Plotting arrows on the target: Callaway 2012 study

The study checks whether the position of each arrow on the target can be recorded with a mouse click without losing accuracy compared with measuring it by hand. One archer shot 72 arrows at 70 metres on a 122 cm face, scoring 649; every hole was measured to the millimetre and every end photographed. Ten operators, who were not required to know anything about archery, then entered the arrows from the 12 photographs onto a target drawn on a computer.

The clicked coordinates followed the measured ones very closely: correlations with the measurement ranged from 0.977 to 0.996, and agreement between operators from 0.969 to 0.997. On average the error in distance from the centre was 0.74% of the target radius, under 1% for all ten. Operators tended to place arrows slightly closer to the centre horizontally and slightly further out vertically. On score, two operators put an arrow in the neighbouring ring, one of them three times and the other once. The three shooting statistics derived from the coordinates (two measures of accuracy and the mean radius of the group) also stayed close to those calculated from the measurements, with mean errors between 0.57% and 1.53%. The largest discrepancies involved two arrows, one of which was hidden in the photograph by the arrow next to it.

The shooting followed the FITA round at 70 metres, 12 ends of 6 arrows. Each end was photographed with a compact camera (a 12-megapixel Nikon Coolpix) placed square to the target, 80 cm away with the lens 130 cm above the ground and no zoom; then, as the arrows were pulled, the authors measured the coordinates of the centre of each hole to the millimetre. This measurement is the reference.

The software, written in Matlab, displayed a 122 cm face with the regulation rings: the operator clicked the position of each arrow with the mouse while looking at the photograph, in shooting order, and could zoom in on both the photograph and the target. The operators were 7 men and 3 women, mean age 29.5, with 4 minutes per end as in competition, which was always enough. Validity was estimated by correlating each operator's coordinates with the measured ones, axis by axis; agreement between operators with the intraclass correlation coefficient; error as mean difference, mean absolute error and root mean square error, and as a percentage of the target radius.

The sample that matters is small in two senses: a single archer, whose level and bow are not reported, and a single target photographed at close range in easy conditions. The operators were not required to know archery and each did the task only once, so there is no information on how consistent the same operator is over time. Input was by mouse on a computer, and the authors themselves warn that on a phone or tablet, with a finger, the result would need checking again. With several archers on one target and tight groups, overlapping arrows, already behind the largest errors here, would be more common.

Some of the figures need care. The tables give the errors in centimetres, but the values (6.92 mean absolute error, for instance) only match the percentages of the 61 cm radius if read as millimetres. In the table of coordinate errors the mean absolute error and the root mean square error are identical for every operator, which only happens if all the errors are the same size. The abstract swaps the two statistical tests relative to the method section, and the scoring errors are given as 0.3% and 0.15% in the results but as 4.1% and 1.3% in the discussion. The overall conclusion stands, but the exact values should be taken with a margin.

For an archer the question is simple: if I record where my arrows landed by clicking on a drawn target, can I rely on the data? According to this study, yes, at least when working from a good photograph with a mouse: the mean error is a few millimetres on a 122 cm face, far less than the width of a ring. This matters because a scorecard loses the shooting order and the position of the arrows, whereas coordinates make it possible to work out where the centre of the group is and how wide it is, and to compare them between equipment set-ups or between sessions.

Phone apps for plotting arrows do the same job, but with a finger and often standing in front of the boss: the study did not test them. Two observations apply there too: overlapping arrows are the main source of error, and a badly placed arrow can drag the following ones with it if the eye uses it as a reference. According to the authors, an archer plotting their own arrows at the target starts with an advantage over someone working from a photograph, because they can step closer and look at each hole.