Archers choking in shoot-offs: Bucciol 2020 study

Two economists collected from the World Archery website the results of 120 competitions held between 2013 and 2019, adult recurve and compound, and looked at every head-to-head match that went to a shoot-off. The final sample contains 3,645 shoot-off arrows, shot by archers who appear at least twice in the data (4.76 observations each on average); 74% come from recurve, 43% are women and the mean age is about 26.

The shoot-off arrow scores 9.088 on average, against 9.148 for the mean of the ends in the same match. Allowing for the archer and the match, the shoot-off score is 1.1% lower than in the first end (p < 0.001), while the differences from one end to the next are minimal. The drop is mainly among men, from 9.25 in the first end to 9.167 in the shoot-off; among women it goes from 9.002 to 8.982, a difference that is not significant. The gap between the two drops, however, is not significant either (p = 0.064).

Comparing shoot-offs with one another, those shot at World Cup events, World Championships and the 2016 Olympics score 0.9% lower than those at less important competitions. Split by sex, the effect is significant only among women (2.3% lower) and not among men. Finals, semi-finals and quarter-finals, on the other hand, do not change the shoot-off score compared with earlier rounds. Each extra point in the mean end score goes with about 7.3% more in the shoot-off; having twice as many matches behind you goes with a shoot-off score 1.4% lower; women shooting at home score 2.7% more, and those who reach the shoot-off by winning the fifth end score 1.8% more.

The data come from the World Archery results pages, downloaded in December 2019: for each match, the score of every arrow or every end, the shoot-off, the type of competition, the round, the two archers' seeds, age and country. Junior, master and para-archery divisions are excluded, and when a match had more than one shoot-off arrow only the first counts. Of the roughly 2,210 matches that went to a shoot-off, 3,645 observations remain once only archers with at least two appearances are kept and 38 incomplete rows are removed.

The first comparison sets the shoot-off beside the five ends of the same match, with a regression on the logarithm of the mean score and fixed effects for archer and match. The second explains the shoot-off score by type of competition, round and their combinations, using a Poisson model (PPML) with archer fixed effects, which compares each archer with himself or herself across different shoot-offs. The controls are the mean end score, the difference in seeding, the bow division, age, competing at home, the country's world ranking points, experience, continent and a time trend. The robustness checks repeat the analyses with the median end score, with a linear model and without the lowest 5% of shoot-off scores.

The effects are small: 1.1% of 9.15 points is about a tenth of a point per arrow, and the shoot-off is a single arrow compared with the mean of three. Integer scores cluster heavily on 9 and 10, so a few very low shoot-offs can carry weight; the authors remove them in one of the checks and the results hold, but a ring score cannot show how far the arrow landed from the centre. Pressure itself is not measured but inferred from the situation: the shoot-off comes after fifteen arrows, with different timing and rhythm from the ends, and the authors discuss fatigue without being able to rule it out entirely.

The sample covers only competitions with arrow-by-arrow results on the World Archery website, and only matches that reached a shoot-off. Recurve and compound are analysed together even though their matches follow different rules (set system and cumulative score). The effect among women at the major events and the home effect come from subgroups, with many variables tested, and remain to be confirmed. The figure of 3,645 counts shoot-off arrows, not archers. The text puts the share of world-level events at 53%, the table at 57%.

What matters for archers is the size of the effect. In the shoot-off, the archers in these competitions lose on average about a tenth of a point compared with the ends of the same match: a small drop, but one that counts because at that moment a single arrow decides who goes through. The round, by contrast, shows no sign of a decline: a shoot-off in a final goes no worse than one in an earlier round. What weighs is the type of competition, and in these data only for women.

The study does not say why this happens or how to avoid it, and it does not measure what the archers feel. The experience result runs against intuition (more matches behind you, slightly worse shoot-offs), and the authors offer an explanation they cannot test. For anyone preparing for competition, it shows where the drop is concentrated: in the single arrow that decides the match, more than in the ends.