The post Gamer Genotypes, version 2 appeared first on Ludometrica.

]]>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:

where is the rating that user gives to game . The residual, , is what will be used by the algorithm.

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

where is the number of games with category that user rated, and is the set of games with category that user rated. is meant to be a measure of how much user enjoys games with category . It is increasing in the number of games rated and increasing in the average residualized rating.

I then run a principal components analysis on . The '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.

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]]>The post Gamer Genotypes (A Principal Components Analysis of User Ratings) appeared first on Ludometrica.

]]>So, after a brief hiatus due to work getting busy, I'm back and ready for some more analysis of board gaming data. During this time, I was able to download individual user ratings for each game in the BoardGameGeek database. This incredibly rich dataset allows us to do more sophisticated analysis that wasn't possible with just the games data.

For this post, we're going to run a **principal components analysis** (PCA) on individual users' ratings data. Essentially, what PCA does is take a high-dimensional dataset and break it down into a few "principal components" that together explain most of the variation in the data. A principal component is a vector that points a certain direction in the data. As an example, if most BGG users either love wargames and hate party games, or hate wargames and love party games, then one of our principal components will point in the direction of high wargame ratings and low party game ratings. Users who love wargames and hate party games will have a high value for that component, and users who hate wargames and love party games will have a low value.

By breaking ratings data down into principal components, we can learn about what the most common groups of preferences are among BGG users.

**Data and Methodology**

The data comes from BGG's database on individual user ratings for each game. All users and all games are used, including expansions, for a total of over 7 million ratings. For each user, I compute the average rating they gave to games of different mechanics, categories, and types. Specifically, I compute the average rating given to:

- Each mechanic and category in BGG's official list of mechanics and categories
- Playing time between 1-30 minutes, 31-60 minutes, 61-120 minutes, 121+ minutes
- Game weight between 1-2 / 2-3 / 3-4 / 4-5
- Max players=2, Max players=3-4, Max players=5+

Of course, not every user gave a rating to a game in each of these groups. To deal with this, I seed each user with a single 5.5 rating for each of the above categories. This has the added benefit of pushing up the average rating when the user has rated more games out of a given category, but with decreasing marginal returns (going from 1 to 5 ratings in a category has a big effect, but going from 100 to 105 has a small effect). This is also consistent with BGG's practice of computing their Bayesian average rating by seeding games with a number of 5.5 ratings in addition to actual user ratings.

The final dataset contains the average ratings by game category for 151,000 users. Because the ratings categories are all the same units, I did not rescale them before running the PCA.

**Results**

I will focus on the first four principal components. The scree plot below shows that by the time we reach the fourth component, the additional explanatory power gained by additional components starts to become small and fairly constant.

The first four components will also have the most natural interpretation, as we shall see below. For each principal component, I will show the top positive factor loadings (high ratings) and the top negative factor loadings (low ratings)

**Principal Component 1: The "General Gamer Gene"**

Top Positive Factor Loadings | Top Negative Factor Loadings | |
---|---|---|

1 | Game Weight: 3-4 | None |

2 | Playing Time: 121+ Minutes | |

3 | Category: Economic | |

4 | Category: Civilization | |

5 | Mechanic: Card Drafting | |

6 | Mechanic: Simultaneous Action Selection | |

7 | Mechanic: Action Point Allowance System | |

8 | Mechanic: Area Control / Area Influence | |

9 | Mechanic: Worker Placement | |

10 | Category: Science Fiction |

PC1 is interesting because it loads positively on all game categories, with an emphasis on longer, weightier games, and giving high ratings to broadly popular mechanics like card drafting and worker placement, and categories like "civilization" and "economic". PC1 does not load negatively on any of the factors, indicating that the predominant driver of PC1 is enjoying a broad range of games, and (importantly) having rated many diverse types of games. For this reason, I call PC1 the "general gamer gene".

**Principal Component 2: The "Thematic vs. Strategic Gene"**

Top Positive Factor Loadings | Top Negative Factor Loadings | |
---|---|---|

1 | Category: Fighting | Category: Farming |

2 | Mechanic: Variable Player Powers | Category: Economic |

3 | Category: Horror | Mechanic: Worker Placement |

4 | Category: Adventure | Category: Industry/Manufacturing |

5 | Mechanic: Cooperative Play | Category: City Building |

6 | Category: Role Playing | Mechanic: Area Enclosure |

PC2 clearly delineates a preference for thematic vs. strategic games. It loads positively on categories and mechanics that generally foster immersive, thematic experiences, and loads negatively on categories that have weak theme, and are thus more focused on purely strategic interactions. For this reason, I call PC2 the "thematic vs. strategic gene".

