(Victor J. Blue/Bloomberg)

As it turns out, there are strict conditions on who can qualify for principal reductions: Homeowners have to be facing imminent default, they can’t be backed by Fannie or Freddie, they must occupy their home, and their mortgages have to be serviced by one of the five firms that were part of the agreement.

All told, Gayer estimates that just 5 percent of total underwater mortgages will qualify. Of these eligible borrowers, the average underwater homeowner would receive about $20,000 in principal reduction, although the agreement mandates bigger reductions for the most distressed borrowers that could raise the total amount of principal reduction to $34 billion.

By comparison, officials had originally estimated that up to a million homeowners could receive principal reductions under the deal — twice Gayer’s total. Gayer openly admits that his estimate is just a back-of-the-envelope calculation that relies on different data sources and “simplifying assumptions,” detailing his full methodology here.

Outside of the principal reduction, there are other ways that homeowners will benefit from the settlement as well, with $3 billion dedicated to refinancing for homeowners who are up-to-date on paying their mortgages, and payments of up to $2,000 to homeowners who were foreclosed upon. But Gayer’s calculations could spur on those who believe the settlement has fallen short of expectations.