In the book "Fightnomics" by Reed Kuhn, the author noted that reach, though not height, provided a statistically significant advantage in striking exchanges. That is, the guy with a reach of over two inches won more often than not when the fights spent most of their time on the feet. So, we have proof that having a longer reach relative to your opponent, regardless of height, can be helpful.

I don't think it matters significantly in relation to body mechanics. How would they be more agile? Incidentally, reach is measured fingertip to fingertip, which can be deceiving. If someone has wide shoulders, their arm length might not actually be a whole lot greater than someone with a similar reach, but narrower shoulders. Long fingers can also throw off the measurement.

As a general rule the person with the smallest reach has to work harder to get past their opponents guard. If their opponent knows how to use their reach they will be keeping them at a distance and trying to line up shots. If the reaches are the same but one person is taller the taller person has a slight advantage in normal stand up fighting as they will be able to take advantage of the distance. (its all to do with triangles that pythagorous rubbish ull never use outside of school)

Interestingly when the fight is taken to the ground a longer reach is normally a disadvantage as all the work is close up if you have long flailing arms and elbows, they are easier to grab, but harder to pull out of holds.

For example GSP is 178 and has 193 cm reach, and shogun is 185 with 193 cm reach. Does it matter if your reach is longer than your height in terms of body mechanics? For example if someone is 185 high with 185 cm reach, and someone is 170 cm high with 185 cm reach , will the 170 be in advantage because his body is more agile or sth like that?