Interesting, "Twice I found a blank entry in the place of my first turn speed. "
So... I have actually seen this before, through not from a human player, but from the AI. See:
https://www.warlight.net/MultiPlayer?GameID=11521096 (yes, that is me trying to pick fast. ) Here the AI is apparently the slowest player (Cycle position 3.)
Anyway, I presume that is what you mean by empty box?
I also have AI empty box here,
https://www.warlight.net/MultiPlayer?GameID=11520147, However in that game <-- I can hoover over the empty box, and it gives me start/end time. (unlike in the first linked game.) This shows that an Empty box, at least in this case, equals a recorded pick time of 0.000.
Can you see start/end time by hoovering over the box? This may actually prove that you "picked so fast that the system thought I picked in no time" :)
Do you have the game link to it?
Edited 7/7/2016 00:07:43