How have studies revealed that one third of babies being born present complications by having their umbilical cord wrapped around their neck.

A nuchal cord is when the umbilical cord iswrapped around the baby's neck. This happens during pregnancy as the baby moves and turns.
There's a wide variation in numbers given, but it happens during pregnancy somewhere between 15 and 37 percent of the time. A little under half of them will resolve by the time of delivery.
Umbilical cords are thick and fat. A gelatinous substance called Wharton's Jelly supports the two arteries and single vein of the umbilical cord.
I delivered a baby just last week whose umbilical cord looked like this. The baby was absolutely fine.

When a nuchal cord or an umbilical cord knot becomes very tight, this can result in abnormalities of the fetal heart rate or even stillbirth. Luckily this is rare.
We can sometimes identify these with ultrasound. When we do, it presents a dilemma. Although they are generally have no significance or complication, it can be very stressful when patients think about their baby having a cord around the neck. I have heard various arguments about whether or not patients should be told.
In my clinical experience, I see a nuchal cord at the time of delivery around 15 to 20% of the time. Occasionally there are double or even triple nuchal cords (or body cords and other strange variations). Usually the baby delivers without any management of the cord. Sometimes I have to unwind the cord or even very rarely clamp and cut the cord to accomplish delivery.