DC Comics, K-Means Clustering, Logistic Regression, Propensity Modeling

Recipe 011: DC Super Hero Throw Down: Propensity Modeling

FerraraTom

I want you to remember, Clark…In all the years to come… in your most private moments… I want you to remember my hand at your throat… I want you to remember the one man who beat you.

Chilling quote isn’t it?  That was said by Batman to Superman during the The Dark Knight Returns, a comic book miniseries written and drawn by Frank Miller.

One of the greatest debates in comic book lore and a fun discussion to have is pitting up two superheroes against each other… Who wins and why?  The below data story will introduce a data science approach to answering this debate.  To have fun with it… I’ve thrown characters from the video game Injustice 2 into a Superhero Thrown Down Tournament.


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Before we dive into the tournament and the results of the throw down, I’d like to touch on the approach: Propensity modeling.

Propensity modeling has been around since 1983 and is a statistical approach to measuring uplift (think return on investment).  The goal is to measure the uplift of similar or matched groups.

The heart of this approach lies within two machine learning approaches (segmentation and probability.)

Why propensity modeling for this exercise?  I wanted to rank my superheroes for the bracket using statistics (i.e. Batman is not getting a number one seed.)

35 characters were segmented on strength, ability, defense and health.  For the propensity score I gathered ranking information from crowd sourced websites and surveys.  Using this I was able to give an intangible skill score.  The reasoning was I wanted the medium of comics to do the majority of the work for me.  Comics are stories and the narrative drives the inner core of a character.  The higher a character is on a fan sourced website I’m assuming they are written well and are timeless.

Next step was to take the mean of the intangible skill score and flag those characters above the average (this will be my dependent variable for my logistic regression to calculate a propensity score).

What was thrown into the propensity model?  The skill sets gathered from the Injustice game, the assumption here is a character of Superman’s skill set would be written much differently then say Catwoman.

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Now it’s time for our throw down.

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The top four characters by propensity score were:

Cyborg

Supergirl

Aquaman

Black Adam

To determine a winner in the throw-downs characters were put up against each other in 11 categories.


Round 1 Takeaways:

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Our number one seed Cyborg nearly lost to Atrocitus. The result was 6-2-5, that’s read as six wins, 2 ties and 5 losses.

There were no upsets in the first round of play.  A few characters did not win a single category in their match-ups:

Harley Quinn (vs. Captain Cold)

Green Arrow (vs. Batman)

Black Manta (vs. Black Canary)

These three characters were ill-equipped to take on their opponent, it is possible they would have advanced given a new opponent.

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Round 2 Takeaways:

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Cyborg (our number one seed) defeated Captain Cold by a larger difference (+3 winning categories) compared to the previous match-up against Atrocitus, but he scored one win less.

We begin to see upsets in Round 2:

Robin defeated Black Adam by 1 winning category.  Wonder Woman defeated Firestorm by 4 winning categories.  Batman defeated Supergirl by 3 wining categories.

On propensity scores these were upsets, but from comic book debate standpoint you could argue these, i.e. given enough time to prepare Batman could defeat Supergirl.

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Round 3 Takeaways:

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Cyborg falls to Superman, loss by 4 categories.  This was the biggest fight Superman was given in this tournament to date (in both previous rounds he had 9 winning categories).

The upsets keep coming in:

Robin sneaks in a win again by 1 winning category (over Brainiac). Wonder Woman defeats the top seed in her region of the bracket (Aquaman) by 4 winning categories.  Batman defeated Green Lantern by 3 winning categories.

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Final 4 Takeaways:

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Robin’s Cinderella story comes to an end at the hands of Superman (winning in 9 categories).  Robin did fair better than those previously who gave Superman 9 category wins… Robin won in 2 categories.

Batman was able to upset Wonder Woman, by 2 winning categories.  We’re set for a championship round, the original who wins… Batman Versus Superman!

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Our winner is…

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Superman defeats Batman.  Superman did not win in a landslide.  Batman loss by two categories but he was able to win in 5 categories.  Previously the highest total win categories against Superman were 3 winning categories.