**Principal Component 3: The "Wargamer Gene"**

Top Positive Factor Loadings | Top Negative Factor Loadings | |
---|---|---|

1 | Category: Wargame | Game Weight: 1-2 |

2 | Mechanic: Campaign / Battle Card Driven | Mechanic: Set Collection |

3 | Mechanic: Hex-and-Counter | Playing Time: 1-30 Minutes |

4 | Category: World War I | Category: Card Game |

5 | Category: World War II | Mechanic: Card Drafting |

6 | Category: Political | Category: Party Game |

PC3 is basically the wargamer gene. As you can see, users with a high PC3 love war games, and they tend to dislike short, casual games.

**Principal Component 4: The "Social Gamer Gene"**

Top Positive Factor Loadings | Top Negative Factor Loadings | |
---|---|---|

1 | Category: Party Game | Game Weight: 3-4 |

2 | Category: Deduction | Playing Time: 121+ Minutes |

3 | Category: Spies/Secret Agents | Mechanic: Hand Management |

4 | Mechanic: Voting | Mechanic: Dice Rolling |

5 | Mechanic: Memory | Category: Economic |

PC4 is the "social gamer gene". These users prefer party games, and especially games where there is some kind of social deduction involved. They appear to dislike games that take too long, or have mechanics that might be considered fiddly, like hand management and dice rolling.

**Disclaimer: These are not gamer categories, but gamer genes**

One thing I should mention is that these aren't meant to be buckets that we can place gamers into. The point here isn't to put a user into the "wargamer" bucket and another user into the "social gamer" bucket. Rather, these are gamer genes that we all share, in either positive or negative quantities. So if I'm someone who likes social games ** and **wargames, but I don't like thematic games, I'm going to have low values for PC2, and high values for PC3 and PC4. If I additionally play and rate lots of games, I'll also have a high value of PC1.

**My personal gamer genotype**

An interesting exercise you can do with PCA is to calculate the value of each principal component for any given user, as long as you have their game ratings. Since I have the ratings for all users, I can additionally rank users along each component. Here are my personal values along each component, expressed as a percentile of all users:

General Gamer | Thematic vs. Strategic | Wargamer | Social Gamer | |
---|---|---|---|---|

ekung | 55 | 71 | 52 | 45 |

Basically, what this says about me is that I'm a fairly average BGG user, except that I have a relatively stronger preference for thematic games than most users. I already know why this is, as I've rated highly a number of cooperative fantasy themed games, like Pathfinder ACG, Lord of the Rings LCG, and Shadows Over Camelot. So I think it's a fairly accurate depiction of who I am as a gamer. I tend to think that I'm more of a social gamer than the 45th percentile, but in fairness this isn't reflected in my ratings, since I think the only social games I've rated are Dixit and The Resistance.

**Conclusion**

I was fairly surprised at how clearly some common stereotypes for gamer personalities came out from the principal components analysis. It tells us that there's some truth to those stereotypes on average, even if every individual is different. What do you think? If you'd like your own gamer genotypes analyzed, drop a comment with your BGG username and I'll post it.

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]]>The post Exploring the relationship between Game Weight, Playing Time, and Ratings appeared first on Ludometrica.

]]>Exploring these relationships was rather simple. Again, I'm starting with the set of all non-expansion games published between 2004 and 2014 with at least 100 user ratings on BGG. Then, I simply made scatter plots, which you can see below.

Based on the figure above, it seems there's almost a pure linear relationship between average rating and weight. Moreover, the slope of the linear fit is pretty much the same regardless of playing time! This was a bit of a surprise to me, as I thought that the slope would be higher for short games.

These are raw averages. What about the Bayesian average, which is what BGG actually uses to compute board game rankings? (The Bayesian rating pulls games with few user ratings towards 5.5)

We get pretty much the same story. Although the relationship between rating and weight does not look at linear as before, we still see that the slopes of the best linear fits do not differ that much across playing-times. If anything, it's the long games that have the steepest slope. I suppose the way to think of this is that if you're going to spend over an hour playing a game, it'd better have at least some level of depth and complexity involved!

