This is in response to the Magic: the Gathering World Championship that just finished, which featured some great Magic played in a highly questionable format. It had three giant flaws:
- It buried players far too quickly. Assuming every match was a coinflip, each of the 16 players started with a 6.25% chance to win. Going 2-0 or 2-1 in draft meant you were just over 12% to win and going 0-2 or 1-2 in draft meant you were just under 0.5% (under 1 in 200) to win. Ouch. In turn, this meant we were watching a crapload of low-stakes games and the players involved were just zombies drawing to worse odds than a 1-outer even if they won.
- It treated 2-0 and 2-1 match record in pods identically. That’s kind of silly.
- The upper bracket was Bo1 match, with each match worth >$100,000 in equity. The lower bracket was Bo3 matches, with encounters worth 37k (lower round 1), 49k, 73k, and 97k (lower finals). Why were the more important matches more luck-based?
and the generic flaw that the structure just didn’t have a whole lot of play to it. 92% of the equity was accounted for on day 1 by players who already made the upper semis with an average of only 4.75 matches played, and the remaining 12 players were capped at 9 pre-bracket matches with an average of only 6.75 played.
Whatever the format is, it needs to try to accomplish several things at the same time:
- Fit in the broadcast window
- Pair people with equal stakes in the match (avoid somebody on a bubble playing somebody who’s already locked or can’t make it, etc)
- Try not to look like a total luckbox format- it should take work to win AND work to get eliminated
- Keep players alive and playing awhile and not just by having them play a bunch of zombie magic with microscopic odds of winning the tournament in the end
- Have matches with clear stakes and minimize the number with super-low stakes, AKA be exciting
- Reward better records pre-bracket (2-0 is better than 2-1, etc)
- Minimize win-order variance, at least before an elimination bracket (4-2 in the M:tG Worlds format could be upper semis (>23% to win) or lower round 1 (<1% to win) depending on result ordering. Yikes.
- Avoid tiebreakers
- Matches with more at stake shouldn’t be shorter (e.g. Bo1 vs Bo3) than matches with less at stake.
- Be comprehensible
To be clear, there’s no “simple” format that doesn’t fail one of the first 4 rules horribly. Swiss has huge problems with point 2 late in the event, as well as tiebreakers. Round robin is even worse. 16-player double elimination, or structures isomorphic to that (which the M:tG format was), bury early losers far too quickly, plus most of the games are between zombies. Triple elimination (or more) Swiss runs into a hell match that can turn the pairings into nonsense with a bye if it goes the wrong way. Given that nobody could understand this format, even though it was just a dressed-up 16-player double-elim bracket, and any format that doesn’t suck is going to be legitimately more complicated than that, we’re just going to punt on point 10 and settle for anything simpler than the tax code if we can make the rest of it work well. And I think we can.
Hareeb Format for 16 players:
Day 1:
Draft like the opening draft in Worlds (win-2-before-lose-2). The players will be split into 4 four-player pods based on record (2-0, 2-1, 1-2, 0-2).
Each pod plays a win-2-before-lose-2 of constructed. The 4-0 player makes top-8 as the 1-seed. The 0-4 player is eliminated in 16th place.
The two 4-1 players play a qualification match of constructed. The winner makes top-8 as the #2 seed. The two 1-4 players play an elimination match of constructed. The loser is eliminated in 15th place.
This leaves 4 players with a winning record (Group A tomorrow), 4 players with an even record (2-2 or 3-3) (Group B tomorrow), and 4 players with a losing record (Group C tomorrow).
Day 2:
Each group plays a win-2-before-lose-2 of constructed, and instead of wall-of-texting the results, it’s easier to see graphically and that something is at stake with every match in every group.
with the loser of the first round of the lower play-in finishing 11th-12th and the losers of the second round finishing 9th-10th. So now we have a top-8 bracket seeded. The first round of the top-8 bracket should be played on day 2 as well, broadcast willing (2 of the matches are available after the upper play-in while the 7-8 seeds are still being decided, so it’s only extending by ~1 round for 7-8 “rounds” total).
Before continuing, I want to show the possible records of the various seeds. The #1 seed is always 4-0 and the #2 seed is always 5-1. The #3 seed will either be 6-2 or 5-2. The #4 seed will either be 5-2, 6-3, or 7-3. In the exact case of 7-3 vs 5-2, the #4 seed will have a marginally more impressive record, but since the only difference is being on the same side of the bracket as the 4-0 instead of the 5-1, it really doesn’t matter much.
