Eleven roses: honest comparison with the counts either side
Nobody buys a count in isolation. The real question at the counter is whether to go up or down from the number already in mind, and eleven sits in the middle of the range where those decisions get made.
It is worth knowing what you gain and what you give up.
Against nine
Two stems make less difference than most people assume. The heads pack into a circle, and each additional bloom adds less to the diameter than the one before it, so the jump from nine to eleven is felt in density rather than width.
What you do get is a fuller centre. Nine can show a gap at the top if the heads are small or the calibre uneven, while eleven closes that gap and gives the florist a spare stem to correct the profile with.
You also cross a line in how the bouquet is read. Up to about nine, most people register the number itself; past that they see an armful and stop counting. If you want the count to be noticed, take fewer stems and a longer cut.
Against fifteen
Fifteen is where a bouquet stops being comfortable. The binding point grows thicker than a wrist. Two hands are needed for anything longer than a short walk. The vessel it wants is a wide, heavy one that many homes simply do not own, and a narrow vase turns the dome into a column. None of that makes fifteen a bad count, but it does mean somebody has to think about where the flowers land.
Eleven avoids all of that while still looking substantial. It travels in one hand, it goes into an ordinary wide vase, and it does not commit the recipient to rearranging a table.
Where fifteen wins is distance. Across a hall, on a stage or at a table set for guests, the larger armful holds its scale, and eleven quietly becomes part of the background.
When a different count is the better call
Some situations answer themselves. A gift left at a reception desk or carried on public transport argues for fewer stems, since a large bouquet spends the journey being protected rather than admired. A large anniversary or a public presentation argues for more, whatever the budget suggests.
There is also the case where the count should not move at all, and the calibre should. Eleven heads of a densely petalled variety read bigger than fifteen small ones, and swapping length or head size costs less than adding stems.
The odd number question
Eleven falls on the odd side, which matters in some traditions and means nothing in others. Where odd counts are customary for the living, it is the safe choice; where nobody counts at all, it passes unnoticed either way.
That is the whole practical value of it. An odd count is rarely wrong and an even one occasionally is, so when you do not know the recipient's habits, the odd number costs you nothing.
There is a building reason too, quite apart from custom. An odd count settles into a spiral around a single central stem, whereas an even one tends to split into two halves that the florist then has to pull back together.
If the recipient in Brooklyn already receives flowers regularly, the count will interest them less than the variety and the shade. At that point eleven roses of one clean colour say more than a larger mixed armful.