I posted a thread about this somewhere else, but to clarify . . . the behavior witnessed suggesting that TFTD did damage on a 50-150% basis may just be an assumption.
I found out from someone else that TFTD generates two random numbers, adds them together, then multiplies by the damage value.
That produces a "peak" average curve similar to rolling two standard dice, making the average more reliable, but still not excluding extremes.
Later on I witnessed this on a rare event when one of my (non armored) soldiers was shot by a Sonic Cannon (130 damage) and he survived and took somewhere around 30 damage from it. According to the 50% scheme he should have taken a minimum of 65 before armor.