What did we learn from diving into the DC data?  Comic book writing and fan perception goes along way in determining who wins a thrown debate.  If we use propensity modeling we can have more even playing field and limit the amount of unfair battles.


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Classification Tree, Game of Thrones, Tree Based Models

Recipe: 009 Game of Thrones Survival of the Fittest

FerraraTom


“When you play the game of thrones, you win or you die.” — Cersei

Let’s bring this quote to life in what I like to call a survival tree of the fittest.  This week’s analysis will focus on the character survival in Game of thrones.  Chow down and enjoy!


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Winter is coming and you’d like to know your chances of survival in the Game of Thrones universe.

Let’s learn from those who have survived to this point and those who have met their unkindly fate.

To do this I’ll build a classification tree with my event being set to is the character alive (1 for yes, 2 for zero).  Classification trees in general test the null hypothesis, when we reach my tree visualization I’ll assign the color red to instances of were it’s highly probable of a character death.  Green leaves will indicate it’s highly probable a character survives… as long as all this criteria is met.

Think of this tree as a really morbid family tree, but since the data is Game of thrones it fits right into place.

The variables have readily available to me (hopefully they have importance) are as follows:

  • House Affiliation
  • Member of nobility
  • Marital Status
  • Gender
  • Family history of deaths
  • Popularity

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From the initial read I see knowing if a character is popular among fans and if they are male hold the highest importance in determining survival.

Also the variables I have available account for 75% of the variability (a 25% miss-classification rate).

Let’s say you moved to Westeros, out of the gate you have a 25.4% chance of meeting your end.  At those odds I’m taking my chances but I should stay under the radar as much as I can, because the data warrants it.

If you become a popular character or are an integral part of the story, your death becomes more meaningful and your probability of survival is worse than a coin flip.

So let’s say you’re a like-able character (you can’t help it), not all is loss, as long as you’re a female.  The highest survival rate is the popular female character group.  This is a classic tale of high risk high reward.

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A classification tree is a great way to visual your data and now I’ll walk us through this Game of Thrones survival tree.

Let’s start at the very top, the tree assumes everyone has a 75% of survival.  Now as the tree splits this Is where the interesting part begins, and our data story begins to unfold.

If you are a popular character you flow to the left side of the tree, your survival rate of 75% now drops to 48%.

Staying to the left side of the tree there is another important split, are you a male or female?  Female characters have a higher probability of surviving (87% if you’re popular and 76% if you’re under the radar).

If you’re a male and you’re popular you have a 42% chance of survival (We’re looking at your Peter Dinklage).

Now here’s the largest caveat to take with this classification tree: I’m assuming it will no longer be relevant after the final season.  Winter is coming and most likely our characters will see their end by hands of White Walkers.


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What have we learned from diving into the Game of Thrones Data?

Everyone has starts off at a 75% survival rate and as your popularity grows your survival rate lessons by 27%.  If you’re a male your survival drops again by 33%.  If you’re a popular female character you are 45% more likely to survive versus your male counterparts.

An interesting tidbit…If you become popular and you are a female (hopefully the mother of dragons) you boast the highest survival rate of anyone in this universe, 87%.

 

After you have consumed this meal, I hope you take these findings and enjoy your episode of Game of Thrones. J  Also as always enjoy the featured pancake recipe below!


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https://gameofthrones.fandom.com/wiki/Game_of_Thrones_Wiki


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Board Games, Logistic Regression, Regression Modeling

Recipe: 008 Likelihood a Board Game Is Universally Loved

FerraraTom

For this week’s analysis I’m taking a different approach to the introduction.  I reached out to @missionboardgame to write the forward.  They are a couple from Turkey who tries their best to inspire people to join board game community.  With out further ado here is there overview of the modern board gaming climate:

We think a successful modern board game should include the following features:

✔️Your decisions should have an impact on the game progress.
✔️Minimal randomness.
✔️No player elimination as possible as there can be throughout the game.