Anyway, based on this simple exploration of the data my hypothesis is **rejected**! There doesn't appear to be any evidence that weight matters differently for short games vs. long games. Of course, weight and playing time are themselves *highly* correlated. Perhaps it would make more sense to split "weight" and "playing time" into three orthogonal components: rules complexity, strategic depth, and playing time. But that's neither here nor there and we have to work with the data we have...

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]]>The post Highly Rated Mechanics and Other Determinants of BGG Rating appeared first on Ludometrica.

]]>A simple way to do this would be to compute the average rating across all games that contain each mechanic, then rank the mechanics. However, this could cause us to confound the effect of a mechanic with the effect of other, correlated factors. For example, if games with **card drafting** usually also have **hand management**, then the effect of the two mechanics would be confounded. To deal with this, I'll be using **multivariate linear regression** to estimate the independent effect of each mechanic on a game's rating.

Since there are a lot of mechanics to consider (51 in total), I also wanted a method that automatically selects the mechanics that seem to matter the most. To that end, I'll be using the **LASSO** method.

Finally, I'll also be throwing in a few other factors that may influence user ratings: the game's weight, its playing time, and indicators for whether it's a wargame, party game, or abstract strategy. The regression is run on all non-expansion games published between 2004 and 2014, with at least 100 user ratings. The dependent variable is BGG's Bayesian rating, which is what BGG uses to construct board game rankings.*

*The purpose of the Bayesian rating is to push games with fewer user ratings towards the middle. As the number of user ratings becomes large, the effect of this Bayesian averaging becomes minimal. A slightly more detailed explanation can be found here.

Without further ado, here are the mechanics that came out of the LASSO regression and their effects:

**The Effect of Mechanics on BGG Ratings**

Rank | Mechanic | Effect |
---|---|---|

1 | Grid Movement | 0.208 |

2 | Player Elimination | 0.204 |

3 | Worker Placement | 0.154 |

4 | Card Drafting | 0.122 |

5 | Variable Player Powers | 0.111 |

6 | Co-operative Play | 0.106 |

7 | Simultaneous Action Selection | 0.083 |

8 | Set Collection | 0.061 |

9 | Hand Management | 0.051 |

10 | Deck / Pool Building | 0.051 |

11 | Area Control / Area Influence | 0.039 |

12 | Partnerships | 0.027 |

13 | Route/Network Building | 0.023 |

14 | Dice Rolling | 0.011 |

15 | Campaign / Battle Card Driven | 0.009 |

16 | Tile Placement | 0.008 |

17 | Point to Point Movement | 0.004 |

18 | Area Movement | 0.002 |

19 | Simulation | -0.003 |

20 | Trading | -0.005 |

21 | Roll / Spin and Move | -0.040 |

22 | Hex-and-Counter | -0.043 |

*How to read this table: The "effect" can be understood to mean the amount by which a game's BGG rating will increase (out of 10) if it had this mechanic. Of course, this estimate is only "local" to the data in the sense that we can't extrapolate too far from the kinds of games we actually observe. Mechanics not selected by LASSO can be interpreted either to have a zero effect, or to be contained by too few games to have a meaningful impact on the data.

As for the non-mechanic factors, here's what LASSO gave us:

**Other Determinants of BGG Rating**

Rank | Variable | Effect |
---|---|---|

1 | Intercept | 5.368 |

2 | Game Weight | 0.252 |

3 | Party Game | 0.023 |

4 | Wargame | -0.010 |

*How to read this table: The "intercept" can be understood to mean the expected BGG rating of a game that has no listed mechanics, a 0 weight, and is not a party, war, or abstract strategy game. The effect of game weight implies that a 1-point increase in weight (out of 5) predicts a 0.252 increase in BGG rating. The effect of being a party game is a 0.023 increase in rating, while the effect of being a wargame is a 0.01 decrease in rating.

