What predicts recurve scores: Spratford 2017

Thirty-nine international-level recurve archers, 23 men and 16 women from four countries with a mean age of 24.7, were measured in the days before a World Cup event. Each shot ten arrows at 70 metres while standing on a force platform, and for every shot the authors recorded the score, the arrow's flight time and the movement of the centre of pressure under the feet: for the second before release and the half second after it.

Of all the variables collected, a step-wise regression kept three: clicker reaction time, draw force and maximum sway speed. Together they account for 42% of the variation in the score of a single shot (F = 8.53, p < 0.001), through the equation score = 8.772 minus 15.955 times clicker time, plus 0.098 times draw force, minus 0.005 times maximum sway speed. Higher-scoring shots went with a faster reaction to the clicker, a heavier draw force and slower sway after release.

Group means were: draw force 24.55 kg, arrow length 644.4 mm, clicker reaction time 0.163 s, sway in the second before release 20.10 mm, sway in the half second after 48.03 mm, sway speed at release 159.87 mm/s, maximum sway speed 235.12 mm/s, flight time 1.24 s, mean score 8.25.

The three variables do not carry the same weight. Between the fastest and the slowest archer at the clicker there were 0.54 points, and between the lightest and the heaviest draw force 0.50 points: on these two measures the archers resembled one another, with a spread of about 10% in both cases. Maximum sway speed varied by 51% and was worth 1.20 points, more than the other two combined; holding clicker time and draw force at the group mean, the model puts 3.8 points between the slowest sway (99 mm/s) and the fastest (636 mm/s), from 8.1 down to 5.4. That maximum always occurs after the arrow has gone, but it is closely tied to the sway speed measured at release (r = 0.80).

The data come from a single session, in a purpose-built facility that allows archers to shoot from indoors at an outdoor target through adjustable windows. The archers warmed up to their usual routine and then shot ten consecutive arrows at 70 metres, with about a minute's rest between each.

The AMTI force platform, 900 by 600 mm, sampled at 1000 Hz from one second before release to half a second after; the signal was filtered with a low-pass Butterworth at 6 Hz, a cut-off chosen after residual analysis. The centre of pressure trace was split into a medial-lateral component, across the face of the target, and an anterior-posterior one, in line with the target; sway speed is simply the distance travelled divided by time.

Clicker reaction time is defined as the interval between the arrow head slipping over the clicker and the release. The click was picked up by a microphone close to the archer; the moment of release was identified on the platform from the exponential change in the moment about the x-axis, a pattern common to all the archers. A dedicated software package called ASHA synchronised the two signals and computed every variable on the spot, so that the archer and coach could see them immediately. Four cameras at 200 frames per second filmed from above, in front, behind and on the target; the target images gave the score and the arrow's flight time.

Draw force and arrow length were not measured: they are the values the archers reported before testing. All the variables went into a step-wise linear regression with the score of the shot as the dependent variable. At the time of testing the cohort had won two gold, five silver and eight bronze medals at international level between them; between the testing and publication they added a further 21, 23 and 25.

Ten arrows per archer, one session, one day. The study is a snapshot of an afternoon of testing rather than of competition: the shooting was done from indoors towards an outdoor target, with a minute's rest between arrows, which is a gentler setting than the shooting line. Draw force and arrow length are self-reported rather than measured, and draw force is one of the three variables in the model.

The regression pools every shot from every archer without separating the differences between archers from the differences between one arrow and the next for the same archer, and it does not allow for the fact that one person's ten shots are not independent of each other. The 42% accounted for means that most of what moves the score of a single arrow stays outside the model.

The most delicate point concerns sway. The maximum speed always occurs after the arrow has left the string, so it cannot have acted on that arrow; the authors read it as the sign of something already present beforehand, and support this with the correlation with sway speed at release (r = 0.80), but the study does not separate the two. The disagreement with an earlier paper, which found the opposite sign, is explained by the difference in instruments, a 1000 Hz force platform against a 15 Hz chest harness: a reasonable explanation, not a demonstration.

Finally, the paper's most quoted conclusion, that strength work for the shoulder girdle would help archers carry a heavier draw force and control the follow through, is a proposal for future research. No training was carried out or measured here. The registry record left the sample size and design blank: the study is cross-sectional and there are 39 participants.

The study puts numbers on three things that get talked about a great deal on the shooting line, and its most useful result is the comparison between them.

The clicker. On average 0.163 seconds pass between the click and the arrow leaving, and across all the archers that difference is worth barely half a point. The authors note that there is a limit to how far the interval can be shortened, since a decision still has to be made, and that below the lowest values seen in their data and in the literature (0.102 seconds) an archer may be anticipating the clicker rather than reacting to it.

Draw force. Between the lightest and the heaviest in the group there were 0.50 points, and the authors are the first to say that reading this as an argument for a heavier bow would be simplistic: the window between archers is narrow, the gain is small, and the drawing shoulder has to hold up for at least ninety arrows a day in competition. The advantage they see in draw force lies not in the score directly but in arrow speed, and so in how long the arrow is exposed to the wind.

Sway. This is the measure on which archers resemble one another least and the one worth most points, 1.20 across the range observed and 3.8 between the two extremes of the cohort. It is worth being precise about what was measured: not steadiness while aiming, but how fast the body moves after the arrow has gone, which in turn goes hand in hand with the speed at the moment of release.

It remains a description, not a recipe. The study did not try to change any of the three variables in any archer, so it says nothing about what would happen to the score if someone worked on them.