Earlier quoted context omitted.
Ha! Thanks for this. I knew that this must be a solved problem but wasn't searching for the right thing. I'll take a look at implementing a better default sort order.
For another similar rating system, there's also this one: https://steamdb.info/blog/steamdb-rating/ Not exactly sure how the two compare.
Compared to Wilson's formula, it's very short, and it's not nearly as difficult to understand the idea behind how it works. One could easily get the question "Why would this random formula give better results than what a very established mathematician came up with?" I can't really answer that, but it would seem a lot of you agree that it does indeed produce better results when rating Steam's games. I can, however, try to give some insight into this.
For one, Wilson's formula isn't really meant to be used quite like this. It takes a rating and the sample size (the number of reviews), and outputs a confidence interval. And a confidence interval basically says that “We are some% sure that the score is between x and y”. If you increase the % of how sure you are, the distance between x and y also increases, and vice versa. But to get a single rating, it's not quite okay to just take the lower bound of that interval.
Secondly, because of what was mentioned in the last paragraph, it always gives us a lower rating than the original. This is clearly the incorrect behaviour, as something that just came out and gets a single negative review will be marked as having a score of 0%. Meanwhile, an established terrible game can have 10 positive and 500 negative reviews, and it will rank higher. This is also the reason why one of the two rules I listed was that all ratings should be biased towards the average.
Finally, while Wilson's formula probably gives us a more “precise” rating, so to say, it's not necessarily what we want to see. There's a lot of mathematics behind why what it does is correct, while the previously mentioned numbers of 2 and 10 that I picked for my formula were rather arbitrary. Still, I selected them so that the result would also account for the high number of reviews when assigning a good score. It's why you'll probably notice a lot less games with a low review count among the top games than before.
I think that's important because a game that is very popular and very highly rated should be ranked higher than a game that isn't as popular and is also very highly rated. Not because we can be more certain that this rating is indeed correct, but because you, as a random person who has yet to try that game, will more probably like it if a lot of other people have liked it as well — if it's not a niche game. And I think this aspect is definitely important and should be accounted for when trying to represent an entire game with just a single number.