2014 USNWR Rankings (Statistics/Biostatistics)

[Igotnothin]

You have to add the two numbers and then divide by two. 

[wine in coffee cups]

^ I think you guys misinterpreted what s/he did. The 2010 rankings are based only on 2009 survey results, while the 2014 rankings are based on averaging the survey results from 2009 and 2013. The two columns are the 2010 ratings and 2014 ratings, and stats_applicant was trying to use the fact that the 2014 rankings are an average to recover the 2013 survey results without the 2009 data mixed in. Looks reasonable to me.

[clurp]

Ah, I see. Apologies. 

[Igotnothin]

lol yuuup

[biostat_prof]

As I have said before, these rankings are useful at the point where they give you information about which programs to consider. And they may also be useful for a student who doesn't have a good idea of what they want to research, since the top-ranked departments tend to have strong faculty in many different research areas. That said, I don't think there is a meaningful way to compare the overall quality of two graduate programs, so take these rankings with a big grain of salt. Let's compare (for example) the biostatistics departments at Hopkins, UNC, and Michigan. Hopkins lost a lot of their best faculty over the past few years and their ranking is arguably inflated as a result. (Indeed, I hadn't realize that they also lost Rafael Irizarry to Harvard. Now #5 is looking really generous for them.) However, they still have Scott Zeger, who is a superstar in the field. Most of the rest of their faculty is very young and unproven, though. You compare Hopkins to a place like UNC, that doesn't have anyone on the same level as Scott Zeger, but I would say that their median tenure-track professor is significantly stronger than at Hopkins. And then you could compare both schools to a place like Michigan, which is outstanding for statistical genetics but fairly weak for most everything else. Which of these departments should be ranked the highest? Beats me.

 

And which department is the best for a given student depends heavily on the student's interests. If you definitely want to do statistical genetics, it's a no-brainer; you should go to Michigan. Between Hopkins and UNC, it's less clear. If you definitely wanted to do some research with Scott Zeger (or some of their other top faculty), Hopkins is the obvious choice. On the other hand, if you're not sure what you want to do, UNC may be better, given that they have more strong faculty in more areas than Hopkins does. One way or another, this scenario illustrates the difficulty of ranking departments and why students should not choose departments based on rankings.

 

It's also worth noting that job placement correlates very poorly with the ranking of the department. Sure, most Stanford graduates are going to do well, but after that there is a lot of noise in the data. One's job prospects will typically depend much more on your advisor and your research rather than the ranking of your department. You'd be much better off going to a lower-ranked school and working with a good advisor than you would with a mediocre or bad advisor at a higher-ranked school. Just to give one specific example, although I don't have data on the placement records for every student at top-ranked biostatistics departments, anecdotal evidence suggests that Michigan has placed more students in faculty positions at top-ranked schools than any other department. I think it's because they are the best at statistical genetics, and that is a high-demand area right now. That still doesn't mean that every student should choose Michigan. As I said earlier, it's a poor choice for someone not interested in genetics. But it also means that one shouldn't choose Harvard over Michigan because one thinks that you have a better chance of getting a good job coming out of a higher-ranked school. It's simply not true.

[biostatsPhD]

Can anyone give some comments on the biostats department at BU?

[qqyyzz]

Honestly, the rankings look fairly reasonable to me, though you could make the case for some programs to move up/down by a couple of ranks. Most of what these rankings measure is reputation, and since perceptions are slow to change they tend not to pick up on "recent" developments (i.e., things that have happened in the past 10-20 years). For example, I think that Iowa State might be a tad over-ranked relative to their current strength, likely because they were a legitimately elite program 25+ years ago.

What has happened with the program in the last 10-20 years that makes it overranked now?

[cyberwulf]

What has happened with the program in the last 10-20 years that makes it overranked now?

 

Agriculture stopped being a major driver of statistical research, and a lot of the money (and interesting problems) went to the biomedical sciences. Without the ag connection, it's not easy to attract faculty and students to a place like Ames, Iowa, so they lost quite a bit of talent.

[cyberwulf]

I wanted to offer a slightly different take, and respond to a few points here:

 

Let's compare (for example) the biostatistics departments at Hopkins, UNC, and Michigan. Hopkins lost a lot of their best faculty over the past few years and their ranking is arguably inflated as a result. (Indeed, I hadn't realize that they also lost Rafael Irizarry to Harvard. Now #5 is looking really generous for them.) However, they still have Scott Zeger, who is a superstar in the field. Most of the rest of their faculty is very young and unproven, though. 