The #5-6 seed will have a record of 7-4,6-4, 5-4, or 5-3, a clean break from the possible top 4 records. The #7-8 seeds will have winning or even records and the 9th-10th place finishers will have losing or even records. This is the only meaningful “tiebreak” in the system. Only the players in the last round of the lower play-in can finish pre-bracket play at .500. Ideally, everybody at .500 will either all advance or all be eliminated, or there just won’t be anybody at .500. Less ideally, but still fine, either 2 or 4 players will finish at .500, and the last round of the lower play-in can be paired so that somebody 1 match above .500 is paired against somebody one match below .500. In that case, the player who advances at .500 will have just defeated the eliminated player in the last round. This covers 98% of the possibilities. 2% of the time, exactly 3 players will finish at .500. Two of them will have just played a win-and-in against each other, and the other .500 player will have advanced as a #7-8 seed with a last-round win or been eliminated 9th-10th with a last-round loss.
As far as the top-8 bracket itself, it can go a few ways. It can’t be Bo1 single elim, or somebody could get knocked out of Worlds losing 1 match, which is total BS (point 3), plus the possibility of going 4-1 5th-8th place in a 16-player event is automatically a horseshit system. Even 5-2 or 6-3 5th-8th place (Bo3 or Bo5 single elim) is crap, but if we got to 4-3 or 5-4 finishing 7th-8th place, that’s totally fine. It also takes at least 5 losses pre-bracket (or an 0-4 start) to get eliminated there, so it should take some work here too. And we still need to deal with the top-4 having better records than 5-8 without creating a bunch of zombie Magic. There’s a solution that solves all of this reasonably well at the same time IMO.
Hareeb format top-8 Bracket:
- Double-elimination bracket
- All upper bracket matchups are Bo3 matches
- In the upper quarters, the higher-seeded player starts up 1 match
- Grand finals are Bo5 matches with the upper-bracket representative starting up 1-0 (same as we just did)
- Lower bracket matches before lower finals are Bo1 (necessary for timing unless we truly have all day)
- Lower bracket finals can be Bo1 match or Bo3 matches depending on broadcast needs. (Bo1 lower finals is max 11 sequential matches on Sunday, which is the same max we had at Worlds. If there’s time for a potential 13, lower finals should definitely be Bo3 because they’re actually close to as important as upper-bracket matches, unlike the rest of the lower bracket)
- The more impressive match record gets the play-draw choice in the first game 1, then if Bo3/5, the loser of the previous match gets the choice in the next game 1. (if tied, head to head record decides the first play, if that’s tied, random)
This keeps the equity a lot more reasonably dispersed (I didn’t try to calculate play advantage throughout the bracket, but it’s fairly minor). This format is a game of accumulating equity throughout the two days instead of 4 players hoarding >92% of it after day 1 and 8 zombies searching for scraps. Making the top 8 as a 5-8 seed is a bit better than the pre-tournament win probability under this format, instead of the 1.95% in the Worlds format.
As far as win% at previous stages goes,
- Day 2 qualification match: 11.60%
- Upper play-in: 5.42%
- Lower play-in round 2: 3.61%
- Lower play-in round 1: 1.81%
- Day 2 elimination match: 0.90%
- Day 2 Group A: 9.15%
- Day 2 Group B: 4.93%
- Day 2 Group C: 2.03%
- Day 1 qualification match: 13.46%
- Day 1 2-0 Pod: 11.32%
- Day 1 2-1 Pod: 7.39%
- Day 1 1-2 Pod: 4.28%
- Day 1 0-2 Pod: 2.00%
- Day 1 Elimination match: 1.02%
2-0 in the draft is almost as good as before, but 2-1 and 1-2 are much more modest changes, and going 0-2 preserves far more equity (2% vs <0.5%). Even starting 1-4 in this format has twice as much equity as starting 1-2 in the Worlds format. It’s not an absolutely perfect format or anything- given enough tries, somebody will Javier Dominguez it and win going 14-10 in matches- but the equity changes throughout the stages feel a lot more reasonable here while maintaining perfect stake-parity in matches, and players get to play longer before being eliminated, literally or virtually.
Furthermore, while there’s some zombie-ish Magic in the 0-2 pod and Group C (although still nowhere near as bad as the Worlds format), it’s simultaneous with important matches so coverage isn’t stuck showing it. Saturday was the upper semis (good) and a whole bunch of nonsense zombie matches (bad), because that’s all that was available, but there’s always something meaningful to be showing in this format. It looks like it fits well enough with the broadcast parameters this weekend as well with 7 “rounds” of coverage the first day and 8 the second (or 6 and 9 if that sounds nicer), and a same/similar maximum number of matches on Sunday to what we had for Worlds
It’s definitely a little more complicated, but it’s massive gains in everything else that matters.
*** The draft can always be paired without rematches. For a pod, group, upper play-in, lower play-in, or loser’s bracket round 1, look at the 3 possible first-round pairings, minimize total times those matchups have been seen, then minimize total times those matchups have been seen in constructed, then choose randomly from whatever’s tied. For assigning 5-6 seeds or 7-8 seeds in the top-8 bracket or pairings in lower play-in round 2 or loser’s round 2, do the same considering the two possible pairings, except for the potential double .500 scenario in lower play-in round 2 which must be paired.
Hareeb's Hangout 