Brown dwarfs are intermediate between planets and stars. They are not massive enough to undergo hydrogen fusion in their cores, as required to be a star, but are too massive to be planets, and can fuse deuterium. Those conditions produce a range from about 13 Jupiter masses to about 80. Some people, however, argue that the distinction between a planet and a brown dwarf should not be about their mass, but about whether they formed in a star-like way, by gravitational collapse, or in a planet-like way, by accumulation of planetesimals in a proto-stellar disc.
WASP was designed to look for transiting Jupiter-sized planets, but brown-dwarf stars are much the same size as Jupiter and so produce planet-like transits. That means we only discover which is which by measuring the mass of the transiting body by radial-velocity techniques.
So we should find brown dwarfs as readily as planets. But we’ve found only two, WASP-30b and now WASP-128b, compared to over 150 planets. That means that closely orbiting brown dwarfs must be much rarer than planets. It seems that star-like, gravitational-collapse formation rarely produces objects with a mass as low as 30 to 50 Jupiters (that’s not enough mass to collapse easily), while planet-like accumulation of planetesimals rarely builds up to mass that high (there aren’t enough planetesimals).
Which means that WASP-128b, newly announced on arXiv today in a paper by Vedad Hodžić etal, is a very rare object, being a brown dwarf with a mass of 37 Jupiters in a 2-day orbit around a G-type star. The nearest comparable object is KOI-205b, at 40 Jupiter masses, though that transits a star that is 2 magnitudes fainter and so is harder to study.