Rules Ratio

From WEM's geeky stat to smoothing, residuals and the new unit "wem"

W. Eric Martin (WEM) ran the BoardGameGeek (BGG) news section for 15 years. Earlier this year, he launched his own outlet1 called Board Game Beat. In between his signature game release updates, he writes entertaining and insightful analyses of the broader hobby. In one of his recent articles πŸ—„οΈ, he proposed the Rules Ratio. The title invites us to geek out about it, so geek out we shall! πŸ€“

What is the Rules Ratio?

The basic idea behind the Rules Ratio is to look at how many rules questions a game generates. It stands to reason that a game with clear concepts and well-written instructions will leave players less confused than a poorly written rulebook. BGG offers a direct proxy for number of rules questions via its forums. Every game listing has a variety of such forums attached, including one titled Rules. Depending on the game, this particular forum might be the busiest, or completely void of any traffic. WEM proposes defining the Rules Ratio2 (RR) as the share of Rules threads3 among all forum threads:

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Debiasing the BoardGameGeek ranking

Bias is a bit of an ugly word, isn’t it? It certainly has become one of those battle phrases in the culture war, where both sides of the argument accuse the other of forcing their biases onto society. Board game reviews frequently need to justify themselves for their biases affecting their views. Dan Thurot πŸ—„οΈ recently wrote a very eloquent piece on the matter, diving deeper into different kinds of biases.

But bias also has a well defined meaning in statistics. Moving from emotions to cold hard numbers, the word bias loses its antagonistic nature and simply becomes a measurement one might want to minimise or remove entirely. Hence, debiasing the BoardGameGeek (BGG) ranking is about asking the question what it would look like if we removed the influence of a particular parameter. One such parameter is a game’s age: we’ve seen in the previous article that ratings have gone up over time, so removing the age bias from the BGG ranking means correcting for this trend.

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What was the best year for board games?

The highest rated years on BoardGameGeek

Corey Thompson (of Above Board TV and Dice Tower Dish fame) recently raised an interesting question on the Board Games Insider podcast:

In what year do you think the best titles (highest rated titles) were released?

He actually answered the question twice, first in episode #328 based on an analysis he ran a couple of years ago and then again in #330 with more up-to-date data. I’m not going to spoil his answer here – the podcast in general is worth a listen – so go and find those episodes on your favourite podcast platform. But of course I couldn’t help but answer the question myself, in the most needlessly thorough way possible. πŸ€“

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A brief introduction to Collaborative Filtering

Recommend.Games explained, part 1: how we recommend games to you

What is a good recommendation?

Collaborative filtering is the workhorse powering the recommendations by Recommend.Games. Over the years, I’ve been asked every now and then how it works. So, I thought it’s high time I outlined the basic ideas behind our recommendation engine.

Let’s first take a step back and talk about recommendations in general. What is it we’re trying to achieve? The answer to this question is far from trivial, and it gets harder when you want to formalise its goals. Maybe a somewhat naΓ―ve approach would be to say that we want to recommend items that the user will like. But recommendations are as much about predicting what the user wants as what they didn’t even know they wanted. Sometimes the most “correct” answer is also the least useful: maybe our #1 recommendation is Wingspan and the user indeed would love to play it - but if they already knew about it, why recommend it in the first place?

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The world of board games

Board game rankings by country

BoardGameGeek (BGG) users can select their country of residence in their profile. The main purpose is to find other users in your region to play face to face or maybe trade games, but but over here at Recommend.Games we obviously cannot help ourselves but to use this information for some interesting statistics. πŸ€“

Let’s start with the usual disclaimer: We will have to rely on whatever information BGG provides. In particular, users can freely choose their country. As mentioned, this is meant to be the country of residence, but some users might rather choose their country of origin – or some outright nonsense. There are 19 BGG users who claim to be from πŸ‡¦πŸ‡Ά Antarctica, for example. While I’m sure that the long polar nights on lonely research stations are perfect for playing board games, I’m not sure if they have a lot of time to rate them on BGG. 🐧 (If they actually did, Antarctica would have 6,880 ratings per 100 thousand residents, which would make them the second biggest board game enthusiasts in the world – only behind the πŸ‡»πŸ‡¦ Vatican’s 6 reported users, resulting in almost 20,000 ratings per 100 thousand residents. πŸ™)

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Has board game rating inequality increased over the years?

Applying the Gini coefficient to BoardGameGeek ratings

The number of ratings per game

Perhaps one of the most controversial choices of the Shut Up & Sit Down Effect article was using the number of ratings1 on BoardGameGeek (BGG) as proxy for “attention” to a game. So let’s double down on that! 😈

If lots of ratings mean a lots of eyes on a game, we can ask questions like: What games get most of the attention? Do few games steal the spotlight? Or is the attention spread out evenly?

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Reverse engineering the BoardGameGeek ranking – Part 2!

This is the second part of a series explaining and analysing the BoardGameGeek rankings. Read the first part here.

Last time I left you with the nice result that BoardGameGeek (BGG) calculates its ranking by taking users’ ratings for a particular game and then add around 1500-1600 dummy ratings of 5.5. This so-called geek score is used to sort the games from best (Gloomhaven) to worst (Tic-Tac-Toe).

One detail however we touched on in passing, but did not resolve, is how that number of dummy ratings develop over time. When the current calculation method was introduced, BGG founder Scott Alden mentioned that this number would be pegged to the number of total ratings, but did not reveal any details. Challenge accepted!

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Reverse engineering the BoardGameGeek ranking

TL;DR: BoardGameGeek calculates its ranking by adding around 1500-1600 dummy ratings of 5.5 to the regular users’ ratings. They called it their geek score, statisticians call it a Bayesian average. We use this knowledge to calculate some alternative rankings.

I often describe BoardGameGeek (BGG) as “the Internet Movie Database (IMDb) for games”. Much like its cinematic counterpart, the biggest board game database not only collects all sorts of information obsessively, but also allows users to rate games on a scale from 1 (awful - defies game description) to 10 (outstanding - will always enjoy playing). These ratings are then used to rank games, with Gloomhaven occupying the top spot since December 2017.

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