Statistics are all good and well for documentation, but personal experiences are all that I can relate to.
My son wanted residential custody as they have "joint custody" meaning major decisions are to be made by both parent. Residential custody was ruled against him. His lawyer and several other lawyers told him that the state supreme court in Iowa had recently ruled in favor of the mother in several situations. I researched it but the legalese stuff got me so I can not tell you if it is true or not, but at least one case I found did indicate that. I consulted my brother who is a lawyer and he concurred that my son could continue to appeal, but the odds were stacked against him. My son's lawyer quoted him a 2-10% probability of winning an appeal (I do not know where he got those percentages, but it was his lawyer's experiences) and that at a minimum would be $5,000.00 IF things progressed as quickly as possible and would probably in the range of $10,000.
If things are really changing, I am happy for those fathers who got custody when they sought it. As I said, all I can go on is my personal experiences.