There is no correct single answer to your question because it depends on many factors such as what was done, when was the surgery performed, how much bleeding during the operation, etc. Your surgeon, who you trusted to operate on your face, is the best person to respond to you.
There are many variables that go into how much the tip may drop after the surgical procedure. Depending upon whether or not there were structural cartilage grafts, the placement of the incisions, and the variable healing process for each individual person.
The nose can droop after rhinoplasty. However, a competent board-certified rhinoplasty surgeon should thoroughly evaluate you nose pre-operatively. They will make an assessment of the potential of drooping. If they think it could happen, they will perform additional procedures (such as a strut) to minimize the chance of it happening. Best wishes.
Taping and swelling usually lead to a more upturned tip immediately after the surgical procedure that we expect to reverse during healing. Over the longer term there is some loss of tip support elevation and most but not all patients. The drop however should not be very noticeable but more on the subtle side in my opinion.Discuss what to expect during your rhinoplasty recovery with your board-certified plastic surgeon and enjoy your results. Understand that the nose changes for 12 to 18 month period following rhinoplasty and generally speaking simply improves with time.
If the nose is very long and skin very thick, (long skin sleeve) then the nose may drop significantly. However this condition is not that common. In my practice, some small drop, is expected in the average case..
Depending on the position of the tip prior to rhinoplasty, and the nasal anatomy, the tip can raise, stay the same, or droop. These changes are usually quite predictable prior to surgery.
An experienced nasal surgeon will recommend the appropriate measures to achieve a good postoperative tip position. Often this requires support of the tip, particularly if the nose is large and tip support is poor. Likewise if the tip is large but already positioned high, reduction in tip cartilage will cause the tip to raise further.
As in most facial surgeries, balance of the columella and alar regions with the tip and dorm is important, so an artistic sensibility is important in nasal surgery.
A good tip position is one of the most important goals in rhinoplasty. Projection (how much it sticks out) and rotation (how much the tip is upturned/drooped) contribute to this outcome.
Depending on the surgeon and surgical technique, the tip may be set at the time of surgery with no expectation for movement. The nose will be more firm with this technique. Another technique creates a less firm tip with an expectation for a small amount of tip drop after surgery. The surgeon anticipates this drop and starts the tip slightly higher in surgery.
Swelling in recovery masks the result regardless of technique. Every rhinoplasty patient will have to wait for the swelling to dissipate to see the end result.
Talk with your surgeon and keep up with the follow-up appointments for the best outcome.
The amount of tip refinement and definition will increase as the swelling resolves. The tip rotation (how upturned it is) will also improve - as the swelling decreases the tip will drop a bit.