Shot timing and recurve accuracy: Callaway 2016 study

Fifteen recurve archers each shot 30 arrows at 18 metres, 450 shots in all, and for every arrow fourteen timing variables plus the distance from the centre were measured. Taken together in a regression model, those variables account for 7.7 per cent of the variation in distance from the centre. The rest, more than nine tenths of it, stays outside.

The final model keeps five factors. Two point the expected way: the more the clicker-to-release time varies from one arrow to the next, the further from the centre the arrow lands, and the faster the arrow, the closer it lands. The third is the pre-shot time before the bow goes up: the longer it is, the worse the shot. The other two run against current intuition: a longer aiming time goes with an arrow closer to the centre (the simple correlation between aiming and distance from the centre is minus 0.117, p = 0.013), and a longer follow-through goes with an arrow further out.

The mean times across the fifteen archers show how long each piece of the shot lasts. The pre-shot phase, from touching the arrow in the quiver to the fingers being on the string, lasted 13.6 seconds on average, with a minimum of 5.9 and a maximum of 29.7. Then the set-up, from fingers on the string to the highest point of the bow arm, 2.2 seconds; the draw, up to the string touching the face, 2.5 seconds; aiming, up to the release, 3.5 seconds, ranging from 0.4 to 10.1. The time between the clicker falling and the release was 173 milliseconds on average, with a minimum of 99 and a maximum of 238 and a standard deviation of 24. The follow-through lasted 1.3 seconds. Mean arrow speed was 223 kilometres per hour, from 190 to 246.

How much those durations vary within the same archer is worth noting. Relative to their own mean, aiming varied by 24 per cent on average and the follow-through by 14, while the clicker-to-release time varied by only 6 per cent and arrow speed by half a percentage point.

The archers were 12 men and 3 women, mean age 41, with 19.6 years of practice on average and a self-reported FITA score of 1,182 out of 1,440: a mixed-level group, from university through county to national and international, with different coaches and clubs. They shot with their own equipment after their own warm-up, 10 ends of 3 arrows with no time limit, on a vertical three-spot 40 centimetre face at 18 metres, under controlled laboratory conditions.

The authors start from the observation that nobody in the literature defines the phases of the shot the same way, and that a phase is often confused with the event that starts it. Here the phases are defined by their trigger events: the pre-shot phase starts when the archer touches the arrow in the quiver and ends when the fingers are placed on the string; the set-up ends when the bow arm reaches its highest point, before the drawing hand moves back; the draw ends when the string touches the face; aiming ends when the string leaves the fingers; the clicker-to-release time runs from the sound of the clicker to the string leaving; and the follow-through ends when the archer first lowers either arm.

The phase times were read frame by frame by an expert from video shot with a Casio Exilim FH-25 at 210 frames per second, perpendicular to the shooting direction. The clicker-to-release time came from the audio, with an AKG microphone half a metre behind the archer at shoulder height pointing towards the bow, recorded at 24 bit and 96 kHz: the signal allows the click and the release to be located. Arrow speed comes from the same signal, as the time between the release and the sound of the impact on the target.

For each archer, out-of-range values in each phase were removed using a threshold on the residuals, and then for every shot the percentage variation relative to the mean of that archer's 30 arrows was calculated. The outcome of the shot is not the score but the straight-line distance from the centre, computed from the impact coordinates with Pythagoras, using a method the same author had already validated. The analysis is a stepwise multiple linear regression, with the residuals checked for homoscedasticity and a threshold of 0.05.

The limit is the result itself: a model accounting for 7.7 per cent of the variation leaves everything else out. The authors claim it as useful, since in performance any percentage gain counts, but it also means that phase durations are not enough to say where an arrow will go, and that a coach measuring only times would be working on a small part of the problem.

The sample is small and deliberately mixed: fifteen people, three of them women, a mean age of 41 and levels running from university to international. The variety is intentional, meant to show that Heller's result from a homogeneous group holds outside it, but it makes the model an average portrait of very different archers. The authors themselves note that with high-level archers only, arrow speed would probably drop out of the model, because draw weights would be more alike.

The statistics deserve a careful look. The 450 shots enter as independent observations although they come from fifteen people shooting thirty arrows each, and the paper does not account for that clustering; a stepwise regression, in turn, chooses its predictors from the data and so risks an optimistic estimate of fit. Of the model's five variables, three (speed, pre-shot time, aiming time) enter as absolute values and therefore carry between-archer differences with them, while only the variation in clicker-to-release time is normalised on the individual mean. In the text the follow-through coefficient is printed as 0.98, an impossible value next to the others, and is in all likelihood 0.098.

The most counterintuitive result, longer aiming bringing the arrow closer, contradicts at least two earlier studies, and the authors do not hide it: they offer as an explanation the habit of over-aiming at short distances, which at 18 metres would cost the archer the rhythm of the shot, and write that for this reason the work should be applied only to indoor shooting. That is a plausible explanation, not a test of one.

Finally, pre-shot time is the one variable with many observations lost to outlier removal (414 shots of 450), and the number of arrows per archer is low for estimating the individual variability of a phase that swings, like aiming, by a quarter of its own mean. The text read for this record is the author's archive copy, with table numbering incomplete in a couple of places.

The figure that stays with you is the relation between timings and outcome: it is small. Across 450 arrows at 18 metres, fourteen measures of duration and regularity accounted for less than a tenth of how far the arrow landed from the centre. Anyone timing their own shot is looking at something that matters, but little next to everything else.

Within that little, the variable that enters the model first is the consistency of the clicker-to-release time, not its length. It is not the delay itself that goes with an arrow further out, but the fact that it changes from one arrow to the next. The study does not explain why, and it tested no intervention: it says only that on shots where that time moved away from the archer's own mean, the arrow tended to land wider.

Two descriptive numbers are useful for comparison. The clicker-to-release time in this group averaged about 173 milliseconds, within a range from 99 to 238, and repeated with a variation of 6 per cent; aiming, by contrast, changed by 24 per cent. The most repeatable piece of the shot, in other words, is the shortest one, and the piece archers believe they control best is the most variable.

A caution sits inside the model itself. Arrow speed appears in it as a favourable factor, but the authors warn against reading that as an invitation to raise draw weight: in a mixed-level group, speed also picks up the difference in equipment between a university archer and an international one, and weight raised ahead of the body can cost precision and shoulders. They recall that speed can also be found through tiller, brace height, the number of strands in the string, the points and the release. As for longer aiming scoring better, it is the most fragile result: it holds for 18 metres, contradicts other work, and the authors themselves explain it by a loss of rhythm typical of short distances.