I just learned that the facility where I am having my BBL done has had 4 deaths in the last five years. Is this normal?

There are 2 key points to consider when undergoing cosmetic surgery:There are numerous practitioners of plastic surgery. However, only a select few are board certified by the American Board of Plastic Surgery (the only board recognized by the American Board of Medical Specialties). Board certification ensures completion of a rigorous training program of at least 6 years (with at least 3 years of dedicated plastic surgery training. Board certified surgeons have also completed written and oral examinations to determine competency and participate in a continuing medical education programs as a prerequisite of maintaining certification. Ultimately, certification ensures a measure of certainty when comparing surgeons. You can be assured that your board certified plastic surgeon has seen and treated it all before and is uniquely qualified to manage you pre-operatively, intra-operatively, and most importantly post-operatively.Patients should ensure that the procedure that they are undergoing is being performed in AAAASF or Medicare/JCAHO approved facility. This will ensure that the highest standards of safety are being adhered to.With regards to your specific question, the record of 4 deaths is concerning. I would recommend getting as much information as possible before proceeding. You want to compare "apples to apples." Same procedure, same surgeon but different patient will make this sort of comparison difficult. You do not (and likely will not) have specific details surrounding the deaths. That being said, complications can happen and any surgeon or facility should be forthright regarding patient concerns as it relates to these issues. They should be able to address your concerns and allay your fears.A few points specific to BBL:Fat embolus is a very serious and known complication of fat transfer (which has been recently spotlighted in the media). While it is true, injection of donor fat into the infra-muscular plane (within the muscle) increases fat viability this does come with a significant increase in risk. There are large vessels deep to and within the muscle which can be inadvertently injected while grafting leading to a fat embolus. The consequences of such a complication are very serious and life threatening.
At the recent American Society of Plastic Surgeons Hot Topics (2016), data from AAAASF (ambulatory surgical certifying body) was presented, suggesting that BBL/gluteal lipoaugmentation demonstrates a dramatically higher risk profile than other surgeries. The Aesthetic Surgery and Educational and Research Fund is convening a task force as well. The hope is that we will have more concrete guidelines for addressing these very serious complications.
That being said, the safest way to avoid fat emboli is to stay in the subcutaneous plane (at the expense of fat viability)and avoid the deeper muscular plane. If grafting of the deep plane is planned, surgeons should consider blunt cannulas, aspiration prior to injection. Using a supra-gluteal approach to minimize the risk of inadvertent intravascular injection has also been proposed.
As always, discuss your concerns with a board certified plastic surgeon (ABPS).

I think that you need to find a top surgeon, but there is a risk of complications that can happen and may or may not be related to the surgical technique.