Its not like 400 players is all there is. You can't use the same refs for every game. Can't make the same 5 camera guys do every game. There's probably another pool of 200 ancillary bodies who don't ever log a statistic that are needed to make it work as NBA entertainment. So your 400 number is already out the window. 400 players still means another (just a guess) 200+ bodies as overhead.
I don't have 400 players.
16 teams x 12 players = 192 players.
Add in your 200 ancillaries and voila 400.
Admittedly, 400 is just a guesstimate, but at least provides some parameter/guidelines for what we're talking, and seems a fair approximation.
I was thinking 3 coaches per team (3 x 16 = 48)
2 trainers, a medic, lockerroom guy, massage guy = best if a team can be limited to 5 extra personnel(?) 5 x 16 = 80.
So I have 20 people per team x 16 = 320. 19 would be 304.
Add in 100 ancillary. And there's 400.
If they need 200 ancillary, you're close to 500.