From my experience if you use the same dino as your opponent you start if you click faster. Which most of the time works for me. Just when i fight my Stegodeus against Indominus Rex (which both have the same speed of 107) i never get to start - even though i click as fast as i can. At first i thought my opponent just was even faster than me. But now after experiencing it like 10 times i start to believe that Indominus is simply faster even though the stats are equal.
Has anybody ever started against Indominus?