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According to Wolfgang Bangerth's answer to Can a professor influence the graduate admissions committee if he or she is interested in a particular student?:

If a professor sends us a note that they'd like to have a student admitted and state that they will take on their adviser role, we [the adcom] will only not admit that student if there are any red flags in the file.

I want to elaborate this more. What are the red flags that he mentions?

I know that they will look at these things: the transcript, the LORs, the SOP, the GRE and TOEFL scores. What is the threshold of them? At the 50% bottom of the applications or what? Is the threshold different from top schools and low tier ones?

I have applied to a top school, to a leading professor, who says that I "would be a terrific addition" to the group. If I can avoid the red flags, how much chance that I will get an admission?

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    For your last question: no, there may be lots of people who "would be a terrific addition" and not all of them can be admitted. Also, how much pull an individual professor has in the admissions process varies by department.
    – Kimball
    Oct 18, 2015 at 11:54
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    In addition to @Kimball 's comment, that is just polite way of responding to any candidate.
    – Dexter
    Oct 18, 2015 at 12:37
  • @Dexter That's why I put that phrase in quotes.
    – Kimball
    Oct 18, 2015 at 16:10
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    Nothing is ever 100%. Trying to parse minuscule details to make guesses about your chances is pointless and will only stress you out. You've submitted your application so your role in this process is done for now. Set it aside and spend your time and mental energies thinking about something more productive. Wait patiently for the result, and deal with it when it comes.
    – Nate Eldredge
    Oct 18, 2015 at 17:10
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    I'm not saying that phrase is just meant to be polite, but it could be, or it could be sincere. Certainly if you've been discussing research and funding that's a good sign. I would say it sounds hopeful, but is not essentially a lock, unless a professor explicitly tells you it is. There are a lot of factors involved, and the committee won't know who are the best candidates (at least on paper) until they look through all the applications.
    – Kimball
    Oct 19, 2015 at 11:31

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What are the red flags that he mentions?

In general, a red flag is anything that makes the application look inappropriate or weak in comparison with other applications. This is a vague term, as you've recognized. It can mean something a little different to each committee member. (I've been in discussions in which one committee member thought something was clearly a worrisome sign while another was completely unbothered by it.)

In practice, when you first look at a group of applications they come across like this. There's a small group that should obviously be admitted, and a large group that don't look like good choices. The latter are the ones with red flags. Then there's a group that look like they could plausibly be admitted, but there are too many of them so further distinctions have to be made. That's the group where support from a potential advisor would be most helpful.

I have applied to a top school, to a leading professor, and they says that I "would be a terrific addition" to the group. Would this mean that if I'm trying to avoid the red flags, 100% that I will get an admission?

It's completely unclear. First of all, it depends on how the admissions committee works. For example, it sounds like support from an advisor helps much more in Wolfgang Bangerth's department than in mine. Without knowing where you are applying, it's impossible to say what will happen in your case.

Furthermore, who knows what this professor's statement means? Maybe they tell lots of people that they would be terrific additions. Maybe you're special but someone even more impressive has also applied. It's not worth spending a lot of time trying to interpret statements like this, since you just don't have enough information to say with any confidence what they mean.

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  • ......Berkeley?
    – Ooker
    Oct 18, 2015 at 13:19
  • @Ooker: This will be a matter of departmental policy, rather than anything university-wide.
    – Anonymous Mathematician
    Oct 18, 2015 at 15:08
  • This answer agrees with what I see in my department. Support from a potential adviser will help a student who is near the borderline for admission; it won't help one who, in the committee's estimation, isn't even close.
    – Andreas Blass
    Oct 19, 2015 at 11:05
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    @Ooker and not only on the department, but also on the political weight of the specific professor, and on how much effort is he willing to put in to get you.
    – Davidmh
    Oct 19, 2015 at 11:19
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Remember, admission is competitive. Avoiding "red flags" (anything which indicates you will not be able to complete the degree respectably), you're competing against all the other applicants for a limited number of admissions. You may have a wonderful application but be just a hair below the other top applicants. There is no 100% for ordinary mortals. And even the exceptional may not get in if the school feels (for example) that this student won't be able to handle the stress of suddenly being only "typical" in the new environment.

Be the best you can be, apply everywhere you're seriously considering going, and cross your fingers.

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