 

1. Scott Zeger has been an administrator (Vice Provost for Research) at Hopkins for the past 6 years, so isn't terribly active in methodological research anymore and I would imagine isn't supervising students. Going to Hopkins because you want to work with him would be a poor choice. 

 

2. I think you're selling the non-Zeger component of the Hopkins faculty way, way short. I'm not on the faculty at Hopkins, so don't have skin in the game in a head-to-head comparison with UNC, but "young and unproven", really? Mei-Cheng Wang is one of the top (if not the top) researchers in survival analysis, Ciprian Crainiceanu is a decent bet to win the Spiegelman award in the next couple of years and along with Brian Caffo leads likely the foremost group in statistical methods for brain imaging, Constantine Frangakis and Dan Scharfstein are famous in the field of causal inference... plus Tom Louis, who is winding down an extremely successful career. And some of their more junior faculty, particularly in statistical genetics, seem to be on a very promising track: Hongkai Ji and Jeff Leek (who is one of the contributors to the widely read SimplyStatistics blog) are already very well-respected in their field and would make fine PhD advisors. Indeed, "senior" assistant and "junior" associate professors are often good choices for students seeking advisors, as they will typically have fewer students than their more senior colleagues and are often at the peak of their productivity.

 

And which department is the best for a given student depends heavily on the student's interests. If you definitely want to do statistical genetics, it's a no-brainer; you should go to Michigan. Between Hopkins and UNC, it's less clear. If you definitely wanted to do some research with Scott Zeger (or some of their other top faculty), Hopkins is the obvious choice. On the other hand, if you're not sure what you want to do, UNC may be better, given that they have more strong faculty in more areas than Hopkins does. One way or another, this scenario illustrates the difficulty of ranking departments and why students should not choose departments based on rankings.

 

1. Most of the prospective students I talk to have little to no idea what area of research they are interested in, so rankings like U.S. News are the only semi-objective source they have. 

 

2. I don't think you're meaning to imply that students should throw out the rankings entirely, as they're obviously helpful for distinguishing between elite and non-elite departments. Sure, it's silly to choose Washington over Michigan purely on ranking, but I assume you wouldn't advise most top students to choose a program ranked outside of the top 10 over Harvard. It's probably more accurate to say that one shouldn't use exact rankings to choose between similarly-ranked schools.

 

 

It's also worth noting that job placement correlates very poorly with the ranking of the department. 

Again, this might be true for places which occupy the top 5-6 spots in the rankings, but you pretty much need to attend a top 10 biostat or top 20 stat department to have a realistic chance at a tenure-track faculty position at a good biostat department.

Edited March 12, 2014 by cyberwulf

[CauchyProcess]

Again, this might be true for places which occupy the top 5-6 spots in the rankings, but you pretty much need to attend a top 10 biostat or top 20 stat department to have a realistic chance at a tenure-track faculty position at a good biostat department.

 

This is perhaps outside of the topic of this thread, but I did very well in undergrad (4.0 upper-divison major courses, ranked 1st in my major at large state school), and for whatever reason did not get accepted to any programs even well below top 20 stat, much less above it. Do you think my chances at getting tenure-track faculty position are low enough that I shouldn't bother with such a route? Should I instead strategically plan my education for a career in industry?

[StatPhD2014]

Honestly, the rankings look fairly reasonable to me, though you could make the case for some programs to move up/down by a couple of ranks. Most of what these rankings measure is reputation, and since perceptions are slow to change they tend not to pick up on "recent" developments (i.e., things that have happened in the past 10-20 years). For example, I think that Iowa State might be a tad over-ranked relative to their current strength, likely because they were a legitimately elite program 25+ years ago.

How do you think these rankings compare to the NRC rankings

[StatPhD2014]

Edit: double post deleted

Edited March 12, 2014 by StatPhD2014

[Stat Assistant Professor]

This is perhaps outside of the topic of this thread, but I did very well in undergrad (4.0 upper-divison major courses, ranked 1st in my major at large state school), and for whatever reason did not get accepted to any programs even well below top 20 stat, much less above it. Do you think my chances at getting tenure-track faculty position are low enough that I shouldn't bother with such a route? Should I instead strategically plan my education for a career in industry?

