Arrow groups widen more than in proportion to distance

9 studies · 183 archers measured

Each circle is a study: its position gives the year, its row whether it is for, against or context, its size how many participants it measured. Light circles are studies on other populations or without archers.

Two papers by the same researcher answer the question by reading competition scores. The first, on two major international competitions in 2013, finds that at seventy metres on the 122 cm face archers score as they do at fifty metres on the 80 cm face, whereas if the group grew in proportion to distance the equivalence would fall at seventy-six metres; and the gap between the two distances grows with the archer's level, which is the opposite of what you would expect if the angular error always stayed the same. The second finds the same equivalence at five world-level competitions with little wind between 2007 and 2009 and turns it into a model: at seventy metres about three quarters of the points lost come from errors that grow in step with distance and a quarter from errors that grow with its square, among them the wind, whose drift grows in exactly that way according to ballistic models. Two limits remain. Everything goes through scores, which mix up how wide the group is with where its centre sits, and the one study that measured group width at several distances, on eight archers, describes the relationship as not significant. And the share that grows with the square is fixed by a calibration the author chose, not derived from the coordinates of the impacts.

Also phrased as: "the group opens in proportion to distance"; "group at 18 and at 70 metres"; "constant angular error"; "group width and distance"; "how much the group widens with distance"

In practice

It is often said that the group opens out like a fan, in proportion to distance, and that from a group at eighteen metres you can predict the one at seventy.

Evidence

1966
Context Archers Published later

58 university students who were beginners: from ten to twenty yards the mean score falls by about 58 points out of 216, and between twenty, twenty-five, thirty and forty yards by about twenty points at each step, even when the step is only five yards; the effect of distance is significant at p < 0.01. It measures points, not group width.

Transfer Effects and Ultimate Success in Archery due to Degree of Difficulty of the Initial Learning · Robert N. Singer
1990
Context Archers Published later

8 experienced archers shooting from eighteen to ninety metres: the relationship between distance and group precision is inverse, that is the group widens as the archer moves back, but the authors describe it as not significant and do not set it against distance. It is the only study that looks at group width at several distances.

Muscular Activity of Different Shooting Distances, Different Release Techniques, and Different Performance Levels, with and without Stabilizers, in Target Archery · J.P. Clarys, J. Cabri, E. Bollens, R. Sleeckx, J. Taeymans, M. Vermeiren, et al.
2011
For Model Published later

Ballistic model of an Easton Protour 470 arrow launched from a compound bow at 79.2 m/s, in a side wind of 1 and 3 m/s: drift grows roughly with the square of distance and linearly with wind speed, so that at 90 m it is 62 per cent larger than at 70 m. It says that at least one source of spread, the wind, grows faster than distance; it measures no archers' groups and says nothing about calm days.

Minimizing wind drift of an arrow · J L Park
2014
For Archers Published later

An analysis of elite recurve archers' scores at two major international competitions: at seventy metres on the 122 cm face the scores resemble those at fifty metres on the 80 cm face, whereas if the group grew in proportion to distance the equivalence would fall at seventy-six metres. The difference between fifty and seventy metres grows with the archer's level.

Analysis of scores and arrow grouping at major international archery competitions · James L Park, James E Larven
2014
For Archers Published later

Qualification scores of men's compound and recurve archers at five world-level competitions with little wind, between 2007 and 2009, read distance by distance: in light wind archers score almost the same at 70 m on the 122 cm face as at 50 m on the 80 cm face (a difference of 2.1 points over 36 arrows in compound at the 2009 World Championships, 0.6 in recurve at the 2007 World Championships). To reproduce these scores the model has to give the group a component that grows with the square of distance, which accounts for 24.1 per cent of the points lost at 70 m and 18.5 per cent at 50 m, and with that correction it predicts scores by distance to within about a point. The split, though, is fixed by requiring the two distances to give the same score at a level the author chose, and in his theoretical classification only wind and sideways bow cant grow with the square of distance. It is the same researcher as the analysis of the 2013 competitions, working on different competitions.

Modelling archers’ scores at different distances to quantify score loss due to equipment selection and technique errors · James L Park
2016
Context Archers Published later

10 male and 8 female experienced recurve archers, thirty arrows from twenty distances for the men and eighteen for the women: the score falls in a straight line with distance (men R² = 0.90, women R² = 0.91), with no jumps at the competition distances. It says there are no shortcuts tied to the distances trained, but it measures points and not millimetres.

