Following a year in which artists gunning for a No. 1 album hawked hoodies, lawn signs and nutritional supplements together with CDs and digital-download codes to boost their sales numbers, Billboard is seeking to bring order back to its flagship albums chart.

The sale of branded merchandise—from sweatshirts and T-shirts to fanny packs and beanies—has become an increasingly popular and lucrative business for many artists, particularly rappers. In recent years, with rising demand for such novelty items, artists have been tying...