The best-matched trio of arrows

What is the trio worth against the full set?

The impacts of a shoot are split into two disjoint groups: the three chosen arrows on one side, all the others on the other. The trio is left out of the second group, otherwise it would partly be compared with itself. Each group is recentred on the target face, its impacts shifted by the vector that brings its centre to the middle, then rescored with the app’s scoring. The two average scores per arrow are compared.

Across the 1,215 sorts, the chosen trio scores 9.141 points per arrow against 8.592 for the rest of the set: +0.549 points per arrow (median +0.469, 95% interval +0.528 to +0.570). The gap between mean and median points to a distribution stretched upwards.

The interval gives the precision of the mean, not the spread between shoots, and it assumes independent sorts: they are not quite independent, as the Robustness section shows. The conversion to a full counted round is only made in the format actually shot, 60 arrows at 18 m and 72 beyond, and makes no sense on the total row, which mixes both.

How the trio is chosen

An arrow sort is a counted shoot in which every arrow carries its number. The impacts of each number then form their own cloud, whose centre and spread can be measured. The question is that of an archer who only takes three arrows: which ones, and for what gain?

Each arrow’s centre, the mean position of its impacts, is plotted on the target face, and coloured by its grouping size, the mean distance of its impacts from that centre. It reads the opposite way to a score: the smaller it is, the better the arrow.

The goal is a trio of arrows that group in the same place, each with a tight individual grouping. The two qualities need not be weighed against each other, because a single measure combines them: the grouping size of all the impacts of the three arrows around their common centre. That is exactly the cloud the archer would shoot with only those three: an off-centre arrow widens it, and so does a scattered one.

Every possible trio is tried: 151 per shoot on average, 120 at the median, 183,773 in total. A sort with six numbers offers only 20, one with twelve offers 220.

The method, in pictures

The arrow-sorting presentation video walks through the whole process: plotting the impacts, the arrow number, the centres and groupings, the search for the trio, the recentring, the recomputed score, then the gain by distance and by level.

Three examples to start with

Here are three real shoots. Each arrow sits on its centre and is coloured by its grouping size. Under each target, the best trio, then any trio whose gain stays within a tenth of a point per arrow of it: below that gap, naming a winner would be arbitrary. Each gain is computed against the rest of the set, recentring the impacts of the three chosen arrows on the face.

What does the rule keep, and what would another keep?

A good trio has two qualities: the three arrows land in the same place, and each groups well. The two middle rows show what each quality alone would give; the last one, what a random trio is worth. Everything is in centimetres, across the 1,215 sorts, and smaller is better.

Each quality on its own sacrifices the other; the single criterion is the only one that sacrifices neither.

How many sorts can be used?

The starting point is the 3,483 existing arrow sorts, that is, counted shoots in which every arrow carries a number. We keep those whose target face, bow type and plotting are usable. Each arrow number then needs at least 6 impacts, with at least 6 numbers and 60 impacts in total: below that, an arrow’s centre is indistinguishable from chance. Finally, shoots at a distance shared by fewer than 20 sorts are dropped: four shoots at 15, 20 and 25 metres, with nothing to compare them to.

That leaves 1,215 sorts, 34.9% of existing sorts, from 467 archers and 113,895 impacts. The last row shows what a rule twice as loose would let through.

What are the analysed sorts made of?

The size of a sort is not a detail: it sets the number of candidate trios, 20 for six numbers and 220 for twelve, and the size of the group the trio is compared with. With six numbers, the trio and the rest of the set weigh three arrows each; beyond that, the trio always weighs less. The control in the next section comes from this imbalance.

How many shoots, and how many archers, carry this gap?

The interval of the result assumes independent sorts. They are not: 1,215 sorts for 467 archers, and nothing stops an archer from sorting often. The “per archer” column redoes the calculation giving each archer one vote: their sorts are averaged first, then the archers are averaged.

The indoor figure moves by 24% depending on the weighting, from +0.381 to +0.471. And the chosen trio beats the rest of the set in 99.9% of shoots, and in all 374 shoots at 70 m. An equipment effect would leave some archers for whom it does not happen: a measure that never moves the other way is mechanical before it is physical.

