Archer's foot position on the line: Park 2019 study

World Archery's rules require archers to shoot with their body above the shooting line, but they say nothing about the feet and do not require the archer to stand centrally. The author reads "body" as the torso: with a torso about 40 cm wide, the distance to the target can vary by about 20 cm forwards or backwards within the rules, so up to about 0.4 metres between the furthest-back and furthest-forward positions. The study calculates how many points that difference is worth.

Using the group model the author has used before, standing 0.2 metres closer gains on average between 0.25 and 0.42 points over 72 arrows outdoors, depending on division and level; standing 0.2 metres further back loses about the same, so the difference between the most forward and the most backward position is roughly double. The gain grows as the skill level falls. Set against the points separating one place from the next in qualification rankings, projected to the 2019 World Championships, it is worth between 44% and 74% of a place for the archers ranked 16th and 32nd. Indoors, at 18 metres over 60 arrows, the gain is larger in proportion, because 0.2 metres counts for more over a short distance: between 0.36 and 1.08 points, or between 61% and 168% of a place (the maximum for 32nd place in the men's compound, where places are 0.27 points apart).

There is also a finding for compound at 50 metres, where each archer has their own target face and the faces sit in two rows: with the boss tilted between 10 and 15 degrees, the upper face is about 10 cm further away, a disadvantage estimated at 30% to 35% of a ranking place. Photographs of 99 finalists at the Berlin World Cup stages of 2017 and 2018 show that 64% stood centrally over the line, 24% further back and only 12% forward.

The calculation uses the author's model in which the arrow group is centred on the target and each arrow's distance from the centre follows a normal distribution, with a standard deviation that depends on an archer skill level index and on distance. Levels from 60, a club archer, to 140, roughly the men's compound world record, were considered. For each level the model gives the expected score at 70 metres for recurve, at 50 metres for compound and at 18 metres indoors for both (with the smaller compound ten ring); the distance is then shortened and lengthened by 0.2 metres and the score recalculated.

To turn points into places, the author uses the trend lines for qualification scores published in an earlier paper of his, projected to the June 2019 World Championships, and for indoor the rankings from the 2017 Indoor World Cup stage in Nîmes. For 16th and 32nd place in each division he calculates the matching skill level, the points separating one place from the next and the gain as a percentage of a place. The photographs of foot positions were taken during the finals of the two Berlin stages (99 archers out of 110), without measurements.

This is a calculation, not a field test: no archer shot from different positions to see whether the score changes as predicted. The model moves the target by 0.2 metres and nothing else; it does not account for the fact that changing the foot position can change balance, shoulder alignment or the repeatability of the shot, which for many archers matter more than a few tenths of a point. The gains are averages over many events, since scores are whole numbers and ties are broken on tens and Xs.

The rules premise is also the author's reading: that "body" means the torso, and that part of the torso over the line is enough, is his interpretation of the text, not a position taken by World Archery, and the rules may have changed since 2019. The Berlin photographs are a small sample, as the author himself says, and only show how archers usually stand. The finding on the upper compound face depends on the tilt of the boss and the spacing between face centres, taken from the values in the rules.

The study puts a figure on an advantage that almost nobody uses: standing as far forward on the line as the rules allow is worth, in the model, a few tenths of a point over 72 arrows outdoors and up to about a point indoors. These are small numbers, but in qualification at major events places are less than a point apart (less than half a point in the men's divisions), and the author estimates that in many cases the shift is worth one ranking place on average. The gain is "free score", in the sense that it does not require shooting any better; the author notes that archers, when he raises it with them, consider it too small to bother with, because they are looking for changes that bring many points.

What the study does not say is whether a more forward position changes the way an archer shoots: someone who has built balance and alignment on a particular foot position gets no data here on what moving it would cost. The reading of the rules is also the author's own, and refers to the text he consulted in 2018. For compound at 50 metres there remains a simple matter of geometry: the lower face is about 10 cm closer than the upper one, though it is normally allocated by the organisers rather than chosen by the archer.