After five sets the board reads 5-5. The rules make no provision for a sixth set, so they call for one arrow: the two archers come back to the line, shoot one each, and whoever puts it closer to the centre wins. The match, the round and sometimes the medal are settled in a little over forty seconds and two shots.
Two views of this rule go round every range. For some it is a lottery, a coin toss with a little ceremony attached; for others the stronger archer comes through under pressure, and the better archer makes that shot better precisely because they are the better archer. A measuring instrument, though, can be asked something more precise than whether it is fair, namely how often it misleads, and that question has numerical answers.
There are two of them. The first comes from a calculation I published in the Lab, where it is set out in full with the code to reproduce it: in the situations where a shoot-off actually happens, that arrow points to the more precise of the two archers between 55% and 57% of the time, only a little better than a coin. The second comes from official competition results, where the shoot-off arrow scores on average slightly less than the arrows shot in the rest of the match. Together they show what that arrow really decides, and they help explain why it weighs more on the line than it counts on the scorecard.
The procedure, in full
In individual recurve a match is the best of five sets of three arrows. Each set is worth two points to whoever scores higher, one each if the two are level, and the match goes to whoever reaches six set points. The arrow total plays no part, because only sets count, and so the format produces an outcome that cumulative scoring could not: if after five sets the board reads 5-5 there is no way to carry on, and the rulebook has to switch to a different procedure.
It then calls for one arrow each and awards the win to whichever lands closer to the centre. Formally there are two criteria in sequence, first the score of the ring and then, on an equal ring, the distance from the centre. But for two arrows striking the scoring zone on a target made of concentric circles the two criteria always coincide, since an arrow closer in cannot end up in a lower-value ring. If the distance is identical too, the archers shoot again.
In international finals the archers shoot alternately, one at a time with twenty seconds per arrow, so a shoot-off amounts to two shots and a little over forty seconds on the clock, plus whatever time the judges need to measure. The procedure has changed over the years: for a while two tens forced a reshoot, and that provision is no longer in place. Compound works differently, because the match is cumulative over fifteen arrows, but there too a tie is settled with a single arrow. The reasoning about the single arrow therefore applies to both bows, while the numbers in the calculation are worked out for recurve, with the set system and the 122 cm face.
Nobody arrives at a shoot-off by accident
Before measuring how often that arrow misleads, there is one point to settle, because it changes how every later number should be read: shoot-offs do not happen between just any two archers, since getting there means having shot five sets without either managing to pull away from the other, and that route alone is already a filter.
The frequency shows it plainly: between two identical archers at 690 points a set match ends five-all in 20.3% of cases, which is one match in five. At ten points apart it falls to 16.8%, at twenty points to 10.8%. The more alike the two are, the likelier the contest is to reach that point, and that is why shoot-offs select similar pairs.
The practical result is that the mean gap between two archers who actually reach a shoot-off runs between nine and fourteen points over 72 arrows, depending on how the field is made up. So the two archers who meet in a shoot-off are not a pair drawn at random but a pair that the arrows already shot could not tell apart.
What a single arrow actually says
Before quantifying the error it helps to look at the mechanism, because it explains both why the rule works and why it achieves so little. An arrow landing near the centre is evidence in favour of the better archer, one landing far out is evidence against, and the strength of that evidence can be calculated point by point across the target.
Take an archer at 690 points against one at 670. An arrow planted one centimetre from the centre is 68% more likely to have come from the more precise of the two. One at twelve centimetres is two and a half times more likely to have come from the less precise, and a little past twelve and a half centimetres exactly three times more likely. Between those two extremes there is a point of indifference, around seven centimetres from the centre, where the arrow says nothing about which of the two shot it.
This leads to a property of the rule that runs against what its critics maintain: looking at who came closest to the centre is the best possible reading of that arrow taken on its own. No other way of interpreting that single shot would do better, because the probability that the evidence favours the better archer rises continuously as the arrow gets closer to the centre, so ranking by distance is precisely ranking by strength of evidence.
Measuring the distance, rather than reading the ring alone, also adds something: reading only the ring value and drawing lots on a tie would lower reliability by about two percentage points, and that is what the judges' measurement to the millimetre is worth.
