B737-800
Flight Crew Air Transport Pilot (ATP)
Situational Awareness
Ground Event / Encounter Loss Of Aircraft Control; Ground Excursion Runway
Flight Crew Regained Aircraft Control; Flight Crew Rejected Takeoff
Human Factors; Weather; Airport
The Tower cleared us for takeoff as we approached the end of the runway; so I decided to do a rolling takeoff. We rolled on to the runway [and] as we straightened out on the runway; I brought the power up and then applied takeoff thrust. The AC started to drift to the right so I applied left rudder; it didn't help so I closed the throttles and turned the tiller to the left. We still we're heading towards the edge of the runway when I started to brake. By this time I had full left rudder and full left tiller and we skidded sideways off the runway into the grass.  The runway surface was damp from the rain that went on through out the night. I wasn't actively thinking about slick surfaces and take off performance degradation but I was aware of the moist surfaces. This did have an adverse affect on my steering of the AC. I have thought this through and these are my assumptions. If I had applied too much thrust when taking the runway; I believe I would have slid off to the left; that did not happen. So after lining up and applying TO thrust I applied the appropriate amount at the appropriate time. I do not believe that the right brake was dragging or malfunctioned and caused the AC to veer to the right as all braking and steering on the taxi out were normal. The only other factor that is relevant is that the right engine didn't spool up the same as the left engine; thus causing the asymmetric thrust vector towards the right side of the runway. That along with the wet/damp runway; degraded my steering ability. The only thing else I could have done different was pull the power back to idle sooner so as soon as it started to drift off the center line.First and foremost; do a standing take off thereby eliminating any variable of differential thrust since the AC would sit still while the thrust settles down before release of the brakes. Not very practical at times but a sure fire way of dealing with it.
[Report narrative contained no additional information.]
B737-800 flight crew reported sliding off the runway at the start of the takeoff roll as a result of slippery conditions and asymmetric thrust spool-up.