Anyone who has shot a few elimination matches knows the feeling: the fifth set ends, you look at the scoreboard, and it reads 5-5. From that moment a whole day's work comes down to one arrow each, and most archers experience it as bad luck that happened to them rather than to somebody else.
The calculation tells a different story. Five-all is a common outcome, and its frequency can be predicted; above all, though, it is selective, because it does not fall to just any pair of archers but to those who are alike. Knowing this changes how you read both the match you have just shot and the one you are preparing for, which is why it matters to the archer before it matters to the rulebook.
The figures that follow come from work I published in the Lab, where the calculation is set out at length and the code to redo it can be downloaded. It is a modelling calculation, not competition data; where competition data exist I bring them in, with a link to the registry entry that collects them.
Why a match finishes level so often
The reason lies in the way set points are awarded, and in particular in one consequence that tends to go unnoticed: a tied set is not a rare event at all. Even between two archers eighteen points apart over 72 arrows, a gap that is anything but negligible, a single set finishes level 23.4% of the time; the stronger archer wins it 56.3% of the time and loses it 20.3%.
Nearly one end in four, then, separates nobody, because each archer takes one point. And since five sets hand out ten set points in all, a single tied set, with the other four split two each, is enough to stop either archer reaching six and leave the match at 5-5. The same happens with three tied sets and the other two split one each, or with five tied sets.
Tied sets are common precisely because a set is short: with only three arrows each, the two set totals are often similar, and the difference between the two archers has little room to show. It follows directly from a format built on short sets.
How often it happens
The frequency can be calculated, and it depends almost entirely on how closely the two contenders resemble each other.
| Gap between the two archers | Set matches finishing five-all | Same pair, cumulative scoring |
|---|---|---|
| Identical archers (690 points) | 20.3%, one match in five | 13.5% |
| 10 points apart | 16.8% | 10.2% |
| 20 points apart | 10.8%, one match in ten | 5.6% |
Set against cumulative scoring, the format used for compound matches, the set system produces more ties at every gap, and the difference grows with the gap: between two identical archers the rate goes from 13.5% to 20.3%, half as many again, while at twenty points apart it goes from 5.6% to 10.8%, nearly twice as many. The increase comes from a scoring method that wipes out margins at the end of every set, so it is a property of the format, not a hidden flaw; I have written about the mechanism in the article on how the set system works.
Compound reaches the same situation by another route. It adds up the fifteen arrows instead of counting sets, but when the two totals are level the tie is settled there too with a single arrow: what changes is the frequency, which the table shows to be lower, not the nature of what happens next.
Across a whole competition
Figures for a single pair translate poorly into the experience of someone competing, who thinks in competitions rather than in probabilities. It makes more sense, then, to look at an Olympic bracket of 64 archers, played over 63 matches in six rounds.
In a typical field, with the top seed at 690 points, the expected number of shoot-offs is about 8.6 across the 63 matches, and across twelve differently composed fields it runs from a little under eight to a little over ten. The same bracket played with cumulative scoring would produce 4.7, a little over half as many: over a whole competition, where widely separated pairs count too, the set system does produce nearly twice as many shoot-offs.
Spread across the rounds, those shoot-offs fall like this: about 3.7 in the first round, 2.3 in the round of 32, 1.4 in the round of 16, 0.7 in the quarter-finals, 0.4 in the semi-finals and 0.2 in the gold-medal final. As a share of matches, a little over one first-round match in ten goes to a shoot-off, while the gold-medal final does so between 16.8% and 19.8% of the time, almost once in five.
The frequency, then, rises as the bracket advances, and the reason is the same one that sets five-all apart from every other situation a competition produces.
Five-all is not a neutral sample
The central point is that a shoot-off does not occur at random among the matches played, but in proportion to how closely the two contenders resemble each other. Every pair enters the shoot-off statistics with a weight equal to its own probability of finishing five-all, and that probability is highest precisely when the two archers are equivalent.
The effect is what statisticians call selection, and an analogy makes it clear. If we judged how reliable a scale is by looking only at the times it showed the same weight for two different objects, we would be looking at exactly the cases in which it told us least, and we would come away with a harsher view of it than it deserves. Five-all does the same thing: it presents us with the matches that the preceding fifteen arrows failed to decide.