Have you looked into the placement at the programs you were admitted to? That might give you an idea as to where they go. That said, my impression is that alumni of "lower-ranked" programs who go the academic route typically get placed at schools ranked lower (not always the case though -- if you have a faculty adviser who is well-known and has connections, it could be a different story).  As some anecdotal evidence, the math department where I got my Master's (ranked 60-70ish in the USNWR for mathematics) had statistics faculty with PhDs from Colorado State and UCSB. Several of the PhD alumni in my dept did manage to get TT positions, but they were generally at lower ranked schools (regional universities and small liberal arts schools that I'd never heard of).

[mittensmitten895]

As some anecdotal evidence, the math department where I got my Master's (ranked 60-70ish in the USNWR for mathematics) had statistics faculty with PhDs from Colorado State and UCSB. Several of the PhD alumni in my dept did manage to get TT positions, but they were generally at lower ranked schools (regional universities and small liberal arts schools that I'd never heard of).

 

Math is a special case.  Most undergrads need high-quality math instruction, and many will need multiple classes.  That's a lot of teaching demand.  Plus, the quality of students/faculty and lower-ranked math programs is still pretty good.  Have you seen some of the stats for rejected math PhDs?  It's crazy competitive and I'm glad I'm not judged against that applicant pool.  In biostats, a successful department is one with access to plenty of collaborators with grants -- there's a reason the current US research infrastructure can't support 100 good biostatistics departments.  I assume pure statistics is somewhere in between, but I don't know and you should make it a point to find out if you're interested in the TT route.  I guess what I'm saying is not to let your experience in math give you a distorted impression of the TT prospects for another field.  Things can be very, very different in different disciplines.  Many people later disappointed by the lack of TT job spent their grad careers enjoying the signs and hints that it was possible (yay! people love me and my research!) while ignoring all of the opportunities to find out whether it was actually true (maybe people love it but the love does not extend beyond a contract position without health benefits...).  After all, the question is not whether someone from University X can get a TT job but what percentage of their TT seekers ended up in suitable positions/how exceptional the University X candidate had to be in order to get the interview.

[Stat Assistant Professor]

Math is a special case.  Most undergrads need high-quality math instruction, and many will need multiple classes.  That's a lot of teaching demand.  Plus, the quality of students/faculty and lower-ranked math programs is still pretty good.  Have you seen some of the stats for rejected math PhDs?  It's crazy competitive and I'm glad I'm not judged against that applicant pool.  In biostats, a successful department is one with access to plenty of collaborators with grants -- there's a reason the current US research infrastructure can't support 100 good biostatistics departments.  I assume pure statistics is somewhere in between, but I don't know and you should make it a point to find out if you're interested in the TT route.  I guess what I'm saying is not to let your experience in math give you a distorted impression of the TT prospects for another field.  Things can be very, very different in different disciplines.  Many people later disappointed by the lack of TT job spent their grad careers enjoying the signs and hints that it was possible (yay! people love me and my research!) while ignoring all of the opportunities to find out whether it was actually true (maybe people love it but the love does not extend beyond a contract position without health benefits...).  After all, the question is not whether someone from University X can get a TT job but what percentage of their TT seekers ended up in suitable positions/how exceptional the University X candidate had to be in order to get the interview.

Thanks for your response. I researched the job placement of alumni on several statistics dept webpages though, and it seems as though it is similar for stats as for math (though not nearly as cut-throat since the academic job market for math is way worse than statistics), insofar as the top tier programs only have faculty who have PhDs from other similarly ranked schools, and mid-tier PhD graduates become faculty at lower ranked schools. Someone with a PhD from a school outside the top 20 probably has no chance of getting a TT position at the top tier stats departments, for instance. The lower the rankings you go, the greater it is the case that those graduates will be taking faculty positions at regional and less-known universities and colleges (i.e. schools that are not well-known outside of the region they occupy). At least this is what I gathered from doing a quick search of alumni placements at the top 30 or so stats programs.

Edited March 12, 2014 by Applied Math to Stat

[mittensmitten895]

Thanks for your response. I researched the job placement of alumni on several statistics dept webpages though, and it seems as though it is similar for stats as for math (though not nearly as cut-throat since the academic job market for math is way worse than statistics), insofar as the top tier programs only have faculty who have PhDs from other similarly ranked schools, and mid-tier PhD graduates become faculty at lower ranked schools. Someone with a PhD from a school outside the top 20 probably has no chance of getting a TT position at the top tier stats departments, for instance. The lower the rankings you go, the greater it is the case that those graduates will be taking faculty positions at regional and less-known universities and colleges (i.e. schools that are not well-known outside of the region they occupy). At least this is what I gathered from doing a quick search of alumni placements at the top 30 or so stats programs.

