Citation needed.
From what I've read, men who choose to contest custody, usually win. That's because he's likely making more money and is therefore in a better financial position to take care of the children.
Women usually get custody because men don't usually contest it. That's not to say that it doesn't come up. But men often trade the threat of a custody battle for other things in divorce proceedings.
P(male wins | male is richer) != P(male wins)
That said anyone quoting statistics should be able to back them up. I encountered the custody figure, along with a lot of other useful information about how the results of divorce are harder on women than men, in http://www.amazon.com/Price-Motherhood-Important-World-Value.... It is an interesting read, though not exactly the sort of thing you want your wife to encounter during her first pregnancy. (Which is how I learned about that book...)
"Despite changes in the law and social custom, custody arrangements remained remarkably stable over the past three decades. National estimates in the 1970's and 80's indicated that women had sole custody of the children approximately 85% of the time, and men retained sole custody 10% of the time, with the remaining 5% spread over a variety of custody arrangements, including grandparent, split or joint custody. More recent data sets indicate that father custody figures may be closer to 15%. " http://www.stanford.edu/group/psylawseminar/Child%20Custody%...
It goes further as said as joint custody became an option an increasing number of family's took that option. This suggestion a large scale imbalance where large numbers of men would like to have more custody but they are far less likely to get it.
Argument ad hominem much? I agree that the author has an axe to grind, but she backs her claims up with research.
And anecdotally her claims match my experience. I've seen a lot of friends/relatives/acquaintances get divorces, and from what I've seen the men generally want to see the kids some, but usually want the women to take the bulk of the child-raising work. Exact visitation arrangements get contested, but men seem more than happy to leave most of the work to the mom.
Biologically you can look at say men’s increased chance of baldness vs. PMS and think men have an advantage. But socially the cost / benefit analysis is harder to balance and harder to suggest that one side has a clear advantage because it comes down to how you weigh different parts of the equation.