Off-centre arrow groups and score: Park 2020 study

The study measures what an off-centre group costs, in other words a badly set sight, and tries to work out how much of the error an archer should correct after each end. In the author's model the loss grows roughly with the square of the group's offset: a group slightly off centre loses very little, one off by one or two rings loses a lot, and for the same offset the better archer, with the tighter group, loses more. To give an idea of group sizes, at 70 metres an archer at level 120 (the value the author associates with elite archers) averages 701.18 points over 72 arrows, with a group standard deviation of 38.3 mm; one at level 100 averages 661.07, with 66.0 mm.

For real competition, target faces were photographed, with World Archery's permission, after the 50 and 30 metre distances at a World Cup stage and at the 2013 World Championships. At the Shanghai stage, over 36 arrows at 50 metres, the average loss from off-centre groups was 2.34 points for recurve men, 2.92 for recurve women, 1.35 for compound men and 1.48 for compound women; the top 20 compound men gave away only 0.30 points on average, and the World Championships gave similar results. One example: a leading recurve archer at the same event shot 335 out of 360 with his group 25.9 mm low and left; centred, the same group would have scored 341, about 12 points more over 72 arrows. On average archers seem to centre their group to within about 60% of its size, with elite compound men the exception.

The second part deals with correction. The centre of a three-arrow end typically lies about 58% of the group size away from the group's real centre, and that of a six-arrow end about 41%: correcting the whole error of a single end means chasing chance. In the simulations the best result comes from moving the sight by only part of the error, with a factor between 0.2 and 0.6 depending on skill level and the initial error. Starting half a ring out and correcting with a factor of 0.2, the typical loss falls to about 1.3 points.

The group is modelled as round: each arrow's distance from the group centre follows a half-normal distribution, with a standard deviation that depends on an archer skill level index and on distance, and the angle is random. The index comes from a method Archery Australia has used since the mid-1970s and runs from about 30 for a beginner to about 120 for an elite archer. For each case 7,200,000 shots were simulated with a Monte Carlo method; the result differs from the direct calculation by less than 0.01 points over 72 arrows. The group offset is applied on the vertical axis, up to a group centred on the line between the 9 and the 8, two rings out.

For sight correction the model simulates the twelve ends of a qualification round starting from an initial error of zero, half, one or two rings (0, 30.5, 61 and 122 mm at 70 metres) and, after each end, moves the sight by a fraction of the observed error, from 0 (never) to 1 (the whole error). The real data come from photographs of the individual target faces used at 50 and 30 metres at two 2013 events, taken with World Archery's permission. The author adds an example from his own bows: with a sight screw of 24 turns per inch and 810 mm between peep and sight, on the compound at 50 metres one turn moves the arrow by 65.3 mm and one click by 6.5 mm.

Everything rests on an ideal group: round, with arrows evenly distributed, and with a single fault, a vertical offset. In reality a group can be oval, wind moves the centre during an event and archers change the sight for other reasons too; in the simulations the group centre moves only through the corrections. The correction-factor strategy has not been tried by any archer in competition: it is the output of a model.

The competition data come from two events in the same year, at 50 metres, and the paper does not say how many target faces were analysed. The author himself notes that these losses are probably underestimated, because archers were already correcting their sights during the distance. The explanation for why elite compound men centre so well (they know where the sight was when the release went, so every good shot tells them where the centre is) is the author's impression, not a measurement. Some percentages in the text on estimating the centre from 36 and 72 arrows do not match the formula used, and this page does not report them.

The study puts a number on something many archers only recognise afterwards, looking at the target face at the end of an event: at 50 metres, at a World Cup stage, recurve archers were giving away two or three points every 36 arrows through off-centre groups, points they could have had without shooting any better. The author reports that when shown a face with an offset group after a round, archers always say they would have corrected it, even when the face is their own: in hindsight it is easy, while shooting it is hard.

The most interesting point concerns how to correct. Three or six arrows are too few to know where the group centre is, and moving the sight by the whole error of one end means chasing chance; in the model a partial correction pays off better, larger in practice ends (the author suggests 0.5) and smaller in scoring ends (0.2 or 0.3). Turning that into clicks requires knowing how far one click of one's own sight moves the arrow at competition distance, which depends on the screw pitch and on the distance between eye, or peep, and sight. The model says nothing about how such a correction affects an archer's confidence or rhythm, and it has not been tested in competition.