Predicting Board Game Collections

Gyges’s Collection

About

This report details the results of training and evaluating a classification model for predicting games for a user’s boardgame collection.

Note

To view games predicted by the model, go to Section 5.

Collection

The data in this project comes from BoardGameGeek.com. The data used is at the game level, where an individual observation contains features about a game, such as its publisher, categories, and playing time, among many others.

I train a classification model at the user level to learn the relationship between game features and games that a user owns - what predicts a user’s collection?

username	status	games
Gyges	ever_owned	1496
Gyges	own	580
Gyges	rated	1425

I evaluate the model’s performance on a training set of historical games via resampling, then validate the model’s performance on a set aside set of newer relases. I then refit the model on the training and validation in order and predict upcoming releases in order to find new games that the user is most likely to add to their collection.

username	years	type	Own
			no	yes
Gyges	-3500-2020	train	24097	421
Gyges	2021-2022	valid	9786	111
Gyges	2023-2028	test	9051	48

Types of Games

What types of game does the user own? The following plot displays the most frequent publishers, mechanics, designers, artists, etc that appear in a user’s collection.

collection |>
        filter(own == 1) |>
        collection_by_category(
                games = games_raw
        ) |>
        plot_collection_by_category()+
        ylab("feature")

The following plot shows the years in which games in the user’s collection were published. This can usually indicate when someone first entered the hobby.

Games in Collection

What games does the user currently have in their collection? The following table can be used to examine games the user owns, along with some helpful information for selecting the right game for a game night!

Use the filters above the table to sort/filter based on information about the game, such as year published, recommended player counts, or playing time.

collection |>
        filter(own == 1) |>
        prep_collection_datatable(
                games = games_raw
        ) |>
        filter(!is.na(image)) |>
        collection_datatable()

Modeling

I’ll now the examine predictive models trained on the user’s collection.

For an individual user, I train a predictive model on their collection in order to predict whether a user owns a game. The outcome, in this case, is binary: does the user have a game listed in their collection or not? This is the setting for training a classification model, where the model aims to learn the probability that a user will add a game to their collection based on its observable features.

How does a model learn what a user is likely to own? The training process is a matter of examining historical games and finding patterns that exist between game features (designers, mechanics, playing time, etc) and games in the user’s collection.

I make use of many potential features for games, the vast majority of which are dummies indicating the presence or absence of the presence or absence of things such as a publisher/artist/designer. The “standard” BGG features for every game contain information that is typically listed on the box its playing time, player counts, or its recommended minimum age.

Note

I train models to predict whether a user owns a game based only on information that could be observed about the game at its release: playing time, player count, mechanics, categories, genres, and selected designers, artists, and publishers. I do not make use of BGG community information, such as its average rating, weight, or number of user ratings. This is to ensure the model can predict newly released games without relying on information from the BGG community.

What Predicts A Collection?

A predictive model gives us more than just predictions. We can also ask, what did the model learn from the data? What predicts the outcome? In the case of predicting a boardgame collection, what did the model find to be predictive of games a user has in their collection?

To answer this, I examine the coefficients from a model logistic regression with ridge regularization (which I will refer to as a penalized logistic regression).

Positive values indicate that a feature increases a user’s probability of owning/rating a game, while negative values indicate a feature decreases the probability. To be precise, the coefficients indicate the effect of a particular feature on the log-odds of a user owning a game.

The following visualization shows the path of each feature as it enters the model, with highly influential features tending to enter the model early with large positive or negative effects. The dotted line indicates the level of regularization that was selected during tuning.

model_glmnet |> 
        pluck("wflow", 1) |>
        trace_plot.glmnet(max.overlaps = 30)+
        facet_wrap(~params$username)

Partial Effects

What are the effects of individual features?

Use the buttons below to examine the effects different types of predictors had in predicting the user’s collection.

Categories

Mechanics

Themes

Families

Publishers

Designers

Artists

Components

Mechanisms

Assessment

How well did the model do in predicting the user’s collection?

This section contains a variety of visualizations and metrics for assessing the performance of the model(s). If you’re not particularly interested in predictive modeling, skip down further to the predictions from the model.

The following displays the model’s performance in resampling on a training set, a validation set, and a holdout set of upcoming games.

metrics |>
        mutate_if(is.numeric, round, 3) |>
        pivot_wider(
                names_from = c(".metric"),
                values_from = c(".estimate")) |>
        gt::gt() |>
        gt::sub_missing() |>
        gt_options()

username	wflow_id	type	.estimator	mn_log_loss	roc_auc	pr_auc
Gyges	glmnet	resamples	binary	0.070	0.870	0.147
Gyges	glmnet	test	binary	0.041	0.829	0.048
Gyges	glmnet	valid	binary	0.053	0.882	0.120

An easy way to visually examine the performance of classification model is to view a separation plot.