In figures, 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. An independent check, done on the whole bracket rather than on the pairs of a field, gives practically the same interval, between 9.2 and 13.7 points.
To put that gap in physical terms, one point on a 72-arrow total is worth about seven tenths of a millimetre of group size, so twelve points of difference, the typical case for archers who end up in a shoot-off, come to a little over eight millimetres. On the target, these are two archers who look very much alike.
The filter is visible in the ten count
Put that way, selection is still only an argument. It becomes something visible if, instead of talking about probabilities, you look at a quantity anyone can count on a scorecard: how many tens each archer shot in the fifteen arrows of the match.
Take an archer at 688 points against one at 670, two archers with a real and measurable difference between them: across all the matches they shoot, their number of tens differs by three on average, and they shoot the same number in about one case in ten. Look only at the matches that ended five-all, however, and the average difference falls to one while the chance of an identical count rises to almost one case in three.
They are the same two archers, with the same difference in ability. All that changes is which of their matches you are looking at. Five-all selects precisely the occasions on which they shot almost indistinguishably, and you can read it straight off the count.
As a point of comparison, consider two genuinely equivalent archers, both at 690 points: across all their matches the difference in the number of tens is 2.1, and their counts match in one case in seven. The filter produced by five-all, in other words, makes two different archers more alike than two genuinely level archers are in an ordinary match, because finishing level means that across fifteen arrows the two produced almost identical profiles.
The bracket as a second filter
On top of the selection produced by five-all sits a second one, which acts along the bracket. Each round eliminates the weaker archers, so those left in resemble each other more and more, and the pairs that meet become progressively better matched.
The figure is stark: the mean gap between the two contenders goes from 15.2 points in the first round to 4.8 in the final. Across six rounds it shrinks by two thirds, and the almost five points of the final are worth a little over three millimetres of group size.
Taken together, the two filters explain why the frequency of shoot-offs climbs round by round, from 11.5% in the first round to 18.7% in the final: the further you go, the more alike the survivors are, and the likelier it becomes that five sets will not be enough to separate them. The bracket does what it is built to do, which is to carry the strongest archers forward, and the growing share of matches that finish five-all is a consequence of that.
For the same reason you might expect upsets to cluster between archers who are close in level. Competition data are less clear-cut here, and the registry treats the idea that upsets concentrate between archers of similar level as contested, because the study that set qualification alongside the brackets sees it in one competition and not in the other.
What the calculation does not look at
These numbers come from a model, and what the model leaves out should be stated precisely. No data on real people goes into the work: the archers at 690 or 678 are synthetic profiles defined by the width of their group, not anybody's scores. Everything comes from the target geometry laid down in the rules, the rules of the competition formats and a statistical model of shot dispersion.
The fields used for the bracket calculations are constructed on paper with just two declared dials, the mean level and how far apart the competitors are, which is why the bracket results should be read as ranges rather than as single numbers. When I write that the final goes to a shoot-off between 16.8% and 19.8% of the time, that range is the result, not an approximation of the result.
Finally, the calculation assumes that every arrow comes from the same distribution as the others, independently of the ones before it, and the essay names this assumption as its weakest point. Within sets, competition data show no effect of what is at stake: across 6,374 sets of international recurve head-to-head matches, the importance of the set does not on its own significantly change the score of the last arrow. On the shoot-off arrow there is a drop, though a small one: across 2,210 matches decided by a shoot-off between 2013 and 2019, drawn from 120 competitions ranging from World Championships to national events, the deciding arrow is worth 1.1% less than the same archer's average in the first set of the match. The registry collects the first finding under the entry on pressure in head-to-head matches and the second under the shoot-off score drop, which rests on a single study and is reported. That drop concerns the arrow that settles the tie, not the fifteen that produce it, so it has little bearing on the frequencies in this article.
How to make a shoot-off less likely
There is a reading of the same table that matters more to the archer than to the people who write the rules, and it lies in the direction in which the numbers move. The probability of finishing five-all falls as the gap grows: 20.3% between two equivalent archers, 16.8% at ten points apart, 10.8% at twenty. The gap works in both directions, since a clearly weaker archer also rarely reaches a shoot-off, and what interests the archer is the gap in their own favour.
