A Win-Rate Model for the Pokémon TCG

Hey everyone! It’s been a long time since I asked for help to my bachelor project. After many months, the project has finally been written, defended, and graded. I could have put it up earlier, but there were a lot of other things I had to attend to first. I might also have forgotten it for a brief moment. :P

I decided to publish my project, however in a slightly different version than the one I handed in. The project itself ended up with top grade, however remember that the project was not graded from a Pokémon player’s perspective, so maybe I missed out something in the paper (seen from a players point of view), but the math should be correct.

The paper is quite extensive for an article and therefore I placed the abstract here and then for those of you, who would like to give it a closer look, you are welcome to download the PDF.

Much attention was given to the method of estimation and still there was a lot more there could be done. Even though the results are stated in numbers, we are still only able to conclude in which direction the effect of a factor would have and if it was weak or strong. This you can read a lot more about in the paper itself.

You can all skip chapter 1, since it would just be boring for most of you. I strongly believe that people here know the game; that chapter only contains introductory stuff.

Chapter 2 considers the data collection and would be nice to read. Going on to chapter 3, it would start to contain a lot of math and would be quite hard for many to read and understand. Don’t worry; the important stuff is contained in chapter 4-6, which certainly is worth reading.

An important notice. This paper was based on the previous season and might not seem worth anything for now, but remember that this model can just be transformed and used in an updated version for a new season and thereby tells us some interesting things.

The estimation method is still valid, but as I indicated in the paper, it can still be improved, which may be done in the future. I’m just glad that I could get the chance to work with it and analyse the game I really like to play.

I hope that you all will enjoy reading the paper. :)


The strategic card game known as Pokémon Trading Card is a dynamic game where a lot of different factors can influence the outcome of a game. This paper investigates what affects a Pokémon TCG player’s win-rate besides luck, with respect to the season 2010-2011. In order to do so a cross sectional dataset containing 84 individuals was collected along with 7 interviews.

Techniques from econometrics are applied in other to determine the effect of the different factors on a player’s win-rate. In a situation where the dependent variable is a coding of qualitative outcome, a probability model is applied to maintain the familiar type of regression. The dependent variable could then be linked to a list of factors, each of them with a different impact on the probability for a higher or lower win-rate.

The model chosen is the logit model due to its mathematical convenience and the fact that the posterior distribution is a continuous probability function which then holds with the theory of probability models. To take account for problems with heteroscedasticity a weighted least-squares logistic regression for grouped data, known as glogit, has been used to estimate the data.

Results revealed a positive effect of experience, playing decks containing a SP-engine and being a Pokémon professor. Ageing proves to have a negative effect on a player’s win-rate. There is no difference whether a player is from the USA or not. Also having family members playing, having a job or playing abroad during the season showed no significant influence on the win-rate.

View the rest: (Removed at the Request of the Author)

Reader Interactions

12 replies

  1. David Rowell

    You have a few errors in your paper, like Magic; The Gathering should be Magic: The Gathering, and “The more a player play test” should be tests. However, it’s a very good paper over-all and perfectly describes the format that I started playing the game in, and the paper itself is a very interesting concept. Good job.

    • Mohamad  → David

      “A few” is an understatement. There are enough grammatical errors within the first three pages to make an English teacher cry his way to the grave.

      Mathematically though, I’m still making my way through the paper to comment on it yet. But props on using the SP engine as a variable; pure search is indeed strong enough to affect a win rate compared to shuffle-draw.

      • Steffen Eriksen  → Mohamad

        Im glad that you point SP variable out. It has indeed a huge impack on a player’s win-rate. I’m not quite sure about the English gramma. True that I’m not a native English speaker or anything like that. But the paper has been through 3 people, who are native speakers. So based on that, I assumed that the gramma was ok.
        Again what is more important here is the results of course. Showing the specially the professor status had a positive impact, although a small one, is quite surprising.

        Also thanks to everyone who read the report and please just come with some comments.

      • Mark Hanson  → Mohamad

        To be fair, this is translated to English. I bet he originally wrote it in Danish or if he didn’t, both him and his professor speak English as a second language. I’ve taken enough Japanese to speak it as fluently as a 10 year, old but I bet I wouldn’t write a grammatically correct research paper no matter how much I tried :P

  2. Eli Norris

    I’ll check this out later as I’m currently at school, but the Abstract certainly attracts my attention and I will certainly give it a good read.

  3. Mark Hanson

    Aw man! I did a project with logit loglinear regression models last year. I’m super interested in reading this and now I’m hopeful I’ll be able to understand most of it!

    p.s. Major win on writing your BSc. on Pokemon TCG. Math people get to have fun topics, provided the math is there :P I know a guy who did a project on stacking different configurations of lego blocks in the corner of a room.

  4. DrMime

    I liked the paper a lot! I’m a little worried, however, about you trying out the variable “agesquare” instead of “age”; the last thing I need at a Pokemon tournament is my opponents telling me I’m 1681 years old.

    • Steffen Eriksen  → DrMime

      Im glad that you liked it. However you are wrong about what you are saying about the “agesquare” variable. When showing the effect of aging, you have to take the derivative of the model w.r.t. age, then it would show a decreasing effect of aging. So that each year will have a smaller negative effect on you winrate until you reach the end of your fourties. Look at page 23 for the discussion about it.
      This was the simplest explanation I could come with. If you want a more detailed explanation, just ask :)

      • DrMime  → Steffen

        Yeah, I think I was joking about agesquare. But it is good to know that, because I’m at the beginning of my forties, I have a few more years of Pokémental decline left before I hit old-man-rock-bottom.

        Joking again, BTW.

  5. Andrew Mann

    I skimmed threw the article, I thought it was interesting, and I’m disapointed that no one (to my knowledge) has attempted to create anything like this for Magic. By doing so they would surely have a much larger test base, and perhaps with 200-300 participants, we’d have a much greater understanding if this model helps to prove/disprove win-ratio (and other related theory).
    Thanks for presenting this to us.

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