# Gamer Genotypes, version 2

Introduction

After getting some feedback from BGG on my previous post, two major issues were identified.  First, the original algorithm put too much weight on average rating relative to number of games rated. This makes users who play a lot of Eurogames, including bad ones, look like they dislike Euros more than someone who played only a few good ones. Second, the original algorithm did not normalize the ratings in any way. So users who are more stingy with their ratings appeared to dislike more games, and users who rated more bad games in a certain category appeared to dislike that category.

Two improvements are made to address these issues. First, I "residualize" the ratings to take out user and game fixed effects.  To do this, I run the linear regression:

$r_{ij} = dummy_i + dummy_j + e_{ij}$

where $r_{ij}$ is the rating that user $i$ gives to game $j$. The residual, $e_{ij}$, is what will be used by the algorithm.

Then, for each user $i$ and category/mechanic $k$, I compute:

$x_{ik} = 1 - \exp\left(-\frac{N_{ik}\log 2}{100} \right) + \frac{1}{N_{ik}+1} \sum_{j \in J_{ik}} e_{ij}$

where $N_{ik}$ is the number of games with category $k$ that user $i$ rated, and $J_{ik}$ is the set of games with category $k$ that user $i$ rated. $x_{ik}$ is meant to be a measure of how much user $i$ enjoys games with category $k$.  It is increasing in the number of games rated and increasing in the average residualized rating.

I then run a principal components analysis on $x_{ik}$.  The $x$'s are centered, but not scaled, as they are all of the same units.  As before, the first four principal components roughly correspond to "types" of gamers that we are already familiar with.

Principal Component #1: The Thematic Gamer Gene

Top Positive Factors Top Negative Factors
1 Mechanic: Role Playing PT: 1-30 minutes
2 Category: Adventure Game Weight: 1-2
3 Mechanic: Variable Player Powers Category: Abstract Strategy
4 Category: Fighting Category: Animals
5 Mechanic: Co-operative Play Mechanic: Area Enclosure
6 Category: Miniatures Mechanic: Set Collection
7 Category: Horror Mechanic: Route/Network Building
8 PT: 121+ minutes Mechanic: Tile Placement
9 Category: Wargame Mechanic: Pattern Building
10 Category: Exploration Category: Children's Game

PC1 loads positively on categories and mechanics associated with fantasy, horror, and sci-fi theme-driven games. In fact, "science fiction" is the 11th positive factor and "fantasy" is the 14th. These are your sword-swinging, blaster-pistol-wielding, zombie-and-dragon slaying gamers. PC1 loads negatively on light games and abstract games.

Principal Component #2: The Eurogamer Gene

Top Positive Factors Top Negative Factors
1 Category: Economic Category: Party Game
2 Game Weight: 3-4 Category: Humor
3 PT: 121+ minutes Game Weight: 1-2
4 Category: Farming Category: Deduction
5 Mechanic: Worker Placement PT: 1-30 minutes
6 Category: Civilization Mechanic: Roll / Spin and Move
7 Category: City Building Category: Movies / TV / Radio theme
8 Mechanic: Variable Phase Order Mechanic: Partnerships
9 Mechanic: Area Control / Area Influence Category: Horror
10 Category: Industry / Manufacturing Mechanic: Role Playing

PC2 loads positively on factors associated with Eurogames. These are the farmers, city-planners, and captains of industry in the gaming world. PC2 loads negatively on light games, and possibly games with low strategy.

Principal Component #3: The Wargamer Gene

Top Positive Factors Top Negative Factors
1 Category: Wargame Mechanic: Co-operative Play
2 Category: Political Category: Adventure
3 PT: 121+ minutes Category: Fantasy
4 Mechanic: Voting Mechanic: Card Drafting
5 Category: World War I Mechanic: Set Collection
6 Max Players: 2 PT: 31-60 minutes
7 Category: Negotiation Game Weight: 2-3
8 Category: Modern Warfare Max Players: 3-4
9 Mechanic: Campaign / Battle Card Driven Mechanic: Variable Player Powers
10 Game Weight: 4-5 Category: Fighting

PC3 loads positively on factors typically associated with wargaming. These are the armchair generals and the grognards. PC3 loads negatively on an eclectic collection of factors, but mostly associated with the PC1 and PC2 (thematic and eurogames)

Principal Component #4: The Social Gamer Gene

Top Positive Factors Top Negative Factors
1 Category: Bluffing Max Players: 2
2 Category: Negotiation Category: Wargame
3 Category: Deduction Mechanic: Campaign / Battle Card Driven
4 Mechanic: Voting Category: World War I
5 Category: Party Game Category: World War II
6 Mechanic: Simultaneous Action Selection Category: Miniatures
7 Category: Space Exploration Mechanic: Simulation
8 Category: Spies/Secret Agents Mechanic: Grid Movement
9 Mechanic: Partnerships Category: Abstract Strategy
10 Category: Civilization Category: Adventure

PC4 loads positively on elements associated with games of social deduction and party games. These are the gamers who like hidden roles and sussing out the traitor. Interestingly, PC4 loads negatively on factors mainly associated with wargaming. It should be noted, however, that the magnitude of the negative factor loadings in PC4 is outweighed by the magnitude of the positive factor loadings in PC3. So someone who likes both wargames and social games may have high values for both PC3 and PC4.

The BGG Genotype Analyzer

Using Shiny, I created a tool that can analyze any BGG user's genotype (as long as they have 10 or more ratings.) Check it out!

Conclusion

With the new improvements, I've gotten much better feedback from BGG users who, for the most part, now feel like their genotypes represent their tastes better.

The algorithm still isn't perfect though, as it's difficult to find the right balance of importance between the quantity and quality of ratings. In fact, we may want to weigh their relative importance differently depending on the user. For example, two users may both enjoy wargames, but user 1 may play and rate lots of wargames, but hold them to a higher standard, thus giving them middling ratings, while user 2 may only rate a few wargames, but rate them very highly. Whether or not we can distinguish different types of reviewing behavior among users is an interesting statistical question in and of itself.