Another thing to consider with grenades (and other explosive items such as mortar rounds) is that when they hit the ground they channel most of their explosive force upwards and out.
When I was in the Aussie Army the basic drill for a grenade landing near you was to immediately go prone because there is a good chance that the fragments will miss you. This is because the ground itself will force the explosion to form into something like a V-shape, pushing up and out rather than around.
You're still going to be hit with the concussive effects and there is still the chance you'll be hit by fragments but being prone increases your odds of missing serious injury and for not being killed outright.
<evil Referee trick> Of course, a skilled thrower (and more so if he isn't being shot at, at the time) might be able to time his throw so that the grenade explodes while it's still in the air - then all bets are off!
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