Thirty-one years ago, hordes of media and onlookers camped out near St. Mary's Hospital in London, waiting for the arrival of the newest royal heir.

Since the birth of that heir, now-expectant father Prince William, medical science has mapped the human genome, cloned a sheep and created a vaccine to protect against chickenpox.

But when it comes to medicine's skill at predicting the arrival of the royal baby — reportedly due Saturday for Prince William's wife, Kate, the Duchess of Cambridge — not much has actually changed.

"If you're taking an office pool and trying to pick a day, we are as bad at that now as we were 30 years ago," said Hyagriv Simhan, chief of maternal fetal medicine and vice chair of obstetrics at Magee-Womens Hospital of University of Pittsburgh Medical Center.

And even though doctors have made advances toward accurately predicting due dates, they still can't explain what makes one baby stay snugly in the womb while others bust out ahead of schedule.

"Should I be able to answer that question, I would receive the next Nobel Prize in medicine," said Eugene Scioscia, vice chair of obstetrics and gynecology for the West Penn Allegheny Health System in Pennsylvania. "It's been studied ad nauseam, and we don't know."

Pregnancy is still dated, as it has been for decades if not centuries, primarily by the date of the mother's last menstrual period, Scioscia said.

The biggest change in the field has been ultrasound technology, which was just getting started in pregnancy use in the early 1980s.

Using ultrasounds, pregnancy can be dated much more accurately. And the earlier the ultrasound, the more accurate the date. The advent of first-trimester genetic testing, which has become popular in the past decade, has pushed ultrasounds earlier and earlier, Scioscia said, meaning that women have a better sense of their due dates than they did even a decade ago.

Home pregnancy tests have helped, too, he said, because women are aware of their pregnancies closer to the date of their last menstrual period.

"We can really narrow someone's due date in terms of accuracy quite well," Scioscia said.

But even if the due date is known to the minute, that doesn't mean that a baby will come out on time. "It happens when it's going to happen," Simhan said. For the majority of women, he said, that day is between 38 and 40 weeks.

A 2002 study found that 52 percent of spontaneous births — those that did not involve cesarean sections or inductions — took place between weeks 37 and 39. After 42 weeks, the chance of stillbirth increases substantially, Simhan said. Decades ago, women were allowed to go beyond 42 weeks more frequently, because the dating of the pregnancy was much more of a guessing game.

Regardless of the timing of this royal birth, the first communication with the public is likely to be with an official notice on a glass-fronted easel at Buckingham Palace. Depending on the time of day, a 41-gun salute will then take place in Hyde Park.

And then — and only then — will the palace begin to announce the birth via Twitter — yet another advance since the last royal baby watch outside St. Mary's.