 

I'm sure you took this into consideration in other ways, but the data you're presenting here do not answer what I would consider to be the more important question for someone wondering if he or she has a shot at a TT position after attending University X.  That question is: "among new University X PhD graduates actively pursuing the tenure track option, what is the probability of landing a job at a tier 1, 2, ... , n department?"  Your argument is missing the denominator necessary for that type of calculation.  I freely admit it's a difficult denominator to get, but its absence cripples attempts to accurately assess TT prospects.  Moreover, there are a whole slew of steps in between accepting a PhD offer and starting a TT job search, and you should know where people entering University X with TT intentions typically drop out along the way (including why, what happens to them instead, and how they feel about it).  You can't get that information by looking only at the (relative) successes, i.e., grads who end up in faculty-like positions in departments worthy of your consideration.

 

I'm not trying to say you personally haven't thought it through.  I'm sure you have.  I'm just trying to point out the difficulty in drawing meaningful conclusions from the available information.

[Stat Assistant Professor]

I'm sure you took this into consideration in other ways, but the data you're presenting here do not answer what I would consider to be the more important question for someone wondering if he or she has a shot at a TT position after attending University X.  That question is: "among new University X PhD graduates actively pursuing the tenure track option, what is the probability of landing a job at a tier 1, 2, ... , n department?"  Your argument is missing the denominator necessary for that type of calculation.  I freely admit it's a difficult denominator to get, but its absence cripples attempts to accurately assess TT prospects.  Moreover, there are a whole slew of steps in between accepting a PhD offer and starting a TT job search, and you should know where people entering University X with TT intentions typically drop out along the way (including why, what happens to them instead, and how they feel about it).  You can't get that information by looking only at the (relative) successes, i.e., grads who end up in faculty-like positions in departments worthy of your consideration.

 

I'm not trying to say you personally haven't thought it through.  I'm sure you have.  I'm just trying to point out the difficulty in drawing meaningful conclusions from the available information.

I guess I was just trying to convey that pedigree does seem to matter for getting TT jobs and that if you *graduate* from a "lower ranked" school, you could still potentially get a TT position but it would be more likely to be at an even lower ranked or unranked department (not that there is anything wrong with this -- hell, even community college TT jobs are perfectly respectable, and there are certain perks of being at lower tier colleges than at R1's... my dad is a professor with a PhD from Yale, and he turned down job offers at R1s to teach at a mid-tier school because he thought his chances at getting tenure would be better). 

 

Statistics does not seem that different from math in this regard.

[statshopeful2014]

Here's some data for PhDs in statistics regarding placement.

 

Harvard: http://www.stat.harvard.edu/alumni/PhD.html

Chicago:http://galton.uchicago.edu/people/alumni-phd.shtml

Wisconsin: https://www.stat.wisc.edu/doctoral-graduates

Penn State: http://stat.psu.edu/alumni

 

Of those who tenure track at these schools, the majority seem to have landed a position at solid schools with the exception of Wisconsin where academic placement seems poor.  Chicago, Harvard, Penn State seem to place half in academia (post-docs, non-TT included) and industry.  At a quick glance, it appears getting on the TT is far from a given even after attending an elite school.  Now why this is the case is hard to ascertain.  Some graduates might find academia is not for them and go to industry despite having opportunities to continue, there might be no suitable academic offers, or the money offered in industry is too good to turn down.  Maybe some faculty more experienced in this matter could comment.   

 

Additional thoughts: I guess one should be weary of doing a PhD in Statistics with the sole intention of becoming a professor since clearly, many do not go that route.

Edited March 12, 2014 by statshopeful2014

[wine in coffee cups]

Of those who tenure track at these schools, the majority seem to have landed a position at solid schools with the exception of Wisconsin where academic placement seems poor.  Chicago, Harvard, Penn State seem to place half in academia (post-docs, non-TT included) and industry.  At a quick glance, it appears getting on the TT is far from a given even after attending an elite school.  Now why this is the case is hard to ascertain.  Some graduates might find academia is not for them and go to industry despite having opportunities to continue, there might be no suitable academic offers, or the money offered in industry is too good to turn down.  Maybe some faculty more experienced in this matter could comment.   

