Which animation is chosen depends on where a guard is injured. This is based on the guard's hitbox.
Arms are split into hand / lower arm / upper arm, legs into foot / lower leg / thigh. Then there's the head, chest and the funny 'gut'. The chest hitbox comes out further than gut so covers the top part, and the legs cover some of the bottom part when they are at a good angle. Any gun(s) and hat also have their own hitboxes.
HAND / FOREARM / UPPER-ARM / FOOT / SHIN / THIGH #2 : 2.1 #9 : 2.27 #15 : 2.27 #4 : 2.77 [THIGH only] #12 : "7.63"** GUT / GUN (LTK) #10 : 2.27 #1 : 2.5 #11 : 2.83 #16 : 2.9 #8 : 2.93 #13 : 2.93 #6 : 3.9 [GUT only] #14 : 20.13 [GUN] #3 : 3.9 BODY / HEAD #2 : 2.1 #9 : 2.27 #10 : 2.27 #15 : 2.27 #1 : 2.5 #4 : 2.77 #11 : 2.83 #16 : 2.9 #8 : 2.93 #13 : 2.93 #3 : 3.9 #6 : 3.9 [HEAD only] #5 : 8.03 * [HEAD only] #7 : 8.13 ** this unique thigh death is strange because it's actually 2 animations back to back. The 2nd one is triggered directly by the assembly in a hacky way. I didn't want to dig too deep for 1 animation, but I took a bit of a guess and arrived at this figure. It's 0.2s less than Henrik's figure which is a lot even considering that it has twice the opportunity to overrun - 7.73s is probably more accurate. * I think this counts as an easter egg - whenever this animation is triggered there's a further 1% chance of it playing out the full version instead, which lasts 13.63s instead of 8.03s.
Each of the animations under each body part is equally likely - i.e. the arm has a 1 in 4 chance to give the best death animation, and the thigh has a 1 in 5 chance of the unique slow animation. The head / body / gut have left and right (reflected) versions of each of their animations, while the other body parts only have the one corresponding to their side of the body.
If possible, it is advised to aim for the legs/arms for the best chance at the shortest animations.