How much of the gain is signal?

Three trios compared with the same rest of the set, over the same 1,215 sorts: the best, the one the rule keeps; the worst in the same ranking; and the average of all candidates in each shoot, which is a trio picked at random.

The third row measures the asymmetry between the two groups: as soon as a sort has more than six numbers, the trio weighs fewer impacts than the rest, its centre absorbs more chance, and that advantage is gained without any sorting having taken place. It cancels out by construction on the 262 six-number sorts, where both groups weigh three arrows each.

This control does not bound the selection bonus: keeping the best of 151 candidates is precisely what it removes by construction. Until the trio is chosen on some ends and scored on the others, +0.549 remains an upper bound, and nothing in the analysis says by how much.

Does the gain depend on the archer’s level?

A shoot’s level is its average per arrow before any recentring, scaled to the counted round actually shot: 60 arrows at 18 m, 72 at 70 m. The upper bands are narrower, where archers crowd together; whatever falls outside is grouped on one row rather than silently dropped.

Gap, in points per arrow

Share of the margin left up to 10

In points per arrow, the gap depends strongly on level: from +1.089 down to +0.474 at 70 m. But points per arrow are not a neutral unit: the score caps at 10, and an archer whose rest of the set already scores 9.7 has only 0.3 points left to gain, while an archer at 7.2 has 2.8. An upper band that gains fewer points has not benefited less from sorting: it simply had less left to take.

Measured against that margin, gap ÷ (10 − recentred score of the rest), the gap is flat at 70 m: 39.3%, 39.6%, 38.4% and 38.8% across four bands, while in points it ranges from +78 to +34 over the counted round. It is the unit that varies, not the effect.

Indoors, the same share rises from 35.9% to 54.6%. Two reasons not to read a level effect into it: the top band holds 140 shoots from only 14 archers, ten shoots per archer, and the rest of the set already scores 9.703 out of 10 there, a margin of 0.297 points so small that the share becomes unstable.

And these potential points remain upper bounds. In the 625–650 band at 70 m, the mean of +34.1 points has a median of +33.1, so it is not driven by outliers, but it breaks down exactly like a selection bonus: +40.4 points for shoots with fewer than 9 impacts per arrow, +34.1 for 9 to 12, +25.8 above 12. An archer at 640 out of 720 will not gain 34 points by sorting their arrows; that is what the best trio of a set is worth on paper when it is scored on the impacts that selected it.

Does the gain depend on distance?

Four distances carry enough shoots to be plotted: 18, 50, 60 and 70 metres. 30 m has only 27 and 40 m only 39: they stay in the table, with their counts, but off the chart. A point resting on so few shoots would suggest a bend that is only noise.

In points per arrow, the gap is almost twice as large at long range as indoors. But at 18 m the rest of the set already scores 8.994 out of 10: there was only one point left to take, against 1.771 at 70 m. Measured against that margin, the gradient disappears.

Distance is not assigned at random: 18 m is an indoor round on a 40 cm face, 70 m an outdoor round on a 122 cm face. The chart shows an association, not an effect of distance alone.

Ten real shoots, one per level

One shoot is drawn at random in each of the five score bands, at 18 m and then at 70 m: the ten examples cover the whole scale instead of piling up where archers are numerous, and we did not pick them. The only added constraint is readability: six to twelve numbers.

Each target shows the arrows’ centres, coloured by grouping size, with the chosen trio outlined thickly. Under each target, what the archer actually scored that day, then the trio’s gain over the rest of the set, scaled to the same round: 60 arrows indoors, 72 outdoors.

The gains range from +4.5 to +61.4 points depending on the shoot: the spread between shoots is larger than the average gain itself, and the order does not follow level. Shoot 8, at 601, shows +61.4 while shoot 9, at 647, shows +13.0: two shoots of similar level, a fivefold difference in gain. That is what “upper bound” means: the value of a single shoot depends first on the luck of its impacts.

