Arc System Works' latest multi-platform fighter launched last week with its producter jokingly hoping for a collaboration with NieR Automata in the future, and its sales thus far has been decent considering the game wasn't exactly created from scratch.
According figures by Media Create via 4Gamer, BlazBlue: Cross Tag Battle's launch week sales for Japan was 11,696 units for the Sony PS4 and 4,271 units for the Nintendo Switch, totaling to 15,967 units. Figures include limited edition, but not digital sales which is relatively negligible for the Japanese market.
As a rough comparison, its figures for the PS4 is slighly better than Guilty Gear Xrd: Rev2 (10,609 units), and about half of The King of Fighters XIV (21,525 units). It still beated Marvel Vs Capcom: Infinite (8,273 units).
http://www.4gamer.net/games/117/G011794/20180606071/