People died during tournaments. A splinter off a lance could make it through the eye slit in a helm. Falling off a horse could also be dangerous, even with armor and padding. And, there was always the chance that a small wound could fester and become fatal. Medicine was, lets say, a bit behind our times.

Not as dangerous as you would think; jousting was only done in competition and was a test of strength (lances are seriously heavy - imagine holding a 10-foot oak tree-branch horizontally with one hand...while riding a horse...) and riding skills (as your hands are both occupied by a lance/shield). The lances were blunted and aimed at the shields, as the way one scored points was either to shatter a lance against your opponent or to knock your opponent off their horse. Swords/axes/daggers would also be used, but they were blunted and the goal was a slash, not a stab (as generally you don't stab people from horseback, because it can throw you way off-balance). . Knight's armor was generally thick enough to not allow for penetration, and there was plenty of padding underneath to soften any blows. . Lance jousting wasn't done combatively because it was highly ineffective as a means of combat, so the mortality rate from actual combat is basically zero; obviously sword-based jousting was frequent in combat, so obviously the mortality rate there was relatively high. . Considering competitive jousting was an uncommon event almost exclusively done by nobility (who weren't out to kill each other, at least in that venue), deaths during competition were pretty low.