From The Analytics of Captain Kirk
Q: What factors could increase/decrease the survival rate of red-shirted crewmen?
Besides not getting involved in fights, which usually proved fatal, the crewmen could avoid beaming down to the planet's surface, which is inherent to their end. However, that could result in a court-martial for failure to obey orders.
Besides not beaming down, another factor that showed to increase the survival rate of the red-shirts was the nature of the relationship between the alien life and captain Kirk. When Captain Kirk meets an alien woman and "makes contact" the survival rate of the red-shirted crewmen increases by 84%. In fact, out of Captain Kirks' 24 "relationships" there were only three instances of red-shirt vaporization.
The caveat to this is when Captain Kirk not only meets the local alien women, but also starts a fight among alien locals. The combination of these events has led to the elimination of 4 crewmembers (3 red-shirts).
Here are the statistics:
Red Shirt Death episodes = 18
Episodes with fights = 55
Probability of a fight breaking out = 70%
Kirk "conquest" episodes = 24
Kirk "conquest" + fights = 16
Kirk "conquest" + red shirt casualty= 4
Red shirt death + fight + Kirk "conquest" = 3