This is an old chestnut... old enough that I've already got data on it to hand!
These are the the percentiles of scores for international archers shooting at world cups, world champs and the like in a recent four year period. As some people seem to often suggest theres not much difference at the top end, this is a useful check to see what the numbers actually look like. For example shooting a 664/720 puts you in the 95th percentile of female
recurve scores at this level and as a result makes you a likely international medal contender in the RW category. The same score on the
recurve mens side puts you in the 85th percentile, and firmly in the peloton rather than the leading pack. The same applies for those further away from the top. 631 is a 55th percentile score in the RW category, making it just above average at international tournaments. For RM, the same score lands you in the 30th percentile; meaning if its a big tournament with more than 150 archers you may not even make the cut to 104 for matches.
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People often correctly point out though that there are examples, cases of women outshooting men, in certain finals matches, mixed team events or just at open competitions where there aren't divisions. And this is certainly true. The question is, does it happen enough to make a true open division fair? If it was then the qualifying round should have even scores as well, so looking at the same data in a slightly different way, seeing the distribution of scores should be revealing.
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So what is obvious from this is that within each bowstyle, there is a big overlap, ie lots of male and female recurve archers are shooting 630s, 640s, 650s. This we know already. But the peaks are centred in different places (the mean RW score is 621, the mean RM is 638), and especially as you move to the extremes in either direction one is significantly higher than the other.
This is why whenever anyone chimes in with "I saw this match where the women outshot the men; combine the categories!!!" I roll my eyes. Yes it happens. No it doesn't happen often enough to axe the categories, certainly not at elite level.