The limit lies elsewhere, and it is quantitative before it is conceptual. An archer at 690 puts the arrow in the ten six times in ten, one at 650 three times in ten: the two groups overlap across most of their extent, and a single arrow drawn from two distributions that similar is not enough to say which of the two it came from.
How far apart they have to be for that arrow to notice
The question can be turned round into the one you would ask of a set of scales: what is the smallest difference the instrument can detect? Answering it takes a definition of "better", and the essay adopts a deliberately spare one, namely whoever groups tighter and nothing else, declared before any result was looked at, because defining the better archer as whoever won would make every rule infallible by construction.
With that definition the calculation fits in a single line: the probability that the shoot-off arrow points to the more precise archer depends only on the ratio between the widths of the two groups. The scale on which every answer is read has two fixed endpoints, 50%, which you get by tossing a coin without even looking at the target, and 100%.
| Reliability required | Gap needed (points over 72 arrows) | In group size |
|---|---|---|
| 55 times in 100 | 7.0 points | 4.7 mm |
| 60 times in 100 | 14.8 points | 10.0 mm |
The ten millimetres in the second row deserve a comment, because that is the distance between a top-level archer and a good one, not between two archers who are evenly matched. To reach sixty times in a hundred, a reliability nobody would call satisfactory, that arrow needs almost fifteen points of gap over 72 arrows.
Turned the other way round the picture is clearer still: between two archers five points apart over a full round, which is worth just under three and a half millimetres of group size, the shoot-off points to the more precise archer about fifty-four times in a hundred, only four percentage points better than a coin toss.
And the threshold gets worse as the level drops, for a geometric reason: wide groups overlap far more than tight ones, so the same relative difference becomes harder to read. Reaching 60% reliability takes 12.5 points of gap between archers at 700, 14.8 between archers at 690, 19.3 between archers at 670 and 23.8 between archers at 650. Anyone running a regional competition is therefore working with a blunter instrument than anyone running a world final.
The number that answers the question
Put the two things together, the resolution of the instrument and the fact that shoot-offs select similar pairs, and you get the answer to the original question. In the situations where it is actually called upon, the shoot-off points to the more precise of the two between 55% and 57% of the time.
The number becomes interesting when set against what would happen if shoot-offs took place between archers drawn at random from the field, without the filter of five sets shot level: the same rule would then point to the more precise archer between 57% and 61% of the time, and the whole difference between the two figures comes from the selection.
The resulting diagnosis runs against what you hear at the range: the shoot-off is close to a coin toss not because it reads the arrow badly, but because it is called upon exactly when the two archers are too alike for one arrow to tell them apart. The problem lies in the amount of information, not in the reading: the gap between the two archers is measured over 72 arrows, and the shoot-off has to pick it up with one.
On the bracket, where it matters most
The consequences show up best across a whole tournament: in a bracket of 64 archers, with 63 matches, the set format sends between eight and ten matches to a shoot-off, almost twice as many as cumulative scoring, which would stop at around five.
More interesting is how the two quantities move along the bracket, because they run in opposite directions. In the first round about 11.5% of matches finish in a shoot-off, and the share grows round by round to almost 19% in the final, because as the competition proceeds the archers who remain are more and more alike. Over the same span the reliability of the arrow falls: in the first round it points to the more precise archer between 57% and 61% of the time, in the final between 51.5% and 55.5%. The mean gap between the two contenders goes from fifteen points to five.
In practice about one final in five is decided by a single arrow, and there, of all places, that arrow points to the more precise archer a little over fifty-three times in a hundred, so the instrument becomes least reliable in exactly the round where the stakes are highest.
Why shooting more is not the shortcut it looks like
The proposal that occurs to everybody is to add arrows. It works, and it can be quantified: for a pair twelve points apart, one arrow points to the more precise archer 58% of the time, two arrows 62%, three arrows 65%. The first additions also pay off the most, because the second and third arrows are each worth more than any that follow, and between them they recover two fifths of the whole gain you would get by going up to nine. The cost in time is modest too: two extra arrows each in alternate shooting is four shots, a little over a minute.
