B737 Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 212; Flight Crew Type 4822
Situational Awareness
Ground Event / Encounter Loss Of Aircraft Control; Ground Excursion Runway
Flight Crew Requested ATC Assistance / Clarification
Human Factors; Weather
After normal FO landing; I took control of aircraft approximately 80 knots.  I knew there was an aircraft behind me and we had to clear at the end.  Since braking action was reported as fair I decided to high speed taxi to about the two board.  I applied brakes with no deceleration. I increased braking to max manual.  I attempted to steer aircraft onto taxiway and tried to redeploy reversers but once I realized we were going to overshoot; I closed reversers in order to minimize damage.  After aircraft stopped; I was a little in shock; but realized I had to take further action.  I got a 'remain seated' PA out; started APU; got the engines shut down; asked the FA's if everyone was okay. We informed ATC; FODM; did parking checklist; and submitted [a] report.
I landed the aircraft in the touchdown zone but beyond the 1;000 [feet] markers; went MAX reverse; the speed brakes deployed; and the autobrakes began to work well quickly. I could see the 3;000 feet runway marker down the runway in front of us; so I knew we had a little less than half the runway remaining (somewhere between 3;500-4;000 feet left by my estimate) and we were quickly slowing around 100 knots. Since I did not feel that we needed MAX brake pressure for our planned runway exit anymore; the aircraft was slowing well and braking action appeared to be good; I stated that I was switching to manual braking to slightly decrease our braking. My intent was to still brake strongly; but less than MAX autobrakes since we [planned to] roll to and exit at the end.Almost immediately as I said this; the Captain said; '100 knots; I have the aircraft.' I released my brake pressure and gave him the aircraft with 'You have the aircraft.' He immediately proceeded to stow the reversers and speed brake in an effort; I assume; to help decrease our deceleration rate and get close to the end sooner thus not make the other aircraft go around. The deceleration decreased significantly. Shortly after; I still hadn't made the 80 knot call and could see the 2;000 feet remaining marker approaching. I stated to the Captain 'You really need to start slowing the plane down.'I still did not sense much deceleration; but could begin to feel the aircraft skidding. We slowed through 80 knots and I made the '80 knots' call. I was still not comfortable with the deceleration rate and hadn't received a verbal reply to my statement of needing to slow down; so I pressed as hard as I could on the brake pedals just in case he was not at MAX manual pressure. I think this happened around the 1;000 feet remaining marker. Around this point; I believe the Captain went into reverse again; but I don't fully remember. I could sense the Captain was trying to steer for [the exit] but the aircraft skidded in a diagonal. It came to a stop shortly thereafter.I am not sure at what speed we exited the pavement; but it felt like it would have been quick even for a dry runway. When the aircraft stopped; the Captain told the passengers we went off the runway and to remain seated. I told ATC that we were off the end of the runway and would need a tug. He asked the flight attendants if everything was okay in the back. They replied it was. ATC asked if everyone was okay. I replied yes. I ran the After Landing Flow. I asked if he wanted to shut down the engines. He replied that he did; so we started the APU and shut down the engines and did the Parking Checklist.
B737 flight crew reported they slid off the runway after landing on a slick runway.