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	154
phenrickson	own	145
phenrickson	rated	100

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	-3500-2021	train	26240	122
phenrickson	2022-2023	valid	10291	17
phenrickson	2024-2028	test	8587	6

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	0.019	0.961	0.210
phenrickson	glmnet	test	binary	0.007	0.956	0.011
phenrickson	glmnet	valid	binary	0.009	0.963	0.140

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	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
1	Hansa Teutonica	Mousquetaires du Roy	Mansions of Madness	Archipelago	Lewis & Clark: The Expedition	Orléans	The Gallerist	Star Wars: Rebellion	Stop Thief!	Brass: Birmingham	Maracaibo	Unmatched: Little Red Riding Hood vs. Beowulf	Boonlake	Frosthaven	TerraFyte
2	Middle-Earth Quest	Troyes	Gears of War: The Board Game	Keyflower	Rococo	Alchemists	Blood Rage	Sherlock Holmes Consulting Detective: Jack the Ripper & West End Adventures	Azul	Cosmic Encounter: 42nd Anniversary Edition	Era: Medieval Age	Unmatched: Cobble & Fog	Unmatched: Battle of Legends, Volume Two	Endless Winter: Paleoamericans	Unmatched: Teen Spirit
3	Age of Conan: The Strategy Board Game	Earth Reborn	Rune Age	Descent: Journeys in the Dark (Second Edition)	Glass Road	Nyakuza	7 Wonders Duel	Agricola (Revised Edition)	Gaia Project	Century: Eastern Wonders	Clank! Legacy: Acquisitions Incorporated	Gloomhaven: Jaws of the Lion	Imperial Steam	Unmatched: Redemption Row	Unmatched: For King and Country
4	The Adventurers: The Temple of Chac	7 Wonders	Puerto Rico	Wiz-War (Eighth Edition)	Spyrium	Pandemic: The Cure	Food Chain Magnate	Hit Z Road	Pandemic Legacy: Season 2	Azul: Stained Glass of Sintra	Dune	Pandemic Legacy: Season 0	Railroad Ink Challenge: Shining Yellow Edition	Unmatched: Hell's Kitchen	La Granja: Deluxe Master Set
5	Greed Incorporated	Glen More	Tournay	Terra Mystica	Eldritch Horror	Akrotiri	Watson & Holmes	When I Dream	Century: Golem Edition	Railroad Ink: Deep Blue Edition	Blitzkrieg!: World War Two in 20 Minutes	On Mars	Ark Nova	Planet Unknown	Undaunted: Battle of Britain
6	Shipyard	Dominant Species	The Castles of Burgundy	Agricola: All Creatures Big and Small	Caverna: The Cave Farmers	Port Royal	Mombasa	Junk Art	Gloomhaven	Newton	Century: A New World	New York Zoo	Railroad Ink Challenge: Lush Green Edition	Undaunted: Stalingrad	The Witcher: Old World
7	American Rails	Runewars	A Game of Thrones: The Board Game (Second Edition)	Shadowrift	City of the Living	AquaSphere	Plums	Scythe	Sherlock Holmes Consulting Detective: Vanishing from Hyde Park	Betrayal Legacy	The Castles of Burgundy	Century: Golem Edition – An Endless World	Arkham Horror: The Card Game (Revised Edition)	Foundations of Rome	Arkeis
8	Small World	Merkator	Letters from Whitechapel	Targi	Gearworld: The Borderlands	La Granja	Oh My Goods!	Terraforming Mars	Century: Spice Road	Railroad Ink: Blazing Red Edition	Unmatched: Battle of Legends, Volume One	My City	Galaxy Trucker (Second Edition)	Foundations of Rome (Emperor Edition)	My Island
9	Cyclades	The Mines of Zavandor	Mage Knight Board Game	Tzolk'in: The Mayan Calendar	Concordia	Arkwright	Arboretum	Reign of Cthulhu	Spirit Island	Architects of the West Kingdom	Unmatched: Robin Hood vs. Bigfoot	Sherlock Holmes Consulting Detective: An Irregular Meeting	Cartographers Heroes	Nemesis: Lockdown	Deliverance
10	Jaipur	Merchants & Marauders	The Lord of the Rings: The Card Game	Il Vecchio	Eight-Minute Empire: Legends	Nations: The Dice Game	Pandemic Legacy: Season 1	Mansions of Madness: Second Edition	Sherlock Holmes Consulting Detective: Carlton House & Queen's Park	Root	Silver & Gold	Merv: The Heart of the Silk Road	Corrosion	アンドーンテッド：ノルマンディー・プラス (Undaunted: Normandy Plus)	Welcome To...: Collector's Edition
11	Kuhhandel Master	Innovation	Eminent Domain	Suburbia	Nations	Three Kingdoms Redux	Elysium	Iberia	Twilight Imperium: Fourth Edition	Rising Sun	The King's Dilemma	Hallertau	Welcome to the Moon	ISS Vanguard	Fit to Print
12	Ubongo 3D	Firenze	Singapore	Kemet	Cube Quest	Five Tribes: The Djinns of Naqala	Steampunk Rally	Perdition's Mouth: Abyssal Rift	Iberian Gauge	Coimbra	Black Angel	Sherlock Holmes Consulting Detective: The Baker Street Irregulars	Kemet: Blood and Sand – Kickstarter Edition	The Great Split	Unmatched: Brains and Brawn
13	Endeavor	Wars of the Roses: Lancaster vs. York	A Few Acres of Snow	Butterfly Garden	Blueprints	Artifacts, Inc.	The King Is Dead	Great Western Trail	My Little Scythe	Forbidden Sky	Unmatched Game System	Unmatched: Jurassic Park – InGen vs Raptors	Bloodborne: The Board Game	Carnegie	Arkendom Conquista Starter Set
14	At the Gates of Loyang	SNCF: France & Germany	Eclipse: New Dawn for the Galaxy	The Great Zimbabwe	Forbidden Desert	Roll for the Galaxy	Mombasa (Limited Edition)	Arkham Horror: The Card Game	Bunny Kingdom	Belfort: Edición Limitada	Star Wars: Outer Rim	Unmatched: Buffy the Vampire Slayer	Great Western Trail: Second Edition	Unmatched: Houdini vs. The Genie	Dune: Imperium – Uprising
15	FITS	Labyrinth: The War on Terror, 2001 – ?	Risk Legacy	Clash of Cultures	Suburbia + Inc.	Fields of Arle	Codenames	Sakura Arms	Sagrada	Agricola: All Creatures Big and Small – The Big Box	Clinic: Deluxe Edition	Rococo: Deluxe Edition	Cubitos	Return to Dark Tower	Unmatched Adventures: Tales to Amaze

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?