Multiple studies (here, here, here, here) have attempted to figure out the simple question - Is icing after injury beneficial? But unfortunately it’s difficult to conduct a study where the person being iced isn’t aware of their injury becoming cold or not, as the case may be. Therefore the studies have been somewhat underwhelming in the outcomes; mostly inconclusive.

The well known acronym R.I.C.E. (Rest, Ice, Compression, Elevation) is broadly based around the idea of limiting further tissue injury, however it has now come to my attention (via @physiowizz - thanks!) that the old rule is out as ice actually delays healing and the new rule is R.C.E. (not as fun to say, but we cant ignore the science!)

Rest: - Following injury you need to stop using the damaged tissue to prevent further injury ie stop playing. 

Compression: - Support the tissue or limb with compression ie bandage for 48 hours. This helps control swelling and support injured tissues in the important first 2 days. Healing is taking place but it is vulnerable to re-injury.

Elevation: - Lie down, keep the affected limb above heart height, let gravity help drain the excess swelling away.

Not scientific in any way, but from my own experience seeing a sprained ankle that has been managed well for the first 48 hours (using R.C.E.) compared to one that hasn’t, the injury is less painful, faster to return to normal movements and faster to strengthen through rehab.