In practical terms, the defence against a shoot-off is built beforehand, through level. Taking the figures in the table, which hold around 690 points, an archer who improves by ten points on the 72-arrow total cuts the probability of reaching five-all from 20.3% to 16.8% against an opponent who used to be level with them, and from 16.8% to 10.8% against one who was already ten points below. Against someone who was ten points above, the same improvement brings them level, and a shoot-off becomes more likely, not less.
None of this makes practising the shoot-off arrow pointless. If one match in five or six between close archers ends five-all, a season of elimination competitions can bring that arrow round several times, and it is better to arrive having already tried it, because it is the only competition shot taken under conditions that arise nowhere else. The calculation only shows where the larger margin lies: once two close archers reach five-all, the single arrow points to the more precise one just over 55 times in 100, while the level built beforehand decides how often it has to be shot at all.
As for what widens the gap, steadiness as such does not appear to be rewarded by the set format. In the Lab's calculation on the set system, with the same average score, the steady archer wins 45.4% of set matches against one who now and then puts an arrow well outside the group, and 48.5% under cumulative scoring. It is a modelling calculation, and the registry treats the idea that the set system rewards the more consistent archer as not studied. What moves results is the average level, meaning a tighter group, and the way there runs through repeatability of the shot.
A coach can do the sums directly with their athlete: how many matches last season were closed without a shoot-off, and how many finished five-all. The first figure shows how often the gap told before the end, the second how often the outcome was left to a single arrow, and both can be counted off a competition calendar.
How to read a shoot-off, won or lost
All of this has a consequence for the Monday after a competition, and that consequence is why these numbers are worth knowing.
In the model, losing a shoot-off to an opponent of very similar level happens almost half the time even when the tighter group is yours, because between two archers who get that far the deciding arrow comes very close to a coin toss: an archer who loses despite being the more precise of the two has lost a draw that was tilted, if only slightly, in their favour. Real matches add a nuance. In the same analysis of 2,210 matches decided by a shoot-off, each extra point of set average within the same match goes with a shoot-off score 7.3% higher, while position in the bracket adds nothing: the deciding arrow tends to go better for whoever was shooting better that day, not for whoever is the better archer overall. It is a single study, it measures the score of the arrow rather than who won the shoot-off, and the registry treats the idea that the shoot-off rewards the better archer as reported.
The reverse is less pleasant but holds just as well: an archer who wins a shoot-off has legitimately won a match, and nobody can take away the round, the medal or the result; what they have not won is proof that they are better than that opponent.
For both archers, the right way to see it is that a shoot-off exists to close the match, not to measure who is better: it decides who goes through when the format has no sets left to shoot, and it does so in a little over forty seconds. The misunderstanding begins when that closure is taken for a verdict, and it leads to a Monday of technical analysis on a shot that contains very little technical information.
Lower down the levels that arrow says even less. The figures in this article hold for a top-level field, and further down the geometry of the target works against the archer, because wide groups overlap far more than tight ones: two archers at 690 points shoot inside a cloud about four and a half centimetres wide, two at 650 inside one of a good seven centimetres. For the shoot-off to point to the more precise archer 60 times in 100, the gap has to be 12.5 points between two archers at 700, 14.8 between two at 690, 19.3 between two at 670 and 23.8 between two at 650. At regional level, then, a lost shoot-off says even less about an archer's ability than it does in an international final.
For coaches the practical upshot is clear: no training plan should change on the strength of a shoot-off result alone, which at most is one clue to set beside the video, the athlete's own feel and their record. The fifteen arrows that preceded it do contain material worth looking at, because they are fifteen executions rather than one.
Where this goes next
One question this article leaves open on purpose is how much that arrow is actually worth when the moment comes to shoot it. The answer depends precisely on the selection described here, and I have developed it in the article on what the shoot-off arrow decides.
The essay carries the full calculation of the frequencies, the distribution of shoot-offs round by round across twelve different fields, the robustness tests, and the code package with which anyone can redo the sums and check that the published numbers are the ones the calculation produces.