06.08.17

Fully completing Danganronpa 2 requires a shocking amount of time, possibly another full day after completing the main game. Mainly that maxing your Island mode relationship with each character takes a ridiculous amount of in-game days, which requires multiple playthroughs. The light novel took me only about 1-2 hours, and I really enjoyed it. But I skipped maxing my relationship, instead opting to view the dialogue from other people's playthroughs. So that's not entirely the reason why I still didn't start a new game today.

I spent more hours than I care to admit thinking up a new formula with which to give Steam's games a proper rating based on their review percentage and the number of reviews. It took a few tries to come up with something that'd at least seem better than what I previously had. Basically, what I wanted was something that would: a) Estimate the result closer to 50% the fewer reviews it had. b) Get ever more slowly closer to its actual rating as its number of reviews increased but never quite reach it.

I previously used Laplace smoothing and took the base 10 logarithm of the number of reviews so that it would approach the given rating much, much slower than regular Laplace smoothing. α = 0.5, β = 1.0 I had two problems with this. The first one was that I didn't actually understand what this formula was doing. Just that it was moving ratings with a low sample size closer to α / β, ratings with a high sample size closer to the real rating, and that I could control its "adjustment intensity" by increasing or decreasing α and β or the base of the logarithm. The other problem was that it gave highly rated games with a low sample size too good of a rating, and if I were to turn the knob to value the sample size more, then it would start to over-value the sample size on ratings with a high sample size.

So I sat down and started to make a formula from scratch that would fill the criteria mentioned above. After tweaking the numbers I settled on "A game with 10x the amount of reviews should have 2x the score certainty." Alternatively "...half the score uncertainty." would describe it better. So if a game with 1 review had an uncertainty of 100% (certainty of 0%), then something with 10 reviews would have half that uncertainty - 50%, 100 reviews - 25%, and so on. And what certainty means is just how big of a portion of the final rating would be the actual rating, and the remaining would be 50%. Putting that all together: r - (r - 0.5) * 2^{-log₁₀(a + 1)}, where r is the rating and a is the amount of reviews. This definitely emphasizes the amount of ratings more when there aren't many of them, and the actual rating itself when there are. It also has two "knobs" to turn, should I want to adjust it, instead of just the one the previous formula had.

But, uh, I'll get around to a game by the name of Monster Slayers tomorrow.