In my write up on variation in inheritance patterns for Slate last week I did not explore the likely quantitative distribution in any detail (frankly, I think that part is confused or muddled at best). My primary focus though was on the empirical reality of variation, which people utilizing personal genomic services will receive, perhaps to their surprise. But in part triggered by that Slate piece and follow-up discussions at Twitter with Michael Eisen, Graham Coop decided to crunch the numbers. More concretely he took the known patterns of recombination in the human genome (from a paper he co-authored, Broad-Scale Recombination Patterns Underlying Proper Disjunction in Humans), and input these values into a simulation which generated distributions of contribution from maternal and paternal grandparents, How much of your genome do you inherit from a particular grandparent?
As Coop observes, one of the most surprising things is the very long tail of distributions for paternal grandparents. This is due to the lower recombination rates in males. Remember that recombination tends to reduce the variance in transmission from the grandparental generation, so reduced recombination increases the variance. Therefore, you see that 1 in 200 sperm are skewed such that 20% or less of genetic material in the sperm is from one grandparent. Because you have to divide this by half in the fertilized zygote, what this means that in 1 in 200 individuals you have a case where 10% or less of their genome is from one paternal grandparent, and 40% or more from the other! The histogram for females, as you can see, is much less dispersed, though the variation there is not trivial either. I suspect that the scientists at 23andMe almost certainly know the empirical distribution, as they likely have many pedigrees to compare. It would be nice if they shared that with us.