Tiebreakers

Gathering Magic is pleased to welcome Chris Mascioli to the team! If you're unfamiliar with everyone's favorite penguin lover, Chris will cover competitive Magic topics ranging from theory and analysis (such as today's topic) to more detailed and on-going projects (such as the yet-to-be-announced coming next week). Let him know what you think, and be sure to stop back next week for his big reveal!

What Are Tiebreakers?

Tiebreakers are the means used to rank players with the same number of match points. The DCI uses a system that consists of three tiebreakers: opponents' match-win percentage (OMW%), player's game-win percentage (PGW%), and opponents' game win percentage (OGW%). OMW% is usually referred to as the first tiebreaker, as it is the primary method to rank tied players; PGW% is known as the second tiebreaker because it is only used when players have the same number of match points and OMW%; and OGW% is the third tiebreaker and is only used when two players have the same PGW%.

How Are Tiebreakers Calculated?

A player's match win percentage (MWP) is calculated using the following formula:

Number of match points ÷ (Rounds played × 3)

Meaning a player with a record of 5–3 would have an MWP of 15 ÷ 24 = 62.50% and a player with a record of 4–2–1 would have an MWP of 13 ÷ 24 = 54.17%.

A player's OMW% is the average of the MWP of each of his opponent's with two important caveats:

  1. Byes don't count.
  2. Opponents with an MWP lower than 33% counts as 33%.

For example, a player (who went 5–1 [10–4 in games], losing in Round 3) in a six-round event played against players who went 0–2, 4–2, 3–3, 4–2, 3–3, and 4–2 would have an OMW of:

(.33 (raised from 0) + .66 + .5 + .66 + .5 + .66) ÷ 6

Which gives an OMW% of 55.17%.

PGW% is a much easier figure to calculate and is just:

Games won ÷ Games played

And our hypothetical player above would have a PGW% of:

10 ÷ 14 = 71.43%

OGW% is just the average of each opponent's PGW% (and there's no real need to go through an example).

Are Byes Good or Bad for Tiebreakers?

Byes in the early rounds of a tournament are excellent for tiebreakers (and for your overall record, but that's beside the point) as it allows you to avoid people who will statistically have the lowest MWP. For example, if you beat someone Round 1 of a GP (and he drops after accumulating three losses, although this model may not be particularly accurate anymore thanks to PWPs), he will have an average (assuming your opponent has P(win a match) = .5, which is most likely very generous for a player who loses Round 1 of a GP) of .4.

An even clearer example of the importance of byes can be seen by examining two people, one with zero byes and one with three, who both go 7–2 in a GP, losing Rounds 6 and 8 (assuming they play against our aforementioned P(win a match) = .5 in each round) will have the following OMW:

(.4 + .5 + .57 + .63 + .67 + .83 + .78 + .81 + .67) ÷ 9

and

(.63 + .67 + .83 + .78 + .81 + .67) ÷ 6

Which yield 65% and 73%, respectively which is quite a significant difference.

How Much Can My Tiebreakers Change from one Round to the Next?

This depends on how many rounds are in the tournament and how many opponents are below the .33 threshold (since their losses don't hurt you). There is no formula to figure out the maximum tiebreaker loss or gain between the end of the penultimate round and when final standings are determined—the MWP change for each opponent depends on his record between that round. For example, in an eight-round event, the change in MWP for each record is (I went 0–7 in this event):

Opponent Wins Losses MWP MWP with loss Change MWP with win Change
Jillian 1 6 0.33 0.33 0.00 0.33 0.00
Meghann 2 5 0.33 0.33 0.00 0.38 0.05
Rachel 3 4 0.43 0.38 0.05 0.50 0.07
Lucie 4 3 0.57 0.50 0.07 0.63 0.05
Kayla 5 2 0.71 0.63 0.09 0.75 0.04
Kate 6 1 0.86 0.75 0.11 0.88 0.02
TBD 7 0 1.00 0.88 0.13 1.00 0.00

Let's then create three hypothetical players: Chris, Tony, and Daniel. Chris is grinding for PWPs and ends up 0–7, but Tony and Daniel are more fortunate and both end up 6–1, with Tony having an OMW% of 59.8% and Daniel having an OMW% of 50.86%. The most Tony could drop (assuming he draws Round 8 and everyone else loses) is 3.2%, while Daniel can lose is less than a percent. While these sample cases are not particularly useful, they do carry some important takeaways:

  • The higher your tiebreakers are coming into the round, the further you can fall.
  • Even if every opponent loses, the falls and gains will probably never be higher than 4% to 5% given an adequately large event.
Tony OMW% 0.598
Round Opponent Result Wins Losses MWP
1 Nate W 2 3 0.4
2 Kayla W 2 5 0.33
3 Kyle W 3 2 0.6
4 Bob W 5 2 0.7143
5 John L 6 1 0.8571
6 Jay W 4 3 0.5714
7 Ted W 5 2 0.7143
Daniel OMW% 0.5086
Round Opponent Result Wins Losses MWP
1 Julie L 2 3 0.4
2 Rachel W 1 6 0.33
3 Jessie W 2 4 0.33
4 Kevin W 3 3 0.5
5 Martin W 4 3 0.571429
6 Cindy W 5 2 0.714286
7 Josh W 5 2 0.714286

Which Losses Hurt Your Tiebreakers the Most?

In general, the people who take their first loss latest in the tournament have the best tiebreakers.

Is the Record of the People I Lost to More Important than the Record of People I Beat?

No, but this is a common myth. For some reason, people always want to know the record of people they lost to, but they focus much less on the records of people they beat—they are both equally important.

If You Are X–0 Before the Penultimate Round of the Event, Is it Always Safe to Double-Draw into the Top 8?

