Frank Analysis – How Important Is It To Play First?

In Magic, the commonly accepted wisdom is that in most circumstances it is best to play first. But is this actually true, and how large is this advantage?

Let’s first look at this question from an intuitive perspective: The advantage of being on the play is that you can play cards and attack with creatures one turn before your opponent can do so. The downside is that you have one fewer card to work with than your opponent in every turn of the game. However, in the early turns, this extra card usually doesn’t improve your plays, so if you expect the games to take only a few turns, then the speed boost will usually outweigh the extra card. That is, playing first should be better.

But I don’t want to rely on such a flimsy explanation. Let’s take a look at some hard, juicy data!

I have results from recent Grand Prix tournaments and a hypothetical Lightning Bolt format in store for you today. There are too many Magic formats and matchups to give a conclusive answer to the question of how important it is to play first, but I hope that my analysis today can at least yield some new insights.

How often does the higher-rank player win in a Grand Prix Top 8?

For the first game of each match in a Grand Prix Top 8, the player that finished higher in the Swiss rounds chooses either to play first or to play second. Assuming that this player would always choose to play first, we can combine the final Swiss rankings with the outcomes of the Top 8 matches to determine how often the player on the play wins the Top 8 match.

Before scrolling down, take a moment to guess what the percentage could be, and whether or not it will differ between Constructed and Limited tournaments.

Some quick remarks:

  • The nice aspect of this data-set is that these are matches between top players. They made it to the Top 8 of a Grand Prix, after all!
  • I am implicitly assuming that each player in the Top 8 is equally good. This is not far from the truth in my experience. Maybe higher-rank players would win one percent more than lower-rank players if the play/draw rule would not be in effect (because their higher rank signals that they are slightly better at this format) but I am going to ignore this minor effect.
  • The data that I looked at were all non-team Grand Prix tournaments from Malmo 2012 to Mexico City ’14. Why stop there and not collect data on the rest of 2014 or on Pro Tours in that period, you might ask? There is an extremely scientific reason for this: The data collection and especially the subsequent clean-up (when, e.g., names were spelled or formatted differently between the Swiss rankings and the Top 8 matches) had already taken me longer than I had anticipated, and I had to catch my flight to Honolulu.
  • The percentages that I will show are match win rates, not game win rates.
  • I coded the analysis via SAS and SQL. I had to learn those languages for work-related purposes, so I figured I might as well get some extra practice by applying them to this Magic-related problem. The data and code is available here if you’re interested.

On to the results!

For Constructed GP Top 8s: The player who was on the draw in the first game won the match 138 times, and the player on the play won 155 times. So, based on this data, the player on the play in the first game has a 52.9% chance of winning the match.

For Limited GP Top 8s: The player who was on the draw in the first game won the match 106 times, and the player on the play won 118 times. So, based on this data, the player on the play in the first game has a 52.7% chance of winning the match.

These two percentages paint a clear picture that the player on the play indeed has a small edge. I expected that much, but I was surprised to see how close the two percentages were. I had expected the Limited play-first win rate to be substantially lower than the Constructed one. Limited games tend to last a little longer and feature decks with weaker mana bases, after all. I admit that the sample size may not be large enough to draw far-reaching conclusions from this, but it is interesting to see that the two percentages are so close nevertheless.

How often does the player on the play win in a Lightning Bolt mirror match?

Consider the mirror match of the 44 Lightning Bolts, 16 Mountains deck. Suppose that each player mulligans every 5-, 6-, and 7-card opening hand with 0, 4, 5, 6, or 7 Mountains. When these two decks play against each other, how often does the player on the play win?

Again, before scrolling down, take a moment to guess what the percentage could be, and also consider what you would expect to happen if we were to replace the 44 Lightning Bolts with 44 Shocks.

Some quick remarks:

  • The 44 Bolt deck and corresponding mulligan strategy were found to be optimal for a goldfish format in which only Bolts and Mountains were legal, as described in this article.
  • For the game theorists amongst you: Two 44 Bolt decks need not form a Nash equilibrium for this 2-player format. Well, actually a Nash equilibrium would not even appropriate for this setting with chance moves and incomplete information—the refinement of a weak sequential Nash equilibrium may be more applicable. But analyzing that would make things unnecessarily difficult, and I haven’t even gotten into the issues of existence and multiplicity of equilibriums. So let’s just keep things simple, accept these decks and mulligan strategies, and let’s go from there.
  • I simulated 100 million games. You can find the code I used here.

So what are the results?

As it turns out, the Lightning Bolt deck on the play wins 59% of the games. (For comparison with the GP Top 8 matches, this translates to a 63% match win rate.)

Next, let’s see what would happen if we replace Lightning Bolt by Shock, while keeping everything else the same. (Maybe you’d want more burn cards and fewer lands or a different mulligan strategy if the burn cards are less powerful, but let’s just keep the same distribution as the Bolt decks for ease of comparison.) Then, all of a sudden, the deck on the play only wins 43% of the games! (This comes down to a 40% match win rate.) Clearly, when you have to chain 10 rather than 7 burn spells to win the game, drawing an additional card becomes much more important.

Concluding Remarks

The results from this analysis were mostly in line with my intuition: The player who plays first will have a small advantage if the games are over quickly (as in the Lightning Bolt format, where most games end by turn 4 or 5). However, the advantage is less pronounced in slower formats, and when the games take long enough, it can even become better to draw first.

Were you surprised by these results? Were they in line with what you were expecting? Let me know in the comments!

Now let’s board this flight to Honolulu…

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