**Discussion**

It's reassuring that the mechanics LASSO picked out conform to what I view as some of the more common and popular mechanics in boardgaming (i.e. it's good that Crayon-Rail System wasn't picked out.) Among the highly rated mechanics, I was not surprised to see **Worker Placement**, **Card Drafting**, **Cooperative Play**, and **Variable Player Powers** all there. I was somewhat surprised to see that **Grid Movement** rates so highly. I wonder why? I was also surprised about **Player Elimination**. I always thought that player elimination was considered undesirable; but this does conform to results from my previous post suggesting that player elimination is one of the fastest growing mechanics in terms of number of games published. Finally, I was surprised to see that **Variable Phase Order** (Puerto Rico; Race for the Galaxy) was not selected by LASSO. I previously showed that it is one of the fastest growing mechanics over the past decade, but I suppose it still doesn't have enough absolute numbers.

Only four mechanics scored negative effects, though it should be mentioned that negative is completely relative here. Out of those four, two stand out: **Roll/Spin-and-Move** and **Hex-and-Counter**. This conforms to results from my previous post showing that these two mechanics declined the most in terms of number of games published over the past decade. I'm not surprised that the roll-and-move mechanic is one of the worst rated mechanics. I'm not sure what to think about hex-and-counter as I've had limited experience with it.

Moving on to the non-mechanic factors, we see that game weight is clearly the most important. A one-point increase in game weight predicts a 0.25 increase in rating. This is understandable, as many users think of game weight as a measure of strategic complexity or decision density. I've always wondered whether the weight-to-playing-time ratio would be a strong predictor of rating. Maybe I'll test that some time. The effect of being a party game or a wargame is small, and abstract strategy dropped out of the LASSO regression altogether.

**Conclusion**

The results show us that some of the fastest growing mechanics over the last decade are also the most highly rated ones, and vice-versa with declining mechanics. A limitation of the current approach is that I've not allowed for potentially important interaction terms. For example, perhaps hex-and-counter would hurt the rating of a non-wargame but would increase the rating of a wargame. If that were true, then the current estimate for hex-and-counter confounds these two effects. A more highly interacted model, however, would introduce many more terms and then variable selection becomes even more of an issue! **Dimension-reduction** (i.e. a simpler categorization scheme) seems like it's going to be important, especially for work on the relatively small dataset that is boardgaming. I pointed to some discussion of these issues in my previous post, and I think I will soon be exploring those topics as well.

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]]>The post Popular Mechanics (An Empirical Analysis), Part 1 appeared first on Ludometrica.

]]>**Starting Point: What are the most popular mechanics, in terms of # games published?**

Before embarking on more sophisticated analyses of any topic, it is always good to start simple, and to see what simple descriptive statistics have to say about the data. So let's start by asking the simple question: "What are the most popular mechanics in terms of the number of games published containing those mechanics?" and "How has the popularity of these mechanics changed over time?" To do this, I calculate the number of games published in each year containing each mechanic. I then rank each mechanic by number of games published within each year. Below, I present the Top 10 mechanics, in terms of games published, in 2004 and in 2014.

**Top 10 Mechanics in 2004 by # Games Published***

Rank | Mechanic | # Games Published |
---|---|---|

1 | Dice Rolling | 64 |

2 | Hand Management | 60 |

3 | Variable Player Powers | 34 |

4 | Tile Placement | 31 |

5 | Area Control / Area Influence | 27 |

6 | Set Collection | 27 |

7 | Modular Board | 25 |

8 | Auction/Bidding | 19 |

9 | Hex-and-Counter | 18 |

10 | Roll / Spin and Move | 18 |

* Games with 100+ ratings as of January 2016; Total Published = 249

**Top 10 Mechanics in 2014 by # Games Published***

Rank | Mechanic | # Games Published |
---|---|---|

1 | Hand Management | 129 |

2 | Dice Rolling | 82 |

3 | Variable Player Powers | 61 |

4 | Card Drafting | 58 |

5 | Set Collection | 58 |

6 | Area Control / Area Influence | 49 |

7 | Deck / Pool Building | 41 |

8 | Tile Placement | 37 |

9 | Modular Board | 32 |

10 | Co-operative Play | 30 |

* Games with 100+ ratings as of January 2016; Total Published = 341

The first thing that stands out is simply how much the industry has grown from 2004 to 2014. The growth would appear even more stark if I removed the 100+ ratings restriction. The board gaming industry really seems to have grown tremendously over the past decade.

The top 3 mechanics in both years are **Hand Management**, **Dice Rolling**, and **Variable Player Powers**. These are fairly "neutral" mechanics in the sense that they can go in games of any genre and weight, so it's not surprising that they round out the top 3. It definitely appears, however, that Dice Rolling is not growing at the same rate as the other mechanics. Has dice rolling become less popular over time?

