Thought this was interesting so did some quick research. Numbers are not exact enrollments but close to it. Basically they are all similar in enrollment, if not the other schools actually have more kids and less principals. Not commenting on what this means, just pointing out that if you meant LONGWOOD when you said "schools similar in size", then OK, you are right- but you can't really compare Sachem to Longwood. So here is a more realistic look.
4 Assistants + 1 Principal:
Sachem East (approx. 2200)
Sachem North (approx. 2000)
3 Assistants + 1 principal:
Commack HS (approx. 2400 students)
Pat-Med (approx. 2800 students)
Ward melville (approx. 2000 students)
Every school has pretty much the same problems. Pat-Med is fullof gang & drug problems. If any school needs more AP's it's Pat-Med.
Ward Melville & Commack have their fair share of drug problems but they tend to be dealt with privately.
Longwood's problems in the high school are far less than you would tend to believe.
Sachem's drug & gang problems are just as bad as any other school but the parental support is lacking.
Cudos to all the parents involved in your children's life and their education. It the rest who are bringing this school district down.