The answer is to apply to enough places so that you get 10-15 interviews. The problem is that many do not know how many that is for them. For some that means applying to 20 programs. For others, they will not get 10-15 invites no matter how many they apply to. You need an adviser (who is in tune with the match over the last few years) to look at your application and give you some candid advice as to what tier of applicant you fall into.
In my opinion:
If you are top quartile with 240ish step scores, you will get invited to 95% of the places you apply (maybe higher) and will likely match one of your top 3 programs.
2nd quartile with 230ish steps; you will probably get invites to 80% of places you apply and you will likely get one of your top 3-5 choices.
3rd quartile students typically don't have stellar step scores, but sometimes do. Third quartile with 240ish step scores will likely still get 50-70% invite rate. It will likely be 40-50% if you step scores are in the 220-230 range.
4th quartile students frequently have step scores less than 220. This makes it very difficult to make the desired goal of 10 interviews. These students are the ones who really benefit from an adviser taking a close look at their application and giving some candid advice. If the step score is less than 210, strongly consider having a good backup plan. Other things can also throw a monkey wrench into the mix:
-DO students generally have a little tougher time. There remains a bias at many programs. A DO student in the 4th quartile with poor step scores, or no USMLE on record may have a rough time getting a spot. Especially if the school is an upstart school that has been open less than 10 years.
-if you have negative comments on your MSPE, that can be a challenge. One might be overlooked. Two shows a pattern. Three will make it very difficult to match into any spot.
These are just my opinions based on what I have seen over the years. There are a similar number of residency spots, but many more people vying for them since there has been a large expansion/proliferation of medical schools in the past 5 years, so it is much harder to get a residency program than it was 15 years ago. There are still lots of spots though, and the vast majority will get one, but you need an adviser to help you navigate the system.