two groups did not do the same thing. The professionals shot; the beginners drew and let down without releasing. The target was 5 metres away and no score and no impact point were recorded, so nothing here is connected to accuracy. Only one attempt per person was analysed. Draw weights differed (36 to 40 against 30), as did everything else about the two groups: the comparison is between expertise and inexperience in general, not between two techniques. Sex was not analysed, and the authors leave it to later studies. Eye dominance, stabilisers and sight were not controlled for in the beginners, so as not to distract them.

The published text contains two internal contradictions. On sample entropy, the results paragraph says the professionals' values were smaller and reads that as less regularity, while the table shows larger values and the discussion reads larger values as less regularity. On the Hurst exponent, one and the same sentence opens by saying the professionals were more persistent and closes by saying they were less. This record follows the tables. And the comparison on the bow hand's entropy, 0.024 against 0.023, is the only one that does not reach p below 0.01.

The study says nothing about score, measures nothing after the release and does not compare a good archer with a better one: it compares national-team archers with people holding a bow for the first time. Those two groups separate on almost any measure, and the paper's stated contribution is something else: showing that mathematical tools developed for walking and running can also be applied to a movement that does not repeat cyclically, such as the draw.

What is left for an archer is one thing, and it sits in the centre of mass figures. The difference between the groups is largest not at the hands but at the body's centre, 6.3 against 11.2, while the two hands differ only slightly. Someone with eleven years of practice behind them moves the body less, more than they move the hands less. That is consistent with the line of work on postural stability and supports it from the side of dynamics.

The other two readings, that a lower Hurst exponent indicates continuous minute corrections and a higher entropy a less stereotyped movement, are interpretations of the mathematics rather than observations made on the archers. Nobody saw those corrections, and the paper's title, which speaks of finer and more fluid control, takes them as established further than the data allow.

For anyone filming their own shooting there is nothing usable here: these quantities need a marker system and a laboratory, and the group value cannot be computed for a single person.