From 2004 to 2014, three mechanics fell out of the top 10 and three mechanics entered. The mechanics that fell out are: **Auction/Bidding**, **Hex-and-Counter**, and **Roll/Spin and Move**. The three mechanics that entered are **Card Drafting**, **Deck/Pool Building**, and **Cooperative Play**. Very interesting, and perhaps not surprising. These results certainly line up with my intuition for which mechanics have become more popular over the past decade.

Let's now take a look at which mechanics had the highest increases and decreases in publication rank from 2004 to 2014.

**Top and Bottom 5 Mechanics by Change in Publication Rank from 2004 to 2014**

Rank | Mechanic | Change in Pub. Rank |
---|---|---|

1 | Deck / Pool Building | +44 |

2 | Worker Placement | +38 |

3 | Variable Phase Order | +24 |

4 | Co-operative Play | +15 |

5 | Player Elimination | +15 |

47 | Commodity Speculation | -15 |

48 | Simulation | -16 |

49 | Roll / Spin and Move | -21 |

50 | Secret Unit Deployment | -22 |

51 | Hex-and-Counter | -22 |

We can clearly see how much the deckbuilding mechanic has grown. It shot up 44 ranks, from last to #7, since 2004. The influence of Dominion (2008) is widely known and clearly felt in the data. I was surprised to see that **Worker Placement** has gone up so many ranks, as I thought the mechanic had already been around for a while by 2004, but perhaps it wasn't popularized until later. To round out the top 5, we have **Variable Phase Order** which increased by 24 ranks, and **Cooperative Play** and **Player Elimination**, which both rose by 15 ranks. I was surprised to see that player elimination had grown so much, as I was under the impression that this was an undesirable element and removing it is a good thing (i.e. The Resistance in relation to Mafia-like games).

Finally, let's take a look at 5 mechanics which fell the most in publication rank. Three of those, **Simulation**, **Secret Unit Deployment**, and **Hex-and-Counter** are typically associated with wargames. Are wargames on the decline? According to the data, 40 wargames with 100+ ratings were published in 2004 and only 19 in 2014. The two other mechanics in the bottom 5 are **Commodity Speculation** and **Roll/Spin and Move**. I'm not sure what to think about stocks and commodities games, but I'm not surprised to see that roll-move has declined significantly, especially in the set of games that would attract over 100 ratings on BGG.

**Growing Mechanics and their Influential Games**

Let's wrap up by taking a look at the actual publication patterns over time for some of the top growing mechanics. In particular, let's do the following exercise. For each of the following 5 fast-growing mechanics: deckbuilding, worker placement, variable phase order, cooperative play, and card drafting, let's plot the number of published games over time alongside the release dates of some influential games with that mechanic. As for which games to include, I'm just going to use one or two games that I personally most associate as an "early" or "canonical" example of that mechanic. (Side note: I think it's wild that we could fairly describe a game that is less than 8 years old, i.e. Dominion, as "canonical". It speaks to the amount of innovation that is going on in board games and what a great time it is for the hobby.) Here are the graphs:

Most of the games that I immediately thought of as being associated with a mechanic do appear to be published before the popularity of that mechanic starts taking off. The most stark example is, obviously, Dominion, but we can see for example that both Puerto Rico and Race for the Galaxy are in the early flat region for variable phase order. The one exception to this was 7 Wonders in card drafting, but this is probably just attributable to me having some present-bias and not really knowing the history of the mechanic that well. For example, I didn't know that Ticket to Ride was considered as having a card-drafting mechanic until writing this post (which could explain why card drafting was already somewhat popular in 2004 relative to these other mechanics that we've looked at.)

**Conclusion**

Well, this was an interesting exercise for me and I hope you found it interesting as well. Nothing really too surprising, I think, but it's good to see some of my intuitions confirmed in the data. What do you think of the results? Do you think the 100+ ratings restriction is too severe or somehow not appropriate? Is the whole endeavor worthless because of the haphazard nature of BGG's mechanics list? Would it make sense to include things like **bluffing** and **deduction** as mechanics, which currently are listed as "categories"? Let me know your thoughts. As always, constructive criticism and suggestions are always welcome! Next time, I'll be using regression analysis to take a look at how different mechanics correlate with a game's average rating.

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