How much can a mediocre letter sink you?

[planner2019]

In the interest of brevity, the situation that I find myself currently in is this: I went from a not-at-all rigorous small state university to an R1 for a PhD program. I failed comps twice and was asked to leave the program a few weeks ago. My advisor, however, has agreed to write me letters if I choose to apply elsewhere next year. He said that he would be honest about my academic weaknesses, though he could potentially foresee not explicitly mentioning the failed exams. He said he would say something to the effect of the fact that I entered poorly prepared and from a non-rigorous background, that I had a huge amount of ground to make up, and that I ultimately wasn't able to make it up in the 2.5 years I was in the program. But that I have (in his words) "made huge amounts of progress" and with additional training, could potentially be successful. He said that he would emphasize the positive. 

My ideal choice would be to attend a 1 year coursework-based masters program in the UK that's part of a research institute specifically dedicated to my field. So it would be a year of intensive training exclusively in my field with a short 50 page thesis at the end. If that program goes well, I may consider going on to a PhD there or elsewhere. But my primary thought was that it would be easier for my advisor to make a case for my pursuing a year of intensive training (which is what I lacked) than it would be for him to make a case for me jumping directly into another PhD program. Along with the fact that this particular one year masters program in the UK is not particularly competitive in regard to admission (though funding is another story). So out of all my options, my guess is that I would have the best shot at cleaning up my academic record by taking this route. 

I still wonder though -- does a lukewarm or mediocre letter, or a letter that specifically mentions academic weaknesses at all -- automatically sink one's application? 
 

[fuzzylogician]

1 hour ago, planner2019 said:

I still wonder though -- does a lukewarm or mediocre letter, or a letter that specifically mentions academic weaknesses at all -- automatically sink one's application? 

A lukewarm letter would make things more difficult. Two issues that come to mind: the first is that LORs tend to be excessively positive, so one that discusses negatives may stand out. Second, this is the letter from your main advisor, so it would be taken more seriously than a letter from someone who doesn't know you as well. That said, there's also the question of how this letter fits in the broader scheme of your application: your other letters, you other documents, your grades, etc. If you eventually do have your advisor's support, it doesn't sound like this will sink your application entirely, though you may be right that starting slower and less competitive is a wise direction to go, to make up for the deficiencies that caused you trouble in the first place. 

[medievalbotanist]

This might depend on your field and to some extent the specific schools you apply to, but a lukewarm (by US standards) may not actually sink you with UK programs. I did a UK masters and am starting a US PhD in the fall and two of my recs were from my UK professors, and everyone warned me that UK letter writers are much less effusive and more likely to mention weaknesses than US letter writers. As such, I think people reading your application won't be taken aback if a letter is overall positive but does mention a significant weakness or two. It can also help if you have space in your application to mention those weaknesses yourself, because then it doesn't look like you and your advisor are on totally different pages. 

[PokePsych]

There's indeed a cultural issue here as well. Europeans tend to write more 'lukewarm' letters (nobody is perfect) and this is not gonna help you in the US. This was something my American reference at an European school really warned me for. And when I read my advisors letter - it was not even half as glowy as he tends to give me comments on my paper. But I got in so whatever haha.

In fact, some European profs may even prefer lukewarm letters - one of my European profs also confessed he doesn't like it when he receives all glowy letters from the US as he'd like to know if he can help the student grow and also in which area. For example, if a student has weaknesses in an area he's also not that great in or has already many students who struggle in (e.g., time management or writing - it can be anything really) then it's probably not gonna be a great working relationship. 

Since your advisor will still mention your potential, the progress you made, and that he believes in you, I don't think it is necessarily a bad letter for a UK school.