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
There’s an amusing chart that shows crewmember deaths (by shirt-color-coded tombstones) in relation to Kirk’s romantic conquests and the number of fights.