If a match is tied after 5 sets for an individual match or 4 sets for a team match, a one arrow shootoff is held. Each archer shoots one arrow, and the highest score wins. If the scores are the same, then the archer or team with the shot closest to the middle of the target wins. As it only happens when two archers or teams have performed almost identically during the match, I was curious to see whether the results of a one arrow shootoff look like a 50:50 chance or whether the winner could be predicted with some level of accuracy based on which archer or team had a higher score during the qualification round, and whether this was different for international or national competitions.
National Competitions in the UK
I used data available on IANSEO to find all individual one arrow shoot-offs in the the female recurve category. The national competitions used were all legs of the National Tour, the British Target Championships, and the UK Masters. There were 19 shoot-offs in 2019, and 29 in 2018. In 2019, the archer with the higher score in the qualification round won the shoot-off 58% of the time, while in 2018 it was 48% of the time. Had I only picked one year to gather data from, it would have looked quite different! Overall, the archer with the higher qualifying score won 52% of the time, with a 90% confidence interval of 40% to 64%.
| Round | percentage won by archer with higher qualification score | number of shoot-offs | number of matches in round |
| 1/32 round | 63% | 8 | 32 |
| 1/16 round | 45% | 11 | 16 |
| 1/8 round | 64% | 11 | 8 |
| Quarterfinal | 60% | 10 | 4 |
| Semifinal | 25% | 4 | 2 |
| Final | 25% | 4 | 2 |
Not all competitions had a 1/32 round, or necessarily even a full 16th round. Overall, it looks like shoot-offs were most common in the later matches. However, the overall numbers are too small to say much about the relative frequencies.
Difference between archer ranks and shoot-off outcome
| Difference between ranks | percentage win by archer with higher qualification score | number of shoot-offs | Error for 90% confidence interval |
| 1-3 | 36% | 11 | 25% |
| 4-7 | 50% | 12 | 24% |
| 8-13 | 54% | 13 | 23% |
| 16-29 | 67% | 12 | 24% |
The larger the difference in qualification round rank between the two archers, the higher the chance of the higher ranked archer winning was. While it looks strange that for the closest-ranked archers, the lower ranked archer won more frequently, it’s a side-effect of there not being many data points – if the result of one match between the closely-ranked archers had flipped, then the probability would have been 45% instead. We can see this in the confidence interval as well. For the shoot-offs where the difference between the ranks was 8-13, I’m 90% confident that if there were an arbitrarily large number of shoot-offs, the percentage win would be between 31% and 77% – quite a wide range and it includes 50%, which is the result we’d get if the match was decided by a coin flip instead.
Conclusions
So overall it looks like the archer who shot the higher qualifying score is slightly more likely to win a one arrow shoot-off, but that it’s still pretty close to a coin flip on average. When there’s a larger difference between the ranks of the two archers, the probability of the archer with the higher qualifying score winning increases – despite the two achers having shot similarly enough during the match to come to a draw.
International competitions
I used the individual female recurve matches from the 2019 World Archery Championships, and all stages of the World Cup in 2019 and 2018. This gave 98 one arrow shoot-offs, of which 47% were won by the archer with the higher qualification score. In 2019, it was 51% and in 2018 it was 41%.
Overall, using a 90% confidence interval for a sample size of 98, the 47% can better be expressed as 38% – 55%. So I’m 90% certain that the true value would fall in that range. I’m 68% sure that the true value is in the range between 42% to 52%. So I really can’t rule out the idea that a shoot-off is equivalent to a coin flip in terms of the result.
For the international competitions, a shoot-off was more likely to happen later on in the competition. This is the same as in the national competitions.
| Difference between ranks | % win by higher qualification score | # shoot-offs | Error for 90% confidence interval |
| 1-10 | 38% | 26 | 16% |
| 11-25 | 56% | 30 | 15% |
| 26-50 | 47% | 34 | 14% |
| 51-93 | 38% | 8 | 29% |
For each group of ranks, a 50% probability is within the range that I am 90% confident is the “true” probability of winning the shoot-off. In other words, I’m not able to confidently say that the 38% probability in the first row is actually different to a coin flip.
Conclusions
So, overall the result of a one arrow shoot-off is not distinguishable from a coin flip, whether we look at national or international competitions. Further, there isn’t a clear relationship between the difference in rank of the archers, or how late in the competition the shoot-off happens.
I was expecting that there might be a meaningful difference for one of those cases. After all, if two archers with very different ranks are having a shoot-off, maybe the lower ranked (higher scoring) archer is having a bad day if the match is that close, or she feels more pressure as she’s “supposed” to win the match and has more to lose, or some other factor.
However, it doesn’t seem to be the case, at least with this amount of data. This analysis was only looking at individual female recurve matches – it’s entirely possible that there’s a different result for male archers, or teams, or other bowstyles.
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