Just a couple of additional thoughts:

• Guessing based on names, could be wrong, but Wisconsin has way more international students from China and South Korea than the other departments, which seem to have more of a mix of Americans and students from other countries in there. Not that students from outside North America can't land solid postdocs or tenure-track jobs (clearly some do), but I think there are marked differences in job and location preferences between international and domestic students. I think Americans tend to have better academic placements for reasons that I can only speculate. Pharma in the US is heavily Chinese and you definitely see that reflected in the Wisconsin placements, maybe particular advisors with strong industry connections feeding a steady pipeline to pharma and some homophily. (Anecdotally, a few years ago, I had to read depositions taken of statisticians working in an American office of a drug company. Even though all of them received their PhDs from mid-ranked US statistics departments and had been at the company for several years, the attorneys still needed to conduct portions of their interviews through a translator and to have emails circulated within the statistics group translated.)

   

• Two-body issues can make placements very challenging, and what might look like an odd choice of postdoc or temporary position could reflect compromises made in order to be near an academic spouse or aging parents.

[Igotnothin]

Yeah it looks like Wisconsin has almost exclusively Asian PhD students. Maybe 90%

[biostat_prof]

I wanted to offer a slightly different take, and respond to a few points here:

 

 

1. Scott Zeger has been an administrator (Vice Provost for Research) at Hopkins for the past 6 years, so isn't terribly active in methodological research anymore and I would imagine isn't supervising students. Going to Hopkins because you want to work with him would be a poor choice. 

 

2. I think you're selling the non-Zeger component of the Hopkins faculty way, way short. I'm not on the faculty at Hopkins, so don't have skin in the game in a head-to-head comparison with UNC, but "young and unproven", really? Mei-Cheng Wang is one of the top (if not the top) researchers in survival analysis, Ciprian Crainiceanu is a decent bet to win the Spiegelman award in the next couple of years and along with Brian Caffo leads likely the foremost group in statistical methods for brain imaging, Constantine Frangakis and Dan Scharfstein are famous in the field of causal inference... plus Tom Louis, who is winding down an extremely successful career. And some of their more junior faculty, particularly in statistical genetics, seem to be on a very promising track: Hongkai Ji and Jeff Leek (who is one of the contributors to the widely read SimplyStatistics blog) are already very well-respected in their field and would make fine PhD advisors. Indeed, "senior" assistant and "junior" associate professors are often good choices for students seeking advisors, as they will typically have fewer students than their more senior colleagues and are often at the peak of their productivity.

 

 

1. Most of the prospective students I talk to have little to no idea what area of research they are interested in, so rankings like U.S. News are the only semi-objective source they have. 

 

2. I don't think you're meaning to imply that students should throw out the rankings entirely, as they're obviously helpful for distinguishing between elite and non-elite departments. Sure, it's silly to choose Washington over Michigan purely on ranking, but I assume you wouldn't advise most top students to choose a program ranked outside of the top 10 over Harvard. It's probably more accurate to say that one shouldn't use exact rankings to choose between similarly-ranked schools.

 

 

Again, this might be true for places which occupy the top 5-6 spots in the rankings, but you pretty much need to attend a top 10 biostat or top 20 stat department to have a realistic chance at a tenure-track faculty position at a good biostat department.

 

For the record, I agree with most of this. I was probably too hard on Hopkins (and I actually didn't know that about Zeger, so my bad), but the point remains that their faculty is much younger (and generally has a much thinner track record) than most of the tenure-track faculty at UNC and Michigan. And I did find it a little weird that their ranking didn't drop at all after losing not only Irizarry but also Giovanni Parmigiani and Francesca Dominici (and I think a couple others) in recent years. My personal opinion is that ranking them so far above UNC/Michigan is not really justified (although this is just my opinion, and I believe these rankings are kind of a silly exercise for the reasons I listed above).

 

When you say a program "outside of the top 10," I assume you mean "outside of the top 10 biostat departments" rather than "outside of the schools ranked in the top 10 by USNWR." I would definitely tell a student to choose Michigan over Harvard if they wanted to do genetics despite their #12 USNWR ranking. But I will say that I wouldn't recommend that a student choose a program other than UW/Harvard/Hopkins/UNC/Michigan in most circumstances if they have an acceptance to at least one of those schools. The circumstances would probably have to imply a combination of a much better funding offer at a lower-ranked school and a strong desire to work with a particular faculty member. Just off the top of my head, someone with a strong interest in Bayesian methods and a generous funding offer from Minnesota may be better going to Minnesota and working with Brad Carlin than taking only one year of guaranteed funding at UNC, for example.

