Oops. I published this earlier but my underlying number crunching had a mistake, which of course I've now fixed.

This is an exercise in statistical curiosity... some game ratings might be dominated by a bunch of pessimists dragging it down, or a bunch of optimists giving it a boost.

There are 25,000 game raters on BGG and 3,500 ranked games. An average ranked game has 260 raters, but that's mostly because a few games have thousands. Half of ranked games have fewer than 90 raters. What if those 90 (or fewer) happen to be characteristically low or high raters, either by chance or because the game attracts mostly negative b*stards to play it?

So I thought I'd check it out. Here's the waffle, followed by the list of most affected games...

First I assigned each user a User Optimism value. This is the average value of their own rating for each game above the game's overall BGG rating. ie how much higher/lower does this user characteristically rate games than everyone else? Raters vary quite a bit in measured "optimism". (Particularly people who only rate one or two games of course.) The standard deviation across all users is about 0.7 of a rating point. The average user optimism is about +0.25 of a rating point, which happens because the more games someone has rated the lower their ratings tend to be so a few pessimistic users can drag all the ratings down. Like this:

Rates # Users Avg Opt Std Dev
1->9 10651 1.03 1.30
->99 11400 0.27 0.67
->999 2876 -0.11 0.56
->9999 10 -0.23 0.51

Then for each ranked game I found the average Optimism for the game's raters. For this bit, I ignored the Optimism rating for any user who rated less than three games, since the granularity of integers would dwarf their optimism measures AND for one-game-raters in particular we'd like to let them have some opinion other than average. Instead I assume anyone with three or less rating has the same Optimism as average everyone else on each of their games.

Then I took the average Optimism and adjusted the game's overall rating, taking into account the Bayesian calculation used on BGG. There's a slight level of approximation because I can't say how many ratings are removed by Aldie's ShillSeeker Filter (tm, pat pend).

The result was a bit of an anticlimax. But you've read this far so you might as well have a look!