[OC] Conditional Probability Relationships Between Popular YuGiOh Cards / Engines
September 27, 2024
[OC] Conditional Probability Relationships Between Popular YuGiOh Cards / Engines
Posted by Yelbuzz
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Using the data hosted on [https://www.masterduelmeta.com/top-decks](https://www.masterduelmeta.com/top-decks) which gives deck lists for user-submitted yugioh decks, I used Python to approximate pairwise conditional probabilities between each card. For example, relationships are of the form “If we observe Spright Elf in a deck, what is the probability that Spright Carrot is also in the deck?”. This would be an outgoing edge from Spright Elf to Spright Carrot in this directed graph with weight equal to that probability. Node size is based on overall card popularity of the form ‘If I’m handed a deck with no information, what’s the probability that it contains Maxx “C”‘ (Spoiler: Very high).
Therefore, large cards are more popular and cards pulled toward the center of the graph tend to be more versatile, as they are pulled in all directions by a wide variety of decks. Cards that work together to form engines (like the Fire King engine shown in slide 3) tend to form clusters due to the high pairwise conditional probabilities between all of those cards, since they are very often packages together. Card clusters on the very outskirts of the graph tend to be cards that make decks containing only that archtype and maybe staples from the center, but themselves cannot be used in a wide variety of other decks.
1 comment
Using the data hosted on [https://www.masterduelmeta.com/top-decks](https://www.masterduelmeta.com/top-decks) which gives deck lists for user-submitted yugioh decks, I used Python to approximate pairwise conditional probabilities between each card. For example, relationships are of the form “If we observe Spright Elf in a deck, what is the probability that Spright Carrot is also in the deck?”. This would be an outgoing edge from Spright Elf to Spright Carrot in this directed graph with weight equal to that probability. Node size is based on overall card popularity of the form ‘If I’m handed a deck with no information, what’s the probability that it contains Maxx “C”‘ (Spoiler: Very high).
Therefore, large cards are more popular and cards pulled toward the center of the graph tend to be more versatile, as they are pulled in all directions by a wide variety of decks. Cards that work together to form engines (like the Fire King engine shown in slide 3) tend to form clusters due to the high pairwise conditional probabilities between all of those cards, since they are very often packages together. Card clusters on the very outskirts of the graph tend to be cards that make decks containing only that archtype and maybe staples from the center, but themselves cannot be used in a wide variety of other decks.
For coloring, I used the cdlib leiden algorithm to identify communities and color based on those. To generate the interactive graph itself, I used the PyGraphistry api. You can mess with this visualization yourself [here](https://hub.graphistry.com/graph/graph.html?dataset=adc70ec2e8a3453a813a6ba76f2b43c0&type=arrow&viztoken=d71e8a79-a926-4cb4-9950-8e0c9307ac7f&usertag=a4107885-pygraphistry-0.34.5&splashAfter=false&info=true&play=15000&edgeCurvature=0.1&precisionVsSpeed=-3&edgeOpacity=0.02&pointsOfInterestMax=5). Note that the colors may not appear in this link (not sure why) and you might have to set them up yourself with the my_community histogram.