 

So I wasn't suggesting that people ignore the rankings entirely. But keep in mind that the rankings are only useful at the point where higher-ranked schools are more likely to have larger numbers of strong researchers (and more money, which is also important), but at the end of the day, your advisor and your research will matter much more than the ranking of your department. Going to Berkeley and working with Mark van der Laan will almost certainly put you in a better position than going to Harvard and working with someone unknown. And while what you say about having trouble finding an academic job at research university coming from schools outside of the top 10 is probably true, that has more to do with the fact that for the most part these schools have very few (or no) faculty involved with methodological research.

[biostat_prof]

In response to the discussion elsewhere on this thread, interpret the placement data from various schools very carefully. Not every person who finishes a PhD program wants (or has any interest whatsoever in) a tenure-track job at a research university. Some people simply prefer industry. Others want to find a job near a significant other or friends or family or in a favorite part of the country. (You'd be surprised how many students won't apply to jobs in places where there is snow or in places with no place to buy fresh seafood or strange criteria like that.) I had a student who graduated a couple years ago who turned down multiple tenure track offers to take a non-faculty job near where her husband lives. I had another student who voluntarily took an hourly programmer job despite several publications (one in a top-tier methods journal) because she had just had a baby and wasn't willing to relocate since she relied on her in-laws for child care. And, well, there are also students who come out of good departments who don't get good jobs because they worked with an unknown faculty member and never published anything. It's not the school that is holding them back; it's their own lack of productivity.

 

The only really common denominator is that if you want a job in academia, your best bet is to publish as much as possible in top-tier methods journals and try to get recommendation letters from someone reasonably well-known in the field. Both of these things are generally easier to do at higher-ranked departments. But it's still possible at lower-ranked departments provided you have a good advisor. I can't say it enough times: your advisor's reputation is much more important than the ranking of the school.

[statshopeful2014]

In response to the discussion elsewhere on this thread, interpret the placement data from various schools very carefully. Not every person who finishes a PhD program wants (or has any interest whatsoever in) a tenure-track job at a research university. Some people simply prefer industry. Others want to find a job near a significant other or friends or family or in a favorite part of the country. (You'd be surprised how many students won't apply to jobs in places where there is snow or in places with no place to buy fresh seafood or strange criteria like that.) I had a student who graduated a couple years ago who turned down multiple tenure track offers to take a non-faculty job near where her husband lives. I had another student who voluntarily took an hourly programmer job despite several publications (one in a top-tier methods journal) because she had just had a baby and wasn't willing to relocate since she relied on her in-laws for child care. And, well, there are also students who come out of good departments who don't get good jobs because they worked with an unknown faculty member and never published anything. It's not the school that is holding them back; it's their own lack of productivity.

 

The only really common denominator is that if you want a job in academia, your best bet is to publish as much as possible in top-tier methods journals and try to get recommendation letters from someone reasonably well-known in the field. Both of these things are generally easier to do at higher-ranked departments. But it's still possible at lower-ranked departments provided you have a good advisor. I can't say it enough times: your advisor's reputation is much more important than the ranking of the school.

 

Interesting observations. 

 

When it comes to an advisor, how much say does a student have in who they choose to work with?  Do students typically get they advisor they ask for?  Or is the process somewhat random?

[StatPhD2014]

Interesting observations. 

 

When it comes to an advisor, how much say does a student have in who they choose to work with?  Do students typically get they advisor they ask for?  Or is the process somewhat random?

its definitely not random, it depends on how many students the advisor currently has and whether he is willing to work with you

[biostat_prof]

its definitely not random, it depends on how many students the advisor currently has and whether he is willing to work with you

 

In my experience it's very rare for advisors to turn away a student outright. However, they may sometimes tell a potential student that they have a lot of other students and hence won't have time to devote to them. But the only cases where I have heard of advisors turning students away is when the student has a poor academic record or a reputation of being difficult to work with. That said, sometimes there is strong pressure to work with a particular professor if that professor is willing to fund you and you don't have another funding source lined up. Rarely does that hurt you, though, except at the point where you may end up working on a project that isn't your preferred choice. Usually the best-funded professors also tend to be the most productive ones.