Thanks for the reply, @paulj

Your Figure 9 looks promising. That's a more plausible distribution of show ratings, rather than the bimodal distribution under the current rating system.

One other idea I just had, which would address the point that @zeron and others have made... We see users mostly rating shows 4 or 5 rather than using the full range. Personally I think this is fine. However, if we want to "spread out" the resulting scores, the site could display each show's percentile ranking, in addition to (or as an alternative to) its avg star score.

So --- just making numbers up --- a given show might say: "Show rating: 3.914, 42nd percentile among all Phish shows"

That way we would have an absolute measure as well as a relative measure of each show's quality.