Base Power = 25 × min(6, (Target's Current Speed / User's Current Speed))
(Gyro Ball's Base Power Formula)
Source
According to Bulbapedia, Current Speed counts, meaning Speed drops affect Gyro Ball. It is possible for a Pokemon to be so slow (or the opponent so fast) that stat stages don't boost Gyro Ball's power, because it maxes out at 150 Base Power. Here is some calculations:
With Neutral Speed:
0 Atk Bronzong Gyro Ball (38 BP) vs. 0 HP / 0 Def Abomasnow: 96-114 (34.1 - 40.5%) -- guaranteed 3HKO
With -1 Speed:
0 Atk Bronzong Gyro Ball (57 BP) vs. 0 HP / 0 Def Abomasnow: 144-170 (51.2 - 60.4%) -- guaranteed 2HKO
With Paralysis:
0 Atk Bronzong Gyro Ball (38 BP) vs. 0 HP / 0 Def Abomasnow: 96-114 (34.1 - 40.5%) -- guaranteed 3HKO
Source
It seems that paralysis doesn't affect Gyro Ball's power but being slower via stat stages (or you opponent's stat stages being higher) does. I used Bronzong because Gyro Ball's Power isn't maxed out against my dummy Pokemon, Abomasnow, so we could tell the difference if stat stages affect Gyro Ball. If your Pokemon with Gyro Ball is slow enough, it doesn't make a difference. :P
Hope I helped!
Note from Meta Ridley:
Iron Ball affects the power of Gyro Ball as well, look at these calcs:
With Iron Ball;
> 252+ Atk Bronzong Gyro Ball (111 BP) vs. 252 HP / 252+ Def Abomasnow: 266-314 (69.2 - 81.7%) -- guaranteed 2HKO
And without Iron Ball;
> 252+ Atk Bronzong Gyro Ball (54 BP) vs. 252 HP / 252+ Def Abomasnow: 132-156 (34.3 - 40.6%) -- guaranteed 3HKO
