Competition distances in archery: Czyż 2016 study

The study asks whether competition distances are, for an archer, anything more than a point on the curve of their own score. Ten men and eight women shooting Olympic recurve each shot 30 arrows from around twenty distances, including the ones they have trained for years and many they had never shot. For each archer the authors then drew the line relating score to distance using only the untrained distances, and asked that line what score it predicted at the competition distances.

The answer is that the competition distances sit almost entirely on the line. Among the men, who compete at 30, 50, 70 and 90 metres, there is no difference between real and expected score at 50 metres or at 90; at 30 and 70 metres the difference is significant, but after correction for multiple comparisons, which brings the threshold to 0.012, only the one at 70 metres survives, with the real score above the expected one (p = 0.001, with a medium effect, Cohen's d of 0.50). Among the women, who compete at 30, 50, 60 and 70 metres, none of the four distances stands apart after correction: the only one significant beforehand was 50 metres, and there the real score was lower than expected.

The second check is on the shape of the curve. If heavily trained distances had an advantage, the relation between score and distance should bend precisely there. The lack-of-fit test says it does not bend: for the men the line across all distances is score equals 312.86 minus 1.3397 times the metres, with a coefficient of determination of 0.90, and for the women 294.55 minus 0.6018 times the metres, with 0.91. In practice, over 30 arrows, a man in this group lost about 1.3 points for every extra metre and a woman about 0.6. The mean total across the four competition distances was 948 points for the men and 1,054 for the women.

The authors conclude that an especial skill, meaning an advantage of one variant of a movement over the others in the same family, appears only after very specific practice limited to a single variant, and not after heavy practice on four. They explain the exception at 70 metres among the men by the Olympic format, which is shot at that distance alone, but present it as a hypothesis to be confirmed.

These are two separate experiments. In the first, ten men each shot 30 arrows from twenty distances, 600 arrows in all: the four competition distances (30, 50, 70 and 90 metres) and sixteen never trained (22, 26, 34, 38, 42, 46, 54, 58, 62, 66, 74, 78, 82, 86, 94 and 98 metres), spaced four metres apart. In the second, eight women each shot 30 arrows from eighteen distances, 540 arrows: the four competition distances (30, 50, 60 and 70) and fourteen never trained (22, 26, 34, 38, 42, 46, 52.5, 55, 57.5, 62.5, 65, 67.5, 72.5 and 75 metres), spaced four metres apart up to 50 and two and a half beyond. In both cases the 80 centimetre face was used at the shorter distances and the 122 centimetre face at the longer ones, with the change between 58 and 62 metres for the men and between 55 and 57.5 for the women, following the international federation's rules. Arrows were shot in blocks over three or four consecutive sessions to cut down the number of sight adjustments; a pilot on two archers, excluded from the analysis, had checked that the extra load was manageable.

The men were experienced archers recruited by email and through archery social platforms worldwide, because enough of them could not be gathered in one country: four from Poland, two from Peru and one each from Argentina, Colombia, Morocco and Mauritius. Among them were an academic world runner-up, a European championship medallist, five national champions, two national silver medallists and a regional champion; mean age 22.7 years, 5.2 years of practice, and 4,326 accumulated training hours by the study's estimate. Of the thirteen who agreed, ten completed: the others withdrew because shooting from distances not used in competition would have interfered with their training schedule.

The women were eight Poles, all national team members: two Olympians, one world championship bronze medallist, and all but one national champions; mean age 24.6 years, 10.4 years of practice, 13.5 hours a week, and 7,943 accumulated hours by the same estimate. The least decorated had been fourth at the Polish championships.

The score at each distance is the sum of the points of the 30 arrows. Accumulated hours were estimated by multiplying years of practice by 52 weeks and by the self-reported hours per week. The presence of an especial skill was tested with Keetch's method, that is by comparing the score expected from the line through the untrained distances with the real score in a one-tailed t test, and then with the F test for lack of fit on the regression computed across all distances. In Poland three master's students collected the data; archers in the other countries were sent the protocol, a prepared spreadsheet and a questionnaire on age, country, training habits, preferred distances and achievements by email, and returned their scores electronically.

The most delicate point is how the data were collected. The men's scores, apart from those of the four Poles, were reported by the archers themselves on a spreadsheet received by email, with nobody supervising. The authors say so and give it as the reason for running the second experiment, with women and with data collectors present. Even so, the exception at 70 metres, the study's only significant result, comes from the less controlled experiment.

Training hours are estimated too, not measured: years times 52 weeks times self-reported hours per week, a formula that ignores interruptions, injuries, periodisation and seasons. By that method one woman reaches 15,600 hours and another 2,912, and the two resulting lines are then compared as though the difference were one of accumulated experience.

The samples are ten and eight people, numbers that make any one-tailed comparison fragile and a correction for multiple comparisons unavoidable, raising the threshold to 0.012. That correction decides much of the conclusion: at 30 metres in the men and 50 in the women the difference is there beforehand and gone after. The lack-of-fit test in the first experiment also deserves a careful reading: its p value is 0.03, and the authors conclude in favour of linearity because they had set the threshold at 0.01.

The design carries two uncontrolled features. The first is the change of target face: moving from 80 to 122 centimetres between 58 and 62 metres creates a step in the relation between distance and score right in the middle of the range, and the linear model does not account for it. The second is the blocked order over three or four sessions: 600 extra arrows in a few days, with distances shot in sequence, mix the effect of distance with fatigue and with sight adjustment, and the order of the distances is not reported. Shooting conditions (wind, light, the range itself) are not described, and for outdoor shooting across a 76 metre span they matter.

Two minor inconsistencies in the text. The list of the men's countries in the body of the article adds up to nine archers and leaves out Morocco, which appears in the table. And for the women's regression the text first says the line accounts for 94 per cent of the variability and a few lines later 91: this record uses the second figure, the one given with the coefficient.

Finally the study's question belongs to motor learning, not performance: it says that competition distances are not privileged relative to the line, not that training them makes no difference. Nobody trained anything in this experiment, and the explanation of the 70 metres by the Olympic format is, in the authors' own words, speculation.

For an archer the most immediate result is not the one the study was looking for, but the line that comes out of it. Score falls steadily with distance, and the fall is quantified: over 30 arrows, about 1.3 points per metre for the men in this group and about 0.6 for the women, with the line accounting for ninety per cent of the variation. It is a steep, predictable curve: between 30 and 90 metres, for the men, that works out at about 80 points over 30 arrows.

The second result concerns the standing of the competition distances. Shooting for years at 30, 50, 70 and 90 metres had not made those four distances better than the archer's own curve already predicted: apart from 70 metres in the men, the competition scores fell on the line drawn from distances never shot. The authors read this as generalisation: practice on four variants builds a representation that works at the intermediate distances too, instead of digging four grooves. None of this says anything about how much to train the competition distances, because nobody in this study changed their training.

It also offers a way of looking at one's own shooting. If the score at an intermediate distance never trained sits where the archer's own curve places it, there is nothing to explain; if it sits well below, the difference is not about familiarity with that distance as such. The exception at 70 metres in the men remains curious, and the authors put it down to the Olympic format, where that is the only distance shot, but they state it as a hypothesis.