In particular, cities with sports other than basketball (like Seattle, which has soccer, pro football, college football, women's basketball, and baseball teams, and could get a hockey team under the proposed arena deal) were unlikely to benefit economically from new basketball arenas.
According to Richard Florida, who wrote about the study (available for purchase here) for the Atlantic,
The study is carefully done and controls for a range of factors. It looks specifically at the economic impact of basketball arenas in metro areas, with an eye to controlling for how dynamic the neighborhood or local area was already. It includes factors that control for whether arenas are located in a downtown neighborhood, and how economically robust the downtown is compared to the surrounding areas, the total number of professional sports teams in each city, and whether the team shares its arena with a hockey franchise
Even in cases where basketball arenas do correspond with higher regional incomes, public tax subsidies for arenas tend to erase those gains. And the more recently an arena was built, the worse its economic impact is on the population. In arenas built during the latter years of the study, which looks at arenas built through 2009, city residents actually lost more than $2,400 in per-capita income. And in cases where city residents did better, that was because of a shift in income from suburban residents---who drive in to cities to go to games---to urbanites, meaning that the region as a whole doesn't benefit from basketball arenas.