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Definitions:

  • Top player: the old platinum-ranked pros, or MPL members. If there isn't enough data for this small group, I'm also interested in the old gold-ranked players.
  • Tournament: an open tournament with several hundred, if not thousands, of players, such as the GPs of old. Small invitationals don't count, although the former Pro Tours are borderline since they're still pretty big.

Last I saw Magic: the Gathering tournaments followed a format where everyone plays Day 1, at the end of which there is a cutoff for Day 2. At the end of Day 2 there is a cut to top 8, where single elimination matches decides a champion. For many players, making Day 2 is an achievement, and a realistic, achievable target.

I am interested in how often the best players in the game make the cutoff for Day 2. Are there statistics for this anywhere?

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I asked professional player Raphael Levy and he said platinum-level pros win about 65% of their matches at this level (it drops to 60% at pro tour level). To reach day 2 one needs 7-2 or better, and platinum-level players get 3 byes, so they need to win 4 out of 6 matches or better.

We can do calculations:

  • p(6 wins) = 0.65^6 * 6C6 = 7.5% chance
  • p(5 wins) = 0.65^5 * 0.35 * 6C1 = 24.36% chance
  • p(4 wins) = 0.65^4 * 0.35^2 * 6C2 = 32.80% chance

Therefore they are about 64.70% to make day 2. If they didn't get three byes, then:

  • p(9 wins) = 0.65 ^ 9 * 9C9 = 2.07% chance
  • p(8 wins) = 0.65 ^ 8 * 0.35 * 9C1 = 10.04% chance
  • p(7 wins) = 0.65 ^ 7 * 0.35^2 * 9C2 = 21.62% chance

For a total of about 33% chance.

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  • This assumes that individual results are independent; while that may be a reasonable assumption at large scale, within an individual tournament I suspect it's going to be not a good assumption. If a player has for one reason or another brought a deck which is good against the field, their chance will be much higher than a third (or much less with a bad deck).
    – Philip Kendall
    Jan 11, 2022 at 8:15
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    @PhilipKendall yeah, it neglects the fact that the average opponent will be stronger or weaker depending on whether one won the previous round as well. I think it's good enough of an estimate though, and it also looks reasonable, e.g. magic.wizards.com/en/content/… here is a Hall of Famer's profile page. Their win rate at GPs is 59.32%. I also doubt we'll get much better estimates.
    – Allure
    Jan 11, 2022 at 8:20
  • You also have the outlier that a superior meta choice or more effective side boarding can on occasion win tournaments. There were occasions where the cawblade was beat by burn decks at certain SCG events only because they where so bent on beating the mirror that they stopped running the kor firewalkers in the sideboard, giving the burn decks a chance.
    – Neil Meyer
    Feb 7, 2022 at 21:16
  • Correction: Zvi Mowshowitz's (the Hall of Famer in my comment above) GP win rate is 62.78%. The site gives 59.32%, but that apparently includes draws and byes. This makes the 65% win rate given by Raphael Levy more believable: 65% win rate on day 1, 60% on day 2, averaging to 62.78%.
    – Allure
    Mar 17, 2022 at 8:37

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