How many crashes are caused by (too) high speeds?

Internationally, it is generally assumed that about one third of fatal crashes are partly due to speeding or to inappropriate speeds (see [9] [12]) for instance). Yet, it is hard to determine precisely whether (a too) high speed is the main cause since, apart from speed, there are other factors that may lead to a crash. It is particularly hard to determine objectively whether a certain speed was too high under the prevailing circumstances.