Specificity vs. Generalizability: Emergence of Especial Skills in Classical Archery · Stanisław H. Czyż, Sarah J. Moss
2019
Context Model Published later

A scoring model used to estimate how much foot position on the shooting line matters: the expected score as a function of level is almost identical for recurve at 70 m and compound at 50 m, while indoors the two curves part because of the smaller compound ten. The outdoor match is built into the model, which is calibrated on that very equivalence, so it is not a new measurement.

Optimising an archer’s foot position to obtain a competitive advantage · James L Park
2020
For Model Published later

A dynamic model of an arrow's flight in wind, which also takes shaft flex into account: the author concludes that drift increases with the square of the distance to the target. It confirms with a fuller model what the 2011 calculation said about side wind, with no archers and no measured groups.

The dynamic behaviour of an arrow in wind · James L Park
2020
Context Model Published later

In the Archery Australia scoring model an archer scoring about 700 has a group with a standard deviation of 38.3 mm at 70 m on the 122 cm face and 25.6 mm at 50 m on the 80 cm face: the ratio between them is about 1.5, while the ratio between the distances is 1.4. The group grows faster than distance because the model is built that way, with a small extra allowance for the extra metres: it is an assumption built in, not a finding.

The impact of off-centred groups on an archer’s score · James L Park

Status history

1966 Not studied The first study in the bibliography to change distance measures how far the score falls, not how far the group widens: in beginners, from ten to twenty yards the average loses about 58 points out of 216, and then about twenty points at each step, even for only five yards. It says that moving back costs, and costs quickly, but the score confuses the spread with the shift of the group's centre: the question is left without a measurement.
1990 Not studied Eight experienced archers shoot from eighteen to ninety metres and the group widens with distance, but the authors themselves describe the relationship as not significant and say nothing about proportion. The question is asked, the answer is not given.
2011 Transferred The first argument in favour comes from a ballistic model, not from archers: in a side wind an arrow's drift grows roughly with the square of distance, and at 90 metres it is 62 per cent larger than at 70. If the wind widens the group, it widens it faster than the distance; but no study has yet measured real groups at several distances, and the claim rests on the calculation alone.
2014 Reported An analysis of the scores at two major international competitions in 2013 gives the first answer from archers: at seventy metres on the 122 cm face archers score as they do at fifty metres on the 80 cm face, whereas with proportional growth the equivalence would fall at seventy-six metres, and the gap between the two distances grows with the archer's level. The same year the same researcher finds the equivalence again at five world-level competitions with little wind between 2007 and 2009, and builds from it a model in which about a quarter of the points lost at seventy metres come from errors that grow with the square of distance. The two readings agree, but they come from the same author, both go through competition scores, and in the second paper the quadratic share is fixed by a calibration the author chose: the evidence in favour is there and it is limited, so reported.
2016 Reported Across twenty distances the score of experienced archers falls in a straight line, with no jumps at the competition distances. It is a result that does not settle the proportion of the group's width, because it measures points and not millimetres, and the status still hangs on the two papers of 2014, by the same author and both drawn from competition scores.
2020 Reported Between 2019 and 2020 three new papers by the same researcher stay at the level of models. A dynamic model of flight in wind repeats that drift grows with the square of distance; the Archery Australia scoring model gives an archer scoring about 700 a group of 38.3 millimetres at seventy metres and 25.6 at fifty, a ratio of 1.5 against 1.4 for the distances, but that is an assumption built into the model; and the score curves for recurve at seventy metres and compound at fifty coincide because the model is calibrated that way. No new measurement on archers: the status stays reported.

Related studies

Theoretical workIl pavimento (The floor): how much of archery is real

Research lines

Studies describe groups of archers, and your own numbers show how far the finding applies to your shooting.

See the full assessment

Cite

APA

Campagna, M. (2026). Arrow groups widen more than in proportion to distance (Version 2). In Evidence Registry. Retrieved 16 October 2026, from https://matteocampagna.com/en/registry/competition/groups-widen-faster-than-distance

BibTeX

@misc{campagna2026_gruppoproporzionaledistanza,
  author = {Campagna, Matteo},
  title = {Arrow groups widen more than in proportion to distance},
  year = {2026},
  howpublished = {Evidence Registry, matteocampagna.com},
  url = {https://matteocampagna.com/en/registry/competition/groups-widen-faster-than-distance},
  note = {Version 2; accessed 2026-10-16}
}

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