I plot the predicted probabilities from the model for every game (during resampling) from lowest to highest. I then overlay a blue line for any game that the user does own. A good classifier is one that is able to separate the blue (games owned by the user) from the white (games not owned by the user), with most of the blue occurring at the highest probabilities (left side of the chart).

preds |>
        filter(type %in% c('resamples', 'valid')) |>
        plot_separation(outcome = params$outcome)

I can more formally assess how well each model did in resampling by looking at the area under the ROC curve (roc_auc). A perfect model would receive a score of 1, while a model that cannot predict the outcome will default to a score of 0.5. The extent to which something is a good score depends on the setting, but generally anything in the .8 to .9 range is very good while the .7 to .8 range is perfectly acceptable.

preds |>
        nest(data = -c(username, wflow_id, type)) |>
        mutate(roc_curve = map(data, safely( ~ .x |> safe_roc_curve(truth = params$outcome)))) |>
        mutate(result = map(roc_curve, ~ .x |> pluck("result"))) |>
        select(username, wflow_id, type, result) |>
        unnest(result) |>
        plot_roc_curve()

Top Games in Training

What were the model’s top games in the training set?

preds |>
        filter(type == 'resamples') |>
        prep_predictions_datatable(
                games = games, 
                outcome = params$outcome
        ) |>
        predictions_datatable(outcome = params$outcome,
                remove_description = T, 
                remove_image = T, 
                pagelength = 15)

Top Games in Validation

What were the model’s top games in the validation set?

preds |>
        filter(type %in% c("valid")) |>
        prep_predictions_datatable(
                games = games,
                outcome = params$outcome
        ) |>
        predictions_datatable(
                outcome = params$outcome,
                remove_description = T, 
                remove_image = T, 
                pagelength = 15)

Top Games by Year

Displaying the model’s top games for individual years in recent years.

preds |>
        filter(type %in% c('resamples', 'valid')) |>
        top_n_preds(
                games = games,
                outcome = params$outcome,
                top_n = 15,
                n_years = 15
        ) |>
        gt_top_n(collection = collection |> prep_collection())