In addition to those, theme, artwork and mechanics are also significant for our decisions while purchasing board games. Therefore, our favorite game is Robinson Crusoe: Adventures on the Cursed Island. It is a cooperative survival game where you are trapped on a deserted island. Each decision you have made previously has an outcome afterwards. The harmony between the theme and the rules is perfectly arranged so that you feel very integrated to the game. By this way, every action you take seems meaningful and logical. Also we love feeling the cooperation among us since we are usually 2 players. – Mission Board Game

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Countless nights I’ve played board games among friends and family.  Every new year’s eve my family and I play Monopoly.  A few reasons: the game-play length, the amount of players, and the simplified game-play.  I have 5 siblings, so saying it’s difficult to find a game for all of us to play is an understatement.

The reasons why we enjoy board games is an interesting topic.  Is it the theme of the game?  Is it the amount of players required?  Has the game received universal praise from critics alike? Is it a common game most households own, and we grew up playing?

All the above-mentioned variables I’ll throw into a logistic regression model and use the Bayes theory of probabilities, to determine the probability of a board game player will rank a game higher than the average score.

During the first read I see the model is statistically significant based on a z score of less than .05.   A few things stand out to me immediately:

1.) Not all variables have a positive relationship to a highly scored board game

2.) There are some strong social elements going on here (i.e. the longer the play the higher the impact may imply games which encourage discussion are rated higher)

3.) Fantasy themed board games are not ranked high (I have a D&D and video games impact theory)

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Before jumping into the positive relationships, I’d like to touch briefly on the negative relationship independent variables.

1.) Fantasy Theme: I included this variable in the model expecting to see a very high positive correlation, but I was very wrong.  To quote Rick and Morty : “Sometimes science is more art than science.”  In the spirit of the quote, I’ll assume there are threats to the fantasy themed board games genre, in the form of Role-Playing Video Games.  The storytelling in this medium has progressed some much in last decade it out paces the anything a board game could offer.

In other words the target audience is leaving.

2.) Major of voters:  This variable is all about the amount of users who share their ranking.  A rule of thumb for rankings, reviews and ratings is those who go through the effort of expressing their opinion either love or hate the product.  The upper and lower confidence levels mirror themselves, because of this skew-ness.

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Next, I’ll discuss the positive relationship independent variables (focusing on those with the highest impact):

1.) Board games with an average game-play of at least two hours or more has the highest positive impact on a user rating a board game score above average.  What makes a game have a long game-play?

Multiple reasons: more players involved, more game-play mechanics, and mostly importantly more discussion.  The soul of any good board game is bringing people together.

2.) The second highest impact comes from the average score displayed from Game Board Geek.  The reason behind this is users see this rating first before submitting their rating.  Think of it like the Rotten Tomatoes effect, people want to feel like they have universally accepted opinions.  Take the beginning of this data story for example, I mentioned Monopoly is a family tradition of mine, this potentially could have swayed your opinion on this board game.  Possibility you could rate this higher than a game, say is fantasy themed, based on this model output.

For your own reference, this model has an accuracy rate of above 70%

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What have we learned from diving into the Board Game Data? 

Board games are most successful when they encourage the spirit and soul of “game night”, a gathering of friends and family discussing and enjoying each other’s time.  Adventure and exploration themes are the majority of the top ten highly successful board game genres.  The longer the game-play does not mean the game is like pulling teeth or the pace is slow.

It is more of an indicator of the amount of players required and the story telling the game has in driving a great game night experience.

 

After you have consumed this meal, I hope you take these findings and enjoy your next game night.  Also as always enjoy the featured pancake recipe below!


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https://boardgamegeek.com/


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Cosplay

Recipe: 007 Comic Con Cosplay and the Drivers of Instagram Engagement

FerraraTom


Halloween has recently passed and it’s a good transition into this week’s analysis;

Let’s face it dressing up on Halloween is the first step to cosplaying at your local comic con.

Cosplay can be a lucrative business if done correct, and many people do.  As you read through this week’s analysis I urge you respect and treat cosplayers as you would any other professional.  It that’s a lot of hard-work and dedication to master their craft as they have.