The problem comes later, and it follows a familiar law: the precision of a repeated measurement grows as the square root of the number of trials. That is why going from one arrow to four multiplies the advantage by 2.13, going from four to sixteen multiplies it by 1.85, and going from sixteen to sixty-four only by 1.45. The returns diminish while the time grows linearly, and no reasonable number of arrows turns a shoot-off into a reliable instrument.
Pressure, put into numbers
The commonest objection to all of this is that the model does not account for pressure, and that a shoot-off arrow is not an arrow like the others. The objection is legitimate, and the essay meets it by quantifying it rather than dismissing it.
Pressure can be expressed as a temporary worsening of the group, measured in equivalent score points, and you can see how far it moves the result. For the typical pair twelve points apart, with no pressure the shoot-off points to the more precise archer 58.3% of the time; with a drop equivalent to ten points it falls to 56.5%, with twenty to 55.2%. Genuinely demolishing the instrument would take a great deal more: a drop of twenty-two points to get down to 55%, of seventy-eight to reach 52%, of a hundred and forty to touch 51%.
That last number shows the scale of it, because a drop of a hundred and forty points would mean an archer at 690 shooting, in that moment, like one at 550. As long as pressure affects the two contenders equally, then, it moves the result by a few percentage points and does not change the conclusion. If it affected them differently, that would be a case the calculation does not cover, and the essay lists it among its limitations.
What happens to that arrow in competition
The calculation treats pressure as an assumption, but in competition results it can be measured. An analysis of official World Archery results from 2013 to 2019 did so, across 2,210 recurve and compound matches decided by a shoot-off and 3,645 shoot-off arrows, comparing each archer with themselves within the same match. That arrow scores 1.1% less than the archer's average in the first set, about a tenth of a point on just over nine, and the drop survives trimming the lowest 5% of scores, so it does not hang on a few bad arrows. In the registry the claim that on the shoot-off arrow archers score less than in the rest of the match is reported: there is one study, but its design fits the question. Put into the model's currency, a tenth of a point per arrow over 72 arrows stays below the ten-point drop that takes the typical pair from 58.3% to 56.5%.
The same study also shows who shoots that arrow better. Each extra point of set average within the same match goes with a shoot-off score 7.3% higher, while the place in the bracket, at equal performance in the match, adds nothing. That is why the claim that the shoot-off arrow rewards the better archer is reported in the registry with a nuance that matters: it rewards whoever is shooting better that day, not whoever is the better archer in general, and the finding concerns the score of the arrow, not who won the shoot-off.
Nor does the drop show up in everyone. In men the shoot-off arrow falls on average from 9.25 in the first set to 9.167, a drop that holds up statistically; in women from 9.002 to 8.982, which cannot be told apart from chance. The claim that the drop on the shoot-off arrow shows up in men and not in women is reported, but it stops there: the test comparing the two drops directly falls short of significance, so it cannot be said that men drop more than women.
Competitions behind you do not help either, at least as far as these data can count them. At the same score in the rest of the match, doubling the number of matches already played goes with a shoot-off score 1.4% lower, mostly among women, while the number of shoot-offs already shot and age make no difference. The claim that archers with more competitions behind them do not shoot the shoot-off arrow better is reported and should be read for what it says: experience does not help, which is not the same as saying it makes the arrow worse, because the effect is small and experience is counted only over the matches in that database, not over a whole career.
That leaves the question that matters most to anyone who reaches the end of a tournament: whether the deciding arrow is shot worse where the stakes are highest. In the same study, at World Cups, World Championships and the Olympic Games the shoot-off scores 0.9% less than at continental and national events, but the drop belongs to the women and not the men, and within the same tournament quarter-finals, semi-finals and finals add nothing. A 2024 analysis of 6,374 recurve sets at three Olympic Games, a World Championships and a European Grand Prix finds instead that the last arrow of the set scores higher at the Olympics. It measures a different arrow, and neither study separates the importance of the event from the strength of the archers who reach it, so the claim that the more important the competition, the worse the decisive arrow is shot is contested in the registry. On the bracket, then, the final remains the round where the shoot-off knows least because of selection, and the competition data do not show that arrow being shot worse there than in earlier rounds.
