Peter Muller has the most succinct summary of this that I've seen in his (very worthwhile) opinion piece on proprietary trading [1]:

Sharpe Ratio, Marketing department

≤ 0: Runs the firm

0.25: Very important; involved in all investment decisions; major focus on asset gathering

0.5–1.0: Secondary

1.0–2.0: Almost superfluous

≥ 2.0: What marketing department?

[1] https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2004/...