When you don't sleep well your body doesn't recover quickly, this is because when your injured your body has to work a lot harder to recover, so you need good quality sleep to counter this.
Believe it or not, when you sleep there is a lot of repair that's going on while your body and brain can rest, this allows more energy to be spent on repairing your muscles through the production of hormones which stimulate growth and repair, allowing the process of healing to take place. During your sleep less blood in needed to get to your brain as it rests, so more blood can be sent to your muscles for recovery.
When we're in pain, our body tends to tense up due to a protective mechanism as a means of guarding us which your brain does automatically to stop you being in any more pain. As a result we stay in alert mode affecting our sympathetic nervous system (our fight or flight response) causing us stay alert and awake using up even more brain power for energy.
We need around 8 hours of sleep per night, but you want to make sure your in a deep sleep for that period of time. Waking up during the night will disrupt your circadian rhythm, this is a sleep rhythm that affects energy, mood and behaviour.
Repair as well as energy is needed for the body to recuperate. So, focus on not just the time but a sound nights sleep.