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The idea of a "magic number" comes from the above chart from Charting Outcomes, which is based on NRMP data on how DO students performed in the ACGME match (in other words, it doesn't count AOA programs at all!). Right now, you only have 3 ACGME programs to rank, putting you at about a 50% chance of success in the ACGME match. However, like gameremdoc says, if you participate in the AOA match and are unsuccessful (i.e. don't match at any AOA programs), the 2 double-dipping programs likely won't rank you to match in the ACGME match, so you'd really only have *1* ACGME program on your list, putting you at a ~30% chance of matching. However, this graph is smoothed out in a way that's pretty misleading, as the below chart shows the actual numbers of matched and unmatched DO students - 50% is more like 40%, and 30% is more like 43%.
The other thing you need to realize is that these data have VERY small sample sizes! Check this out:
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Only 23 students ranked just 1 program, 18 ranked 2, and 20 ranked 3. I'm not great at statistics and can't calculate how powered this sample is, but my intuition says that it's hard to draw generalizable conclusions about likelihood of matching with such small sample numbers. It also looks like people who only ranked 1 program had a higher chance of matching (10/23 = 43%) than people who ranked 3 (8/20 = 40%). I wonder if this is because the people who didn't participate in the AOA match and then went on to rank only 1 program in the ACGME match were ranking the program they did an Away at and had some kind of assurance from the PD that they would be ranked to match based on excellent performance. But again, sample size of 10 matched AOA students is tough to draw conclusions from.
I couldn't find a resource that has similar graphs/charts for how DOs performed in the AOA match, so I can't really predict what an AOA match magic number should be. Anyone with more experience in this able to provide a source for an AOA match magic number?