A simulation study on the 2nd Mythic Championship Qualifier Weekend

The second mythic championship qualifier weekend will be held

on August 15 of this year, with winners feeding into Mythic Championship V. Details of the weekend event can be found here. Day one of the event is a best-of-three standard queue where players play until their 10^th win or their 2^nd loss. The top 128 players of Day One make it to Day Two. Given this, one question that weighed on my mind (besides which deck to play which is still weighing on my mind at the time I am writing this), is how many wins I need to make in order to feel comfortably safe that I will make it to Day Two. Strategically, this question has no value since the best strategy is still to keep playing until elimination. However, I felt that knowing what number of wins is safe will have a positive impact on my perspective, since thinking about doing 10 wins before my second loss seems like a near-impossible task. Thus, I decided to do a short simulation study on the outcomes of the mythic qualifier weekend. In particular, I wanted to know the minimum number of wins for one to be confident that he or she will make it to Day Two, as well as the minimum number of slots that will be decided by tie-breakers.

Simulation Settings

The event will have a maximum of 6000 participants (half from ranked constructed and half from ranked draft). I did not find any details on how players will be paired and so I am just going to assume that they will be paired randomly, depending on who is in the queue. It should be noted that this assumption makes my results more conservative than they actually are. If the matching system enables only people with comparable standings to be matched, then the “safe” number will be lower than my results.

Also, I am assuming that all players will be entering the queue at the same time and are starting and finishing their matches at the same time. This assumption is, of course, not consistent with reality. People will be entering the queue at different times of the day and will start and finish matches at different times. However, this assumption is made because 1.) I have no information on the distribution of the factors identified, and 2.) the assumption made again allows for the most conservative estimates.

Finally, I am assuming that players have equal chances of winning against each other. This is again not an accurate assumption but one that will generally not affect the estimates since it only affects who gets into the top 128, not how wins it takes.

Given this, the algorithm used is generally described as follows:

Step 1: Generate 6000 players

Step 2: Pair players with one another, determine the outcome of each match

Step 3: Remove players who have either made 2 losses or 10 wins

Step 4: Check the remaining number of players, if less than or equal to 128 remains, stop the program. Otherwise, return to Step 2.

The first variable of interest is X, the minimum total wins of players who remain after the program terminates. Since all qualifying players played the same number of games at this point, then the minimum score to qualify will be X+1. This is because at this point, none of the players who were eliminated have a score equal to X+1 and the remaining players are already less than or equal to the number of slots. Those who have exactly X wins may still get eliminated if they get eliminated in their next match, since they are still competing for tiebreaks with the players who have X-2 records and so have been eliminated from the queue.

The second variable of interest is the number of players remaining in the queue when the program terminates. This gives an idea of how many people can get in via tiebreaks.

Finally, I also recorded the number of iterations it took for less than or equal to 128 players to remain. This gives an idea of the maximum score of qualifying players at this point. It is not really of importance but I recorded it anyway.

I ran the simulations under three settings: 6000, 4000, and 3000 starting players. Each setting was ran 1000 times. The program was coded in R.

Results

The following table shows the average of results across 1000 simulations.

Number of Starting Players	Min # of Wins	Safe # of Wins	Minimum Tie-Break slots	Number of iterations
6000	7.306	8	10.434	9.005
4000	7.296	8	49.376	9
3000	6.305	7	21.967	8

As shown from the table, if all 6000 players compete, then the safe number of wins is 8, and those with 7 wins will compete on tiebreaks over a number of slots equal to 10 plus the number of players who got 7 wins (in hindsight, I should have included this among the numbers collected from the simulation). If only 4000 players joined, which was the maximum case in the first qualifier weekend, then 8 is exactly the safe number of wins. With at least 49 slots up for grabs for those who were able to get 7 wins (or less).

Conclusion

Despite increasing the number of possible wins to 10 from 8 in order to account for the fact that there are 2000 more slots for second the mythic championship weekend qualifier, the safe number of wins seems to still be 8, with people who have 7 wins still having skin in the game. Accomplishing such a record is still no easy feat, but at least if I do get to 8 wins, I can breathe a sigh of relief and be confident that I will remain in the tournament the next day.