Predicting Board Game Collections

phenrickson’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
phenrickson	ever_owned	146
phenrickson	own	141
phenrickson	rated	96

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
phenrickson	-3500-2020	train	24405	113
phenrickson	2021-2022	valid	9873	24
phenrickson	2023-2028	test	9095	4

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
phenrickson	glmnet	resamples	binary	0.020	0.959	0.162
phenrickson	glmnet	test	binary	0.006	0.976	0.042
phenrickson	glmnet	valid	binary	0.011	0.977	0.234

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	Cosmic Encounter	Hansa Teutonica	Troyes	Mage Knight Board Game	Descent: Journeys in the Dark (Second Edition)	Rococo	Alchemists	7 Wonders Duel	Star Wars: Rebellion	Sherlock Holmes Consulting Detective: Vanishing from Hyde Park	Century: Eastern Wonders	Maracaibo	Unmatched: Little Red Riding Hood vs. Beowulf	Boonlake	Frosthaven
2	Le Havre	Jaipur	Earth Reborn	A Game of Thrones: The Board Game (Second Edition)	Wiz-War (Eighth Edition)	Lewis & Clark: The Expedition	Pandemic: The Cure	Food Chain Magnate	Scythe	Century: Spice Road	Newton	Clank! Legacy: Acquisitions Incorporated	Unmatched: Cobble & Fog	Railroad Ink Challenge: Shining Yellow Edition	Unmatched: Redemption Row
3	Space Alert	American Rails	Merchants & Marauders	Puerto Rico	Keyflower	Glass Road	AquaSphere	Mombasa	Junk Art	Gloomhaven	Rising Sun	Century: A New World	On Mars	Ark Nova	Unmatched: Hell's Kitchen
4	Byzanz	Age of Conan: The Strategy Board Game	Mousquetaires du Roy	Mansions of Madness	Archipelago	1775: Rebellion	Orléans	The Gallerist	Hit Z Road	Pandemic Legacy: Season 2	Cosmic Encounter: 42nd Anniversary Edition	Era: Medieval Age	Hallertau	Arkham Horror: The Card Game (Revised Edition)	Planet Unknown
5	Battlestar Galactica: The Board Game	Greed Incorporated	Labyrinth: The War on Terror, 2001 – ?	Eminent Domain	Terra Mystica	Gearworld: The Borderlands	Port Royal	Trambahn	Sherlock Holmes Consulting Detective: Jack the Ripper & West End Adventures	Stop Thief!	Azul: Stained Glass of Sintra	Dune	Gloomhaven: Jaws of the Lion	Unmatched: Battle of Legends, Volume Two	Return to Dark Tower
6	Giants	The Adventurers: The Temple of Chac	Tikal II: The Lost Temple	Gears of War: The Board Game	Galaxy Trucker: Anniversary Edition	Caverna: The Cave Farmers	La Granja	Elysium	Agricola (Revised Edition)	Azul	Concordia Venus	Silver & Gold	Pandemic Legacy: Season 0	Cartographers Heroes	The Great Split
7	Roll Through the Ages: The Bronze Age	Middle-Earth Quest	Glen More	A Few Acres of Snow	Il Vecchio	Rise of Augustus	Splendor	Empires: Age of Discovery	Terraforming Mars	My Little Scythe	Coimbra	Cartographers	Undaunted: North Africa	Welcome to the Moon	Endless Winter: Paleoamericans
8	Pandemic	Shipyard	Sid Meier's Civilization: The Board Game	BraveRats	Clash of Cultures	Blueprints	Akrotiri	Oh My Goods!	Mansions of Madness: Second Edition	Century: Golem Edition	War Chest	Tainted Grail: The Fall of Avalon	Unmatched: Buffy the Vampire Slayer	Railroad Ink Challenge: Lush Green Edition	Carnegie
9	Toledo	At the Gates of Loyang	Dominant Species	Ora et Labora	The Great Zimbabwe	Eldritch Horror	The Battle at Kemble's Cascade	Arboretum	Reign of Cthulhu	Gaia Project	Lords of Hellas	The Castles of Burgundy	New York Zoo	Imperial Steam	Undaunted: Stalingrad
10	Diamonds Club	Dice Town	Firenze	The Lord of the Rings: The Card Game	Kemet	NFL Game Day	Isle of Trains	Karuba	Welcome Back to the Dungeon	Sagrada	Root	Blitzkrieg!: World War Two in 20 Minutes	Welcome to New Las Vegas	Kemet: Blood and Sand	Warhammer: The Horus Heresy – Age of Darkness
11	Nefertiti	The Resistance	Paris Connection	Letters from Whitechapel	Mage Wars Arena	Forbidden Desert	Three Kingdoms Redux	Watson & Holmes	Great Western Trail	Folklore: The Affliction	Istanbul: Big Box	Unmatched Game System	Rococo: Deluxe Edition	Galaxy Trucker (Second Edition)	アンドーンテッド：ノルマンディー・プラス (Undaunted: Normandy Plus)
12	Duck Dealer	Macao	Wars of the Roses: Lancaster vs. York	Tournay	The Manhattan Project	Cube Quest	Castles of Mad King Ludwig	Blood Rage	Iberia	Iberian Gauge	Yellow & Yangtze	Unmatched: Robin Hood vs. Bigfoot	Via Magica	Llamaland	Nemesis: Lockdown
13	Planet Steam	FITS	BattleCON Fighting System	Sekigahara: The Unification of Japan	Robinson Crusoe: Adventures on the Cursed Island	Spyrium	Power Grid Deluxe: Europe/North America	GEM	When I Dream	Sherlock Holmes Consulting Detective: Carlton House & Queen's Park	Blackout: Hong Kong	Paladins of the West Kingdom	Merv: The Heart of the Silk Road	Kemet: Blood and Sand – Kickstarter Edition	Foundations of Rome
14	Stone Age	Cyclades	Innovation	Takenoko	Libertalia	Room 25	Camel Up	Runebound (Third Edition)	Honshū	Lisboa	The Estates	Black Angel	Florenza: X Anniversary Edition	Corrosion	Foundations of Rome (Emperor Edition)
15	Wasabi!	Small World	Rattus	Singapore	Agricola: All Creatures Big and Small	Russian Railroads	La Isla	Codenames	Sakura Arms	Bunny Kingdom	Western Legends	Tapestry	Sherlock Holmes Consulting Detective: The Baker Street Irregulars	Rome: Rising Empires	Gateway Island

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?