Third arrow after a miss, women and men: Li 2024

The authors gathered the arrow-by-arrow results of individual recurve matches at five events: the London 2012, Rio 2016 and Tokyo 2020 Olympic Games, the 2021 World Championships in Yankton and the 2021 European Grand Prix in Antalya. They found 6,374 complete three-arrow ends, or 19,122 shots, and asked whether the score of the third arrow depends on how the first two went and on the state of the match. An arrow counted as a hit only if it scored 10; any other score, even a 9, counted as a miss.

The third arrow scored 8.25 on average. After two 10s it scored more than after two arrows below 10: according to the model, after two misses the third was 12.2% lower (exponentiated coefficient 0.878). The authors call this a cold-hand effect. Men did not shoot a significantly better third arrow than women overall (p = 0.225), but they did after two misses, by an estimated 3.5%, and in ends where losing meant elimination while winning only kept them in the match, by 2.4%. On an average arrow of 8.25 points, 3.5% is roughly three tenths of a point.

Two background variables had a much clearer effect: the ratio between the archer's qualification score and the opponent's, and the type of event, with higher third arrows at the Olympics than at the other two events. Shooting order made no difference.

The data come from the official World Archery website and, for London 2012, from an archived copy of the Games website. For each end the authors recorded the archer, the three scores, the shooting order, the type of event and the set points at the time it was shot. The first two arrows were reduced to four combinations (10 and 10, 10 then a miss, a miss then 10, two misses), and the state of the match to four conditions: a set that decides nothing; one that eliminates the archer if lost but does not end the match if won; one that decides everything either way; and one that ends the match if won and changes nothing if lost.

The score of the third arrow was analysed with a Poisson regression corrected for dispersion (quasi-Poisson), with sex interacting with the first two arrows and with the state of the match. To allow for skill, the model uses the ratio between the archer's qualification score and the opponent's. The number of different archers is not given.

The psychological explanation is not the only one possible. The three arrows of an end are shot under the same conditions: if there is wind, or if the archer is struggling that day, all three are likely to go worse, and two 9s followed by an 8 do not necessarily mean that the second miss caused the third. The model controls for skill only through the ratio of the two opponents' qualification scores, which is a relative measure and says nothing about how good the archer is in absolute terms; it does not account for wind and it treats the many ends shot by the same archer as independent. The strong effect of event type, with higher third arrows at the Olympics, suggests that each event's conditions carry a lot of weight.

The difference between men and women also has an alternative reading that the paper does not consider: women generally shoot lower draw weights and slower arrows, which the wind moves more, so in ends made difficult by conditions their scores might drop more for physical reasons. The explanations the authors offer (confidence, anxiety, coping strategies, competitiveness, heart rate) are drawn from the literature, not measured in these archers.

Some things do not add up. There are 1,753 ends of "10 then a miss" but only 675 of "a miss then 10", an imbalance that is hard to explain. At one point the text says the third arrow after two misses is higher than the average in the other situations, the opposite of the main finding; the shooting order variable is defined one way in the text and the other way in the table; and the 3.5% difference is given with p < 0.001 in the text and p < 0.01 in the table.

For anyone shooting head-to-head matches, the study describes a pattern many will recognise: ends that start with two arrows outside the 10 tend to finish with a lower third arrow. What it cannot say is whether this happens because the miss weighs on the mind or because the end was difficult from the start, through wind or a bad day, and the two readings change a great deal how an archer should interpret their own scores.

The difference between men and women is small, around three tenths of a point on the third arrow in the worst situations, and it is not evidence about women archers' ability to handle pressure: with no wind in the model and no measure of absolute skill, it may also come down to equipment and conditions. A coach can use it as a prompt to watch how their own archers respond after two poor arrows, not as grounds for treating men and women differently.