Some morbid weekend reading: "The global health effects of nuclear war," by Brian Martin, published in Current Affairs Bulletin in 1982. A section on overkill:
Many people believe that the capacity of nuclear weapons for 'overkill' means that all or most of the people on earth would die in a major nuclear war. In spite of the prevalence of this idea, there is little scientific evidence to support it.
Many calculations of 'overkill' appear to be made using the nuclear attacks on Hiroshima and Nagasaki as a baseline. Estimates of the number of people killed at Hiroshima from a 13kt bomb range from 63,000 to over 200,000. Adopting a figure of 130,000 for illustrative purposes gives ten people killed for each tonne of nuclear explosive. By linear extrapolation, explosion of a third of a million times as much explosive power, 4000Mt, would kill a third of a million times as many people, namely 40,000 million, or nearly ten times the present world population.
But this factor of ten is misleading, since linear extrapolation does not apply. Suppose the bomb dropped on Hiroshima had been 1000 times as powerful, 13Mt. It could not have killed 1000 times as many people, but at most the entire population of Hiroshima perhaps 250,000. Re-doing the 'overkill' calculation using these figures gives not a figure of ten but of only 0.02. This example shows that crude linear extrapolations of this sort are unlikely to provide any useful information about the effects of nuclear war.