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From City Limits: "The Real Math of An Affordable Housing Lottery" (light competition for middle-income AY units)

In January, the online publication Bklynr wrote, in Lottery Opens Tomorrow For 300+ Affordable Units At 38 Sixth Avenue:
Demand for affordable housing in other Pacific Park buildings has been profound. According to the developer, the lottery for 461 Dean Street received more than 84,000 applications for 181 below-market units; and 535 Carlton Avenue’s lottery drew roughly 95,000 applications for 298 apartments.
Similarly, Curbed called some 179,000 applications for affordable units in those two towers a "tremendous response."

That's par for the course. A 12/15/15 New York magazine article, Affordable Housing Could Look Like This, related, "How long were the odds? There were 925 units available in the complex, and 92,925 applicants — a population roughly the size of Albany — entered the lottery."

And a front-page New York Times article, 1/30/15, Long Lines, and Odds, for New York’s Subsidized Housing Lotteries, similarly recounted long odds and quoted an affordable housing developer: “It really shows how desperate the need is for affordable housing.

535 Carlton affordable housing lottery; mostly middle-income units
But that doesn't quite ring true. There's a desperate need for low-income affordable housing, surely, but not a commensurate need for middle-income housing below-market rates.

And now we have some numbers to back up that common-sense intuition.

In City Limits

As I write in an article for City Limits, headlined The Real Math of An Affordable Housing Lottery: Huge Disconnect Between Need and Allotment, such catch-all statistics camouflage how low-income applicants face crushing odds compared to middle-income ones:
Exactly 92,743 households (not quite 95,000) entered the lottery for the "100% affordable" 535 Carlton tower, city data show. But only 2,203, according to City Limits' analysis, were eligible for 148 middle-income apartments, such as one-bedrooms renting for $2,680 monthly and two-bedrooms at $3,223, affordable to those earning six figures.
...Notably, for 44 two-bedroom apartments renting at $3,223 a month, only 360 households initially qualified. Given that half of 535 Carlton’s units are designated for residents from nearby Community Districts, the 111 applicants with that preference seemingly had a one-in-five chance for 22 apartments.
For the rest of the article, please click here.

Below, some graphics not part of the article. Note the color-coded comparison between unit distribution and distribution of applicants. In other words, the purple wedge represents about half the units, but a tiny fraction of applicants.

The units available


The universe of applicants
Pieces of the pie that jut out from the chart are households ineligible for the lottery. This chart avoids double-counting households that qualify for two income bands by subtracting the overlap evenly between the bands. 
The universe of applicants, alternative version


Pieces of the pie that jut out from the chart are households ineligible for the lottery. This chart does double-count households that qualify for two income bands by counting them in each. That makes Bands 3,4 and 5 slightly larger.
The units available, with rent levels


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