No real introduction here, just a chance to talk — in probably more detail then anyone would want — on tiebreakers in Magic tournaments. This is a superset of information that can be found in Appendix C of the Magic Tournament Rules.

Tiebreaker Components

Match Points

This is the same point total that you see on standings sheets.

  • A win or a bye counts as 3 points.
  • A draw counts as 1 point.
  • A loss counts as 0 points.

So, a player who is 6-2-1 has 19 points.

Game Points

Game points are the same as match points, but counting games instead of matches.

A match that finishes 2-1 will mean the winner will receive 6 game points, and the loser will receive 3 game points.

A match that finishes 1-1-1 will mean both players will receive 4 game points.

Player Match Win Percentage (PMW%)

Your PMW% are your Match Points, divided by the maximum possible number of Match Points that you could receive. (a.k.a. the average of your match points) Two important modifiers here:

  1. Rounds with byes are not included in this calculation.
  2. If the final percentage is below 33.0%, then the PMW% is raised to a floor of 33.0%.

A player who is 6-2-1 has 19 match points out of a maximum of 27, giving them a PMW% of 70.3704%

If that 6-2-1 player entered the tournament with two byes, then the calculation is instead 13 match points out of 21, or a PMW% of 61.9048%.

A player who went 1-4 and dropped has 3 match points out of a possible 15, which is a PMW% of 20.0%. Because this is less than 33.0%, it is raised to 33.0%.

Player Game Win Percentage (PGW%)

This has a similar association to PMW% in the way that Match Points are similar to Game Points: it is the total number of game points that you have received, divided by the maximum number of points you could have received. Here, though, byes are included in the calculation. This means that:

  1. Rounds with byes are included in this calculation, as a 2-0 win.
  2. If the final percentage is below 33.0%, then the PGW% is raised to a floor of 33.0%.

After four rounds, a player has finished their matches 2-0, 2-1, 2-0, and 1-1-1. This means that they have 22 Game Points out of a possible 30, or a PGW% of 73.3333%.

After four rounds, a player has finished their matches 0-2, 2-0 via a bye, 1-2, and 1-2. We’re counting byes here, so this is 11 match points out of a possible 30, which is a PGW% of 36.6667%

Opponent Match Win Percentage (OMW%)

Continuing down the process of averaging things, your OMW% is the average of all your opponent’s PMW%. Add all your opponent’s PMW%, then divide by the number of players.

OMW% is another tiebreaker where byes are not included in the calculation.

After five rounds, a player has played against players that are now 0-2, 2-2, 4-1, 3-2, and 3-1-1. This is ( 33% + 6/12 + 12/15 + 9/15 + 10/15 ) / 5, which ends up being an OMW% of 57.9333%.

An additional piece of clarification here: the average is of all of your opponents, and not all your matches. If you are playing in a Limited Grand Prix and play against the same person three times in the 15 rounds, that person will be counted in the average only once, and not three times.

Opponent Game Win Percentage (OGW%)

Continuing in the tradition, the calculation here is the same as OMW%, but exchanging Match Points with Game Points. OGW% also ignores byes, but note that are just ignoring your byes; byes that your opponents received when calculating their PGW% are still counted.

Opponent Opponent Match Win Percentage (OOMW%)

Keeping up the tradition of averaging other tiebreakers, this is the average of your opponent’s OMW%. Otherwise, it’s the same process as OMW%.

Cumulative

Something different! And complicated!

Before I describe what this tiebreaker is mathematically, the Plain English version of this tiebreaker is the prioritization of winning in early rounds versus late rounds. Put another way, the following players are in the correct standings order, based on their results after four rounds:

  1. W – W – W – W
  2. W – W – W – L
  3. W – W – L – W
  4. L – W – W – W
  5. W – W – L – L
  6. W – L – W – L
  7. W – L – L – W
  8. L – W – W – L
  9. …

If you finish a tournament 5-2, and your first loss is in Round 3, then you will always finish ahead of other 5-2 players who lost earlier, and finish behind 5-2 players who lost later. For a 5-2 player who lost in Round 3, then you look at the round the second loss occurred in the same way.

So, in more mathematical terms, this is handled with the concept of a “Bonus Pool”. When you win a round, your 3 points is added to both your Match Points and your Bonus Pool. Then, at the end of the round:

  • Your Bonus Pool is added to your Cumulative tiebreaker.
  • Your Bonus Pool is divided by 4.

So, let’s run through this with a theoretical player over the course of a few rounds.

  • Round 1, the player wins 2-0. They will end the round with 3 Match Points, and a Bonus Pool of 3.0 as well, which is added to their Cumulative tiebreaker, which is at 3.0.
  • Round 2, the player also wins 2-0. They now have 6 Match Points. The Bonus Pools was divided by four, so it stood at 0.75, and with the win, it becomes 3.75. Adding that to the Cumulative tiebreaker, the player now sits at 6.75.
  • Round 3, the player loses 0-2. The Bonus Pool was divided by four, but because they didn’t win, it will stay at 0.9375, and that value will be added to the Cumulative tiebreaker, which is now at 7.8675.

Breaking Perfect Ties

In smaller tournaments, there is a potential for two players to finish with 100% identical tiebreakers. In these scenarios, there needs to be some mechanism within WER to break these ties. It does so by placing players in the natural ordering of the players, which is the order that they are in inside WER’s internal Local Player Database. This database is ordered based on when the player was first added to the computer’s instance of WER; the first player entered into a fresh install of WER will always finish ahead of all other players with completely-identical tiebreakers.

In larger tournaments using WER, the odds of this occurring are functionally nil, due to some interesting mathematics between tiebreakers, byes, and the 33.0% floor. Describing why that is, though, is for another article. (in tournaments using WLTR, it’s slightly more possible — but still close to nil — due to the 33.0% floor being applied as a 33.3(repeating)% floor)

Tournament Tiebreaker Structures

Individual Swiss Tournaments

Your normal Swiss Tournament is run with four tiebreakers between any given two players:

  1. Match Points
  2. OMW%
  3. PGW%
  4. OGW%

Team Swiss Tournaments

This depends slightly on the tournament software that the tournament is being run on.

All tournaments have the same first two tiebreakers:

  1. Match Points
  2. OMW%

Beyond that, WER tournaments use OOMW% as the third tiebreaker. WLTR tournaments technically have the same additional tiebreakers as an Individual event — PGW% and OGW% — but in practice, those tiebreakers should be irrelevant, as both WER and WLTR Team tournaments report team match results based solely on the team that won. In WER, you’re forced to select 1-0, 0-0, or 0-1; in WLTR, you have full control, but scorekeepers should be entering results in a standardized way, to have the same effect.

Older Tournaments

Before 2016, Team tournaments had had a third tiebreaker, using OOMW%.

In the early 2010s, some premier events (Player’s Championship, World Magic Cup) used the Cumulative tiebreaker as a second tiebreaker, between Match Points and OMW%.

Additional (Random) Notes

When describing percentages in this article, I always rounded to a maximum of 4 digits, because this is the level of rounding that all WotC programs use.

For those curious, when you intentionally draw with a record of 0-0-3, it has the same effect on your PGW% as finishing the match 1-2.

For OMW% and OGW%, there is no need to define a floor, as because the component tiebreakers are all already floored to 33.0%, that means that the average cannot be less than 33.0%

WER does not implement the 33.0% floor on PGW%. This means that both PGW% and OGW% can end up below that value, in a tournament setting. However, for practical purposes, this does not really have an effect on where players finish.