We all know the process is a #s game..but is it ONLY a #s game?1

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For MD, frankly, no.
Depending on your state of residence, that would be an average number of aps (with about a 40% chance of matriculation).
I once came across an applicant who applied to 110 MD schools...it didn't end well.
 
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Barring unfortunately poor-quality application packages, would submitting 25 complete applications essentially GUARANTEE at least 1 offer admission?

No, there are no guarantees. It is not fruitful to think in such terms. There are a number of factors why two applicants with identical stats where one would receive one or more admissions offers while the other may not such as state of residence, demonstrated mission fit, race/ethnicity, language abilities, selected school lists, etc. Just focus on putting together the strongest package you can.
 
Barring unfortunately poor-quality application packages, would submitting 25 complete applications essentially GUARANTEE at least 1 offer admission?
It's just not productive to think about it like this. It is FAR from only a numbers game. Numbers are just the ante to put you into the game. We do NOT all have an equal shot given similar numbers, like a lottery ticket, where more applications equal more random chances at success.

Of course, more applications equal more chances. But every year, literally several thousand people with good to great numbers throw in +/- 25 applications and get completely shut out while thousands of other people with less stellar numbers are accepted. All things equal, more applications are better than less, but all things are never equal!!

If what you are thinking was true, we'd have collectively cracked the code years ago and, "barring unfortunately poor-quality application packages," the applicant acceptance rate would be around 100% instead of around 40%. 🙂 Even taking out people who have no business applying, the acceptance rate of well qualified applicants is still probably no better than 60-70%, depending on how you define "not well qualified."
 
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You have to be a holy man to figure out to the outcomes 😉
 
One way to think about it statistically is to take a look at this table. Find yourself in the grid, and subtract your theoretical acceptance rate from 1. This will give you the likelihood you won't be accepted in a given cycle. You can then take the 16th root (based on the average number of applications per student I could find), to give you the average rejection rate for people in your bracket at your school. Then raise that to the 25th power to see what the likelihood of not being accepted is if you apply to 25 schools. Applying to 25 schools will get you lower, but never guaranteed (for example, an average applicant in this case would increase their acceptance likelihood from ~40% to ~50%).

However, there are serious issues with this because:
(1) The data isn't independent. Being rejected at school X may indicate there is an issue with your application making it more likely you are rejected at school Y
(2) The data doesn't have much resolution. A 3.4 and 3.55 GPA are lumped together, and same with a 517 and 525 MCAT
(3) MCAT and GPA aren't the only factors. Having great EC's, being URM, being a great writer or interviewer can improve your odds while the opposite will decrease your odds
(4) Schools are not created equal. If you only apply to the 25 most prestigious schools you will be at a disadvantage. You need to have a good list tailored to your application.
(5) The number of applications per student may be different at different levels (i.e. a confident 4.0/528 might apply to fewer schools than a nervous 3.5/506)

This whole rant was mainly just to show that the answer is that it is at least partially a numbers game, but we don't have the data to accurately predict what those numbers are. And don't forget, the more applications you try to complete the more drained you might get writing all the time, affecting your writing on other secondaries.

Edit: thought of another issue. (6) MCAT and GPA's are not created equal. An unbalanced MCAT may be considered a red flag, and the trend and rigor of a GPA will also be evaluated by schools.
 
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Barring unfortunately poor-quality application packages, would submitting 25 complete applications essentially GUARANTEE at least 1 offer admission?
It's not playing the Lotto.

Getting accepted is 100% on you. Your app determines if you can get an II. The interview, and the app somewhat, determines your fate.
 
It's a numbers game but you have to meet a certain standard and there's definitely a point of diminishing returns. If you get a 20 on the MCAT and apply to every school you still won't get in anywhere. Likewise if you have a perfect application and only apply to one school your odds aren't great either. Once your numbers are good enough your odds probably increase up to ~25-30 applications but after that adding more schools doesn't really increase your chances all that much.
 
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