It is the avi chai foundation study that provided the intial basis. feel free to research it.
your sentence
“There are 105 boys born for 100 girls. AT year 18 there are 1,890 boys vs 1000 girls. Argument sake, 10.% of the girls marry. That leaves 900 Girls versus 1,790 boys left.”
there in lies your mistake. at year 18 there may be 1890 boys and 1000 girls (it should actually be 1050 based on 105/100).
HOWEVER what you error in is that these 105 boys don’t date those 100 girls. you need to match up the boys who are 22 (or 23) when these girls turn 18. Due to population growth the number of 22/23 year old boys farout number the number of 18/19 year old girls.
what you have explained beautifully is shiddcuh crisis in the chassidishe oilam where the boys beging shidduchim at 18. Perhpas that is the community you are familiar with and thus present your arguments.
Feel free to use this forum but I personally won’t use this fourm anymore to discuss the mathematics. You can look at the tens of old posts if you’d like to see the mathematical expalnation.