I'm 38 weeks with our 3rd baby.
I've noticed that this time around the baby has dropped 3x and then grown back up into my ribs with his head still engaged for the past 3 weeks. Today, however, my midwife actually had a 2cm reduction in fundal height measurement from his latest drop, whereas the previous times he had not dropped enough to affect my fundal height.
With our 1st, there was no dropping at all, he was at -2 station in labor for 19 hours before he moved to -1 station (he was also posterior).
With our 2nd, we dropped 3 days before, then he was at -1 station and went straight on to crowning at +2 station within an hour.
I think the dropping beforehand may indicate a shorter labor since there is more pressure on the cervix and the head has descended somewhat, however I don't think it is related to how much longer until labor ensues. I, too, wish there was a formula to calculate when you would go into labor but I've been losing mucus plug pieces for 3 weeks now and have had on/off stalling labor bouts for 3 weeks as well at this point.
All signs have pointed to labor for 22 days now...sooooo....I'm calling my body's bluff and just hoping labor actually comes at some point, ha!
I'm not having cervical checks performed (not this time) and have been unable to reach my cervix on my own - but then again, I do know that my cervix is unusually high and to the left when non-pregnant AND all the way into very active labor it has been hard for docs to reach my cervix previously, so cervical location is not even a measurable factor for me.