Rank	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022
1	Le Havre	A Brief History of the World	Labyrinth: The War on Terror, 2001 – ?	Ora et Labora	Terra Mystica	Concordia	La Granja	Trans-Siberian Railroad	Agricola (Revised Edition)	Spirit Island	The Edge: Dawnfall	Tainted Grail: The Fall of Avalon	Guild Master	Experior Existencial	Agricola 15
2	Space Alert	Endeavor	Earth Reborn	Ascending Empires	Archipelago	BattleCON: Devastation of Indines	Roll for the Galaxy	Pandemic Legacy: Season 1	One Deck Dungeon	This War of Mine: The Board Game	Nemesis	Western Empires	Pandemic Legacy: Season 0	The Great Wall	Horizons of Spirit Island
3	Battlestar Galactica: The Board Game	Vasco da Gama	Dust Tactics	A Game of Thrones: The Board Game (Second Edition)	Tzolk'in: The Mayan Calendar	Disc Duelers	Fields of Arle	Pixel Tactics Deluxe	Exceed Fighting System	Folklore: The Affliction	Concordia Venus	Pax Pamir: Second Edition	Etherfields	Bloodborne: The Board Game	Frosthaven
4	Byzanz	Kuhhandel Master	Navegador	The New Era	Among the Stars	Gearworld: The Borderlands	Evolution	Grimslingers	Terraforming Mars	Pandemic Legacy: Season 2	Cosmic Encounter: 42nd Anniversary Edition	Bios: Origins (Second Edition)	Eclipse: Second Dawn for the Galaxy	Ankh: Gods of Egypt	Dire Alliance: Horror
5	Prussian Rails	Hansa Teutonica	20th Century	Dungeon Petz	We Didn't Playtest This: Legacies	Eight-Minute Empire: Legends	Dogs of War	Pixel Tactics 4	Scythe	Gloomhaven	Orc-lympics	Core Space	Gloomhaven: Jaws of the Lion	Dirge: The Rust Wars	ISS Vanguard
6	Ghost Stories	We Didn't Playtest This Either	Catacombs	King of Tokyo	Keyflower	Glass Road	A Fistful of Kung Fu: Hong Kong Movie Wargame Rules	Through the Ages: A New Story of Civilization	Reign of Cthulhu	Gaia Project	Newton	Aftermath	Rush M.D.	Blitzkrieg!: World War Two in 20 Minutes	Gateway Island
7	Sorry! Sliders	Win, Lose, or Banana	Cadwallon: City of Thieves	Risk Legacy	BattleCON: War of Indines	Tash-Kalar: Arena of Legends	Pixel Tactics 3	Meow	The Others	878 Vikings: Invasions of England	Lords of Hellas	Living Planet: Deluxe Edition	Switch & Signal	Kemet: Blood and Sand	Undaunted: Stalingrad
8	Duck Dealer	Imperial 2030	Glen More	Dreadfleet	Pixel Tactics	Pixel Tactics 2	Blue Moon Legends	Pixel Tactics 5	The Manhattan Project: Energy Empire	One Deck Dungeon: Forest of Shadows	Dungeon Alliance	Dungeon Universalis	Cosmic Encounter Duel	Nicaea	Libertalia: Winds of Galecrest
9	Okko: Era of the Asagiri	Chaos in the Old World	Sneaks & Snitches	Belfort	The Great Zimbabwe	7-Card Slugfest	Power Grid Deluxe: Europe/North America	BattleCON: Fate of Indines	Arkham Horror: The Card Game	Lazer Ryderz	Tsukuyumi: Full Moon Down	Cloudspire	Unmatched: Little Red Riding Hood vs. Beowulf	Canvas	アンドーンテッド：ノルマンディー・プラス (Undaunted: Normandy Plus)
10	Sixis	Revolution!	51st State	Colonial: Europe's Empires Overseas	Android: Netrunner	Northern Pacific	Doomtown: Reloaded	Star Wars: X-Wing Miniatures Game – The Force Awakens Core Set	Millennium Blades	Zpocalypse 2: Defend the Burbs	Mage Knight: Ultimate Edition	HATE	Gatefall	Assassin's Creed: Brotherhood of Venice	Squadron Leader
11	Combat Commander: Pacific	Eden: Survive the Apocalypse	Zombie in My Pocket	Dungeon Fighter	Ginkgopolis	Eldritch Horror	Thunderstone Advance: Worlds Collide	7 Wonders Duel	Game of Thrones: The Iron Throne	Startups	Kick-Ass: The Board Game	Middara: Unintentional Malum – Act 1	New York Zoo	Gutterfall: Bounties	Marvel Zombies: Heroes' Resistance
12	Mutants and Death Ray Guns	Claustrophobia	The Hobbit	Lancaster	Libertalia	Going, Going, GONE!	Arcadia Quest	The King Is Dead	Mansions of Madness: Second Edition	Wasteland Express Delivery Service	Critical Mass: Patriot vs Iron Curtain	Ancient Civilizations of the Inner Sea	Dwellings of Eldervale	Steamwatchers	Nemesis: Lockdown
13	Roll Through the Ages: The Bronze Age	Dungeon Lords	Warhammer: The Island of Blood	Last Will	Grimoire Shuffle	Caverna: The Cave Farmers	Antike II	Bottom of the 9th	Mechs vs. Minions	Fallout	Champions of Hara	Dungeon Brawler	Europe Divided	Core Space: First Born	One Deck Galaxy
14	Bushido: Der Weg des Kriegers	Dungeon Twister 2: Prison	Sid Meier's Civilization: The Board Game	Puerto Rico	Galaxy Trucker: Anniversary Edition	This Is Not a Test: Post-Apocalyptic Skirmish Rules	The Witcher Adventure Game	Empires: Age of Discovery	Iberia	Flick 'em Up!: Dead of Winter	Shadowrun: Crossfire – Prime Runner Edition	Blitzkrieg!: World War Two in 20 Minutes	BattleCON: Wanderers of Indines	Mint Bid	Sniper Elite: The Board Game
15	Magnifico	Shipyard	Firenze	The Ares Project	Uchronia	Francis Drake	Galaxy Defenders	Piratoons	A Feast for Odin	First Martians: Adventures on the Red Planet	Trapwords	EXO: Mankind Reborn	Lost Ruins of Arnak	Eastern Empires	Pisces: A High-Stakes Fishing Competition

Predictions

New and Upcoming Games

What were the model’s top predictions for new and upcoming board game releases?

new_preds |>
        filter(type == 'upcoming') |>
        # imposing a minimum threshold to filter out games with no info
        filter(usersrated >= 1) |>
        # removing this goddamn boxing game that has every mechanic listed
        filter(game_id != 420629) |>
        prep_predictions_datatable(
                games = games_new,
                outcome = params$outcome
        ) |>
        predictions_datatable(outcome = params$outcome)

Older Games

What were the model’s top predictions for older games?