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A staple at any comic con is the Cosplay culture.  Fans show their appreciation and passion for beloved characters.  Cosplay can also be a lucrative business if you have a strong work ethic, are consistent, and dedicated to your craft.

Get out the hot glue gun and let’s start forming the foam!

I’ve gathered a random selection of Cosplay data from Instagram.  The cosplayers ranged from followers of +3 million to below 2K.  This alone posed an interesting challenge.  How do I normalize and standardize my data to fit into a model?

My solution was to factor in key performance indicators of Instagram success (regardless of being in the realm of cosplay) and implemented an engagement score for each cosplayer (like a customer value score).

To prevent confounding variables (influencers with a direct correlation to each other), I elected to excluded everything which went into the engagement score.

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My initial read shows this model is very predictive of the data sample gather from Instagram and the highest influencer with significance is the images of the Cosplayer where they are exposed (think NSFW but tasteful).  The amount of hashtags impact was skewed to a correlation of the more followers the less to no hashtags are used.


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If you’re a subscriber to this blog and enjoy the Stacks of Stats, you’ll recognize my preference for Q graphs.

There’s a large curl at both tails but most of the data fits well, so there won’t be a need to run a more complex model.

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What could be causing these extreme values towards the end of each tail?

While gathering and visualizing my data, I observed an interesting behavior:

The amount of hashtags deviates and almost has no correlation with engagement.

Driving the skew-ness is two factors:

Newer cosplay accounts use fewer hashtags at the beginning

Well established cosplay accounts use little to zero hashtags with their most recent posts.


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Our data story isn’t complete and once take the exposed variable to the profiling stage and begin to extrapolate the engagement impact, a telling data story begins to form.

For example, this table read as:

DC comics themed Cosplayers whom also happen to be exposed potentially drive nearly 700 more likes than cosplay images fully clothed.

In the case of what has the highest impact?  We can chalk up Nintendo to the champion and most of it is from the Bowsette trend. Potentially driving in a whopping +61K likes.

Interesting enough the runner up from a potential engagement impact standpoint is Scooby-Doo (Velma mostly), and the gap is less than 10K likes.

Does being exposed help all boost all themes of cosplay?  There is one theme in this sample where there was a negative relationship; Anime.  The possible reason behind this relationship is the niche fan base and attention to detail Anime fans have.  i.e. Hard to go as Sailor Moon without the bow.


 

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What have learned from diving into the Cosplay Data?

Being a top cosplayer on Instagram is as delicate as any social media fame.  Every post, every composition, every hashtag, every theme… can make or break your brand.  Not all cosplay needs to have a level of exposure to be successful, but it is a huge driver in engagement.

A few uses of this analysis are if you’re going to theme as Scooby-Do lean towards Velma and there’s enough out there for comparison.

If you’re looking for a large impact and a fan of video games, take dive at Bowsette (drives in a potential +61K likes).

Finally more hashtags does not mean more likes.

There’s more value in posting a cosplay of character you are passionate about and post relevant hashtags for more organic likes.

After you have consumed this meal, I hope you take these findings and improve your cosplay engagement.  Also as always enjoy the featured pancake recipe below!


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https://www.inquisitr.com/5035455/the-5-sexiest-female-cosplayers-to-follow-on-instagram/


 

 

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Regression Modeling

Recipe: 002 Marvel Cinematic Universe Regression Model

 


FerraraTomThere’s is no argument against the Marvel Cinematic Universe being a financial success.  I’ll try to identify variables which can equate to box office success. The goal is to fit a regression model to Box Office USD for Marvel Cinematic Movie releases.
*At the time of cooking Ant-man and the Wasp did not have finalized Box Office USD data (This movie was excluded.) – TF


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Thanks for stopping and chowing down on this Recipe (click the link for a reader’s friendly pdf version of this recipe)

Now try this delicious pancake recipe (with the Ironman Gold and Red finish) courtesy of Crème De La Crumb (Link Below):

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