No, the only record guaranteed to Top 8 is X–1. As the number of people in a tournament approaches the number required for an additional round (128 for seven rounds and 226 for eight rounds), the chance you can double-draw into the Top 8 at X–0 decreases.

Are Pairings Always Random or Is There a Formula?

Pairings, up until the final round of an event, are random. However, the last round of a Swiss event is paired based on a players standing in that event (the player in first is paired against the player in second, third versus fourth, and so on) unless the players have already played each other. This allows players with higher tiebreakers going into the last round to draw against one another and guarantee themselves slots in the Top 8 based on that draw.

Can I Tell My Friends the Results of Another Match?

Yes, as long as you don't give any advice on what they should do with the information, you are free to reveal the result of another match—it is not hidden information. However, if the players in a match are seeking the result of another match, they are not allowed to go through “great lengths” to obtain said information (although asking a spectator to go and check is allowed).

I'm X–0 (or X–1) going into the penultimate (or last) round; can I intentionally double-draw (or draw) into the Top 8?

The last (and most important) question for this FAQ takes some practice to properly analyze and determine. There are usually one or two people at a given PTQ who are swarmed with this question going into the last round (I am usually one of them), and you should probably consult with that person to ensure you're making the correct decision. If you are ever unsure whether it's safe to draw, you should, by default, choose to play the match out; there's no shame in playing a match out and losing, but drawing yourself into ninth ensures you will be the target of ridicule and self-hatred for some appreciable period of time.

There's no real formula to determine whether you'll be able to draw in or not ahead of time (you can try to use a Swiss triangle, but those don't account for draws, and handling pair-downs is a pain in the ass), so the best way to develop the ability to perform this determination is by using real tournament data. I will go through two examples using data from two SCG Open events.

Event 1 – SCG Open: Atlanta – Standard

Standings at the end of Round 8.

Standings at the end of Round 9.

Standings at the end of Round 10.

At the end of Round 8, the standings looked like:

  • Two players with 24 points
  • One player with 22 points
  • Fifteen players with 21 points
  • One player with 20 points
  • Four players with 19 points

Given these standings, the two players with 24 points must determine whether they can draw.

Step 1 – What do the pairings for this round look like?

Since players are paired based on match points, the pairings for Round 9 would look like this:

  • 24 versus 24
  • 22 versus 21
  • Seven tables of 21 versus 21
  • 20 versus 19
  • 19 versus 19
  • 19 versus 18

Step 2 – What point totals will people have next round?

The standings after this round will look like:

  • One player with 25 points
  • Seven players with 24 points
  • One player with 23 points
  • Two players with 22 points

 . . . or . . . 

  • Eight players with 24 points
  • Four players with 22 points

Step 3 – If we draw, what are the pairings like next round?

In the first situation, if both players with 24 points draw the pairings will be:

  • 25 versus 25
  • 25 versus 24
  • 24 versus 24
  • 24 versus 24
  • 24 versus 24
  • 23 versus 22
  • 22 versus 21

This would allow the first two tables to draw, and the remaining four Top 8 slots would go to the winners of the bolded tables. Even if the 22 beats the 21, it is unlikely that the 22 with the lowest tiebreakers going into the round (remember the answer to the question from earlier) will be able to beat out the 24 with the highest breakers.

In the second situation, the pairings would be:

  • 25 versus 24
  • 25 versus 24
  • 24 versus 24
  • 24 versus 24
  • 24 versus 24
  • 22 versus 22
  • 22 versus 22

Here, the first two tables could once again draw (and possibly the third depending on the specific tiebreaker numbers), with the remaining slots going to the winners of the other matches (although the second table of 22 versus 22 has no shot at Top 8).

Therefore, in this situation, the two players with 24 points going into Round 9 can safely draw (and they did so in the actual event).

At the end of Round 9, the standings looked like:

  • Three players with 25 points
  • Seven players with 24 points
  • Three players with 22 points

Given these standings, the ten players with 25 and 24 points must determine whether they can draw.

Step 1 – What do the pairings for this round look like?

  • 25 versus 25
  • 25 versus 24
  • 24 versus 24
  • 24 versus 24
  • 24 versus 24
  • 22 versus 22
  • 22 versus 21

In this situation, the top two tables can safely draw, locking up four of the Top 8 slots. Because the first table of 22s have such high breakers (both are a bit over 65%), the four bolded tables must play out the round with the winner of those matches advancing. In this event, the 25 versus 24 match did not draw (the 24 won), but both players ended up advancing into the Top 8 anyway.

Event 2 – SCG Open: St. Louis – Legacy

Standings after Round 7.

Standings after Round 8.

Standings after Round 9.

At the end of Round 7, the standings looked like this:

  • Two players with 21 points
  • Thirteen players with 18 points
  • Three players with 16 points

Given these standings, the two players at 21 points must determine whether they can draw.

Step 1 – What do the pairings for this round look like?

  • 21 versus 21
  • Six tables of 18 versus 18
  • 16 versus 16
  • 16 versus 15

Step 2 – What point totals will people have next round?

  • Six players with 21 points
  • Two players with 19 points

Step 3 – If we draw, what are the pairings like next round?

  • 22 versus 21
  • 22 versus 21
  • 21 versus 21
  • 21 versus 21
  • 19 versus 19

In this situation, the top three tables are all safe to draw in and are guaranteed a place in the Top 8 (with the bolded tables each awarding the winner a spot in the Top 8). Therefore, the two players at 7–0 after Round 7 can safely double-draw.

At the end of Round 8, the standings looked like:

  • Two players with 22 points
  • Six players with 21 points
  • Two players with 19 points

Given these standings, the eight players with 22 and 21 points must determine whