On YuGiOh Statistics

This post is inspired by this reddit thread, where someone did a fantastic analysis of this year's championship games. Their findings made us wonder, to what degree our own games are affected by who goes first and maxx C. For every game we played in the last few months we recorded, Result (did we win?), Start (did we go first or second?), maxxc (did 2nd player get a maxx C cast) and opponent (what deck did our opponent play). The question we wanted to answer is, when it comes to winning or loosing, how much of it is explained by "going first, with/without maxx C" and by the deck that is played? Whatever percentage remains, must therefore represent "luck in card draw" and how well the game was played. The games were all played in season mode, most of them in diamond and the recent duelist cup. Here is what we found.

Over all, we had a 55.3 % [103] win rate when going first and a 38.6 % [83] win rate when going second. Maxx C makes the first-win/second-loose bias reverse.

We played a total of 186 games and won about 47.8 % of them. And at first this looks like a balanced game play. When looking into just the games, where we went first though, the win rate goes up to 55.3 % [103] and when looking only at games where we went first and our opponent did not get a maxx C (either none was played or we denied it), the win rate goes up to even 67.1 % [79]. Putting win/lose, first/second w.r.t. maxx C side-by-side reveals how stark the effect is. When going second, in general, we had a win rate of just 38.6 % [83], which went up to 69.2 % [13], when we were able to get a maxx C through.

Next we look at the effect of decks that are played. For the length of our recording time we played one deck and never changed it, to not influence the result, so we only look at the effect of our opponent's decks. We labelled decks by what their main line is, so e.g. if the main line is fiendsmith, we labelled it that. A deck that merely contained fiendsmith, but really was about something else, was labelled that and not fiendsmith. Decks that we couldn't label to an archetype were labelled as "misc". And archetypes that we encountered not often enough, were also labelled as "misc". Here is a distribution of what we encountered during our games. 

Close to 40% of times we played, it was against either maliss or ryzeal. We found this stat on masterduelmeta.com that says maliss has a usage rate of up to 42%. We want to say, we are very happy about not having to deal with it that often ourselves.

When looking at our win rates sorted by opponent, we find that most of them are within a 10% band around the 50% mark, which we would expect in a balanced game. Maliss is the only one, where our win rate dropps significantly to around 25%. Since we consider it overplayed and annoying, we find ourselves forfeiting every now and then when merley seeing, that our opponent plays maliss. Note, that we did not include any of those insta-forfeit games into our analysis.

Before we come to a conclusion we must reveal what we've been playing: a combination of blue eyes and Kashtira. Now, this may be a surprise, because these two have no synergy whatsoever. Blue eyes is built around level 8 monster, with syncro summons and playing things from the graveyard, while Kashtira is based on level 7 monsters, XYZ summons and even preventing things from going to the graveyard. We do play them because blue eyes makes us nostalgic for watching the show as a kid, and Kashtira somehow looks and feels good. And it is partly because we play such an unpairable combination, that we wanted to see how much the choice of deck actually affects the outcome of the game. 

Screenshot of us having Shangri-ira, a white dragon and a fiendsmith. May look silly, but it is fun to play and if we go first and the opponent has no maxx C, this deck has an almost 70% win rate. 

We defined four meta states, start_maxxc_yes, second_maxxc_no, ... . The Cramér’s V association of this meta state with the win/loose result was 0.39, which is far larger than a balanced game would have, but still not deterministic. To calculate how much of the win rate is explained by Start/maxxc we did a logistic regression using those two as features. We find that around 12% of the variance in our win rate is explained by who starts and does the second player get to successfully use maxx C. This is significantly higher than if we looked at who goes first alone. But it also leaves around 87% of the win rate to be explained by card draw luck and hopefully skill. When looking at start/maxxc alone as a predictor, it reaches a 69.3% accuracy, which is what we have in mind when seeing the coin flip over who goes first. As a final remark, we want to show the distribution of turn counts, i.e. how many turns the duels lasted. The vast majority of the duels took only one or two turns. Only 15% of the games took more than three turns. But it was actually those duels that lasted a while and had quite a bit of back and forth, that we enjoyed the most, either winning or loosing.

Most games are decided in just the first two turns, but often times even winning isn't fun, if it boils down to us playing solitaire while our opponent is reduced to observe.