Why that arrow weighs more than it counts
If the shoot-off is only a little better than a coin and that arrow scores a tenth of a point less than the others, it remains to be explained why archers on the line experience it as a moment apart. In interviews with eight archers from the South Korean Olympic squad about their relationship with the coach, the shoot-off comes up among the moments of psychological crisis, and several of them describe feeling anxious precisely there, or when their score is not going well. A measurement pointing the same way comes from the 2011 Asian Championships, where fifty-seven national-team recurve archers rated their anxiety a few minutes before each stage: cognitive anxiety, that is how worried they were, went from 3.67 out of nine before the qualification round to 5.21 before the individual matches and 5.05 before the team event, while the feeling of being keyed up stayed high and almost unchanged.
The registry reports both the claim that elite archers' anxiety rises from the ranking round to the matches, and stays high in the team event too, and the claim that head-to-head matches put more pressure on archers than the qualification round. Both share the same limit: it is one competition, at that championship the qualification round eliminated nobody, and the scores of the arrows were not analysed. More reported anxiety does not necessarily mean poorer arrows, either: in the competition data above the drop is a tenth of a point.
What turns worry into collapse is suggested by a single case, and it should be taken as one. A 44-year-old archer with a national ranking lost form precisely in the competitions she considered easiest, indoors, at short distances, in perfect conditions and against less experienced opponents, while outdoors, at long distances and against stronger archers she shot better. This story, reconstructed largely from her own account, is what the claim that an archer falls apart when they feel they have to win, not when the competition is hard rests on, and the registry rates it as reported. It has not been put to the test in a shoot-off, so what follows is my own reading rather than a finding: if what weighs is the duty to win, knowing that between two archers who reached five-all that arrow separates them only a little better than a coin takes away part of the ground that duty stands on.
What the calculation does not look at
The numbers in the calculation come from a model rather than from a collection of results: no data from real people goes into the essay, and the profiles at 690 or 678 are nobody's scores but synthetic archers defined by the width of their group. The calculation rests on three public, impersonal sources: the geometry of the target as fixed by the rules, the rules of the competition formats, and a statistical model of shot dispersion.
The definition of ability is spare by choice, and it leaves out nerve, reading the wind and the capacity to produce the right shot when it is needed, which are exactly the qualities that count most at the moment that arrow has to be shot. It remains a choice, although it has one virtue: a group can be measured, whereas the other qualities have no common yardstick.
The most serious limitation concerns the independence of the arrows. The calculation assumes that the shoot-off arrow comes from the same group as the others, whereas the competition data say it scores slightly less on average, and the essay identifies this as the most fragile point in the whole framework. The section on pressure is there to weigh it: with the same drop for both archers the answer moves only a little, and the drop measured in competition sits below the one the model has already tested.
On the shape of the group, by contrast, the result holds: across nine different shapes, from circular to off-centre or elongated, the band of results stays narrow and none of the shapes brings the shoot-off close to being reliable.
What to do with it, as an archer and as a coach
For the archer, the consequence is that a lost shoot-off is not a verdict on your technique. If you got there, it means that over the previous five sets neither you nor your opponent could pull clear, and in those conditions that arrow is close to a coin toss. Spending weeks analysing the single shot that decided a match means looking for a signal in data that does not contain it.
The reverse holds too, and it is the less welcome half: winning a shoot-off says little about the relative merit of the two archers. The right way to read either case is to look at the five sets that came before, where there are fifteen arrows and a great deal more information.
For coaches there is a consequence for preparation: if one match in five between equals finishes five-all, the shoot-off arrow is a recurring situation rather than an exception, and it pays to train it as part of the routine, with the same sequence used for every other shot. The reason is not that this arrow matters more than the others, but that it is the only arrow shot in conditions that never come up in practice.
Where this goes next
One question this article does not take on is the one the essay develops in full: whether better readings of that situation exist, and what they cost. Some require no extra arrow at all, because they use information already written on the scorecard, namely the fifteen arrows of the match just finished.
The wider picture this sits in concerns the way points are counted in a match, which I have described in the article on how the set system works, and the precision of the ranking that decides who meets whom, which I have written about in how many points it takes to say one archer is better than another.