The calculation redone step by step on one shoot

The shoot is the tenth example: 70 m, 122 cm face, 120 impacts from 11 numbered arrows. The first two rows cover all its arrows: as scored, then with the whole cloud recentred, the difference between the two only measuring how far off the sight was that day. The next three are the shoot’s three best trios, each recentred and rescored, against the rest of the set recentred and rescored on its own.

The “over 72 arrows” column makes the calculation easy to check: 696 for the trio against 668 for the rest of the set (9.278 × 72), which is the 28 points announced.

The two clouds the calculation compares

The impacts are split into two groups, and each group is shifted to bring its own centre to the middle of the face: what is drawn is the position after that shift, the one on which the points are recounted.

Two reading traps, because each target is drawn for itself: the zoom factor differs (×4.6 for the trio, ×2.2 for the rest), and the colour scale is recomputed on each group. The fair comparison remains the centimetres written under the targets.

What this number does not say

1. The trio is the best of 151 candidates on average, and it is scored on the very impacts that selected it: the published figure is an upper bound, not what a future sort will deliver. The “random trio” control does not bound it; it only measures the asymmetry between the two groups.
2. The two groups compared are disjoint, and compared as an average per arrow out of 10, never as totals: the trio weighs around thirty impacts, the rest of the set around sixty.
3. The conversion to a full counted round is a multiplication, made in the format actually shot: 60 arrows at 18 m, 72 beyond. It assumes that every arrow is shot in the conditions of the sort, whereas a real round has ends, fatigue and wind.
4. The unit of observation is the shoot, not the archer: 1,215 sorts for 467 archers, and an archer who sorts often counts as many times. Giving each archer one vote moves the result from +0.549 to +0.640, and 18 m from +0.381 to +0.471.
5. Distance is not assigned at random: 18 m is an indoor round on a 40 cm face, 70 m an outdoor round on 122 cm. Comparing two distances also means comparing two target faces and two seasons.
6. The gap in points depends mainly on what was left to gain. Measured against that margin, it is constant at 70 m, around 39% across four score bands. Indoors it seems to rise with level, but the top band holds 140 shoots from only 14 archers and a margin of 0.297 points: nothing there is conclusive.
7. Distances below 20 sorts leave the analysis entirely, those below 100 sorts only leave the chart: 30 m and 40 m count in the result but are not plotted.
8. Only 1,215 of the 3,483 existing arrow sorts make it through the funnel, 34.9%. Numbering your arrows and plotting every impact is the habit of a methodical archer; nothing says others would gain as much from sorting.
9. The measure compares two recentred clouds on the day of the sort: it assumes the archer re-sights on the cloud they shoot, and it says nothing about the wear of three arrows shot four times as often.
10. The grouping size used here reads the opposite way to the app’s “Grouping” column, which expresses the same idea in target-face zones: both rank arrows in the same order, but no value can be compared one-to-one.

Frequently asked questions

What is an arrow sort?

It is a session in which every arrow carries its number and every impact is plotted with that number. The impacts of each arrow then form a cloud whose centre and grouping size can be measured, which shows which arrows group well, and in the same place.

How many points does sorting your arrows gain?

Across 1,215 sorts from 467 archers, the best-matched trio scores on average 0.549 points per arrow more than the rest of the set: +22.9 points over 60 arrows at 18 m and +49.1 points over 72 arrows at 70 m. This is an upper bound, because the trio is scored on the impacts that selected it.

How do you pick your three best arrows?

By keeping the trio whose combined impacts are tightest around their common centre. This single measure combines the two qualities you want: arrows that land in the same place, and that each group well.

Does arrow sorting help good archers too?

In points, the gap falls with level, because there is less left to gain before the 10. Measured against that remaining margin, it is constant at 70 m, around 39% across four score bands: the drop in points comes from the unit, not from the effect.

Why call it an upper bound?

Because the trio is chosen from 151 candidates on average, then scored on the impacts that got it chosen. Part of the gain therefore comes from that selection. Measuring it would mean choosing the trio on some ends and scoring it on the others, which the analysis does not do.

Analysis computed on 2026-08-25 · Updated 2026-09-10