Dr James Park looks at the probability of an archer winning a podium position.
I occasionally hear comments such as ‘the ranking round is not important – it’s the matches that matter’. Can that be true? Certainly, if you do not win the matches, you will not win a medal, but does the ranking round have any influence on that likelihood?
Looking at the data
The individual competitions at major events consist of a ranking round (now 72 arrows) followed by ranked one-on-one elimination matches. If we have 64 archers competing in the matches (as in the Olympic Games), an archer needs to win 4 consecutive matches to get to the semi-finals and then one more match to win a medal. To win the gold medal, the archer needs to win 6 consecutive matches. Of course, an archer ranked in any of the 64 positions could win those matches and claim a medal or a win, but does it happen in practice?
It is useful to examine the data. I have done so using the results of all major international events from 1995 to 2024. I have included Olympic Games, Olympic Games test events, World Archery Championships, World Cups and World Games, covering both male and female and recurve and compound. All up, that gives us 86 events for archers using compound bows and 94 events for archers using recurve bows. Or, combined, we have 360 events – quite sufficient to show any trends quite nicely, either for each category or combined.
What does the data show?
The charts for each of the categories (male/female, compound/recurve) are close to the same as those for the aggregated events.
The probabilities fall close to exponentially with ranking place. The results show that occasionally an archer with a low rank wins a medal, but the probabilities are very small. The probability of winning a medal for the 16th ranked archer is about 5% and below 16th place it quickly falls to negligible levels. The probability of an archer winning the event falls below 5% by about the 7th ranked archer. Some of the times when a lower ranked archer has done well have been where the archer had equipment or health problems on the day of the ranking round, and in several cases where they had made an error on their score card and consequently the ranking round did not represent their usual skill level.
Higher chance of a win?
Another way to look at the data is the number of archers who rank in the top 8 in the ranking round and then remain in the top 8 after the matches. Also, the number of archers who rank in the top 4 in the ranking round and then remain in the top 4 after the matches. These are shown in figures 3 and 4, together with the 95% confidence limits.
Assume all 8 top ranked archers survive through to the last 32 after the first match. If the ranking position does not matter, we would then expect, on average, only 2 of those archers to survive through to the last 8. However, the data shows that, on average about 4.1 of them survive.
Similarly, if the ranking position does not matter, we would then expect, on average, only 0.5 of the top 4 archers to survive through to the last 4. However, the data shows that, on average about 1.6 of them survive.
That is, the ranking round place is an extremely good indicator of the likelihood of an archer winning sufficient matches to gain a podium position or to win the event.
The above comments are based solely on the actual data, with no speculation. But why might the results show this?
The data also shows that archers (at least those who rank in about the top half of the field – that is, those most likely to win medals) usually shoot at close to the same skill level in ranking rounds and matches. This means that the higher ranked archers have a higher probability of winning a match than a lower ranked archer. When we stack one match after another, the probabilities multiply, and the likelihood of the lower ranked archer getting through enough matches to win a medal falls very quickly. That is, even though a lower ranked archer might have a reasonable chance of winning a particular match, their probability of winning enough matches in succession is very low. The lower ranked archers are dangerous opponents for the top ranked archers, but they are not likely to be medal winners.
The Verdict
Hence, the ranking round matters a great deal, and the place to look for potential medal winners is to those archers who consistently rank in about the top 8 positions in the ranking round.
Did the Top 8 theory work at Paris 2024?
In the men’s individual event, the podium positions were filled by archers ranked 1, 7 and 5; and in the women’s individual event the podium positions were filled by archers ranked 1, 2 and 30.
In the men’s individual event, 2 of the top 4 after the ranking round remained in the top 4 after the matches and 7 of the top 8 remained in the top 8 after the matches; and in the women’s individual event 2 of the top 4 after the ranking round remained in the top 4 after the matches and 5 of the top 8 remained in the top 8 after the matches.
That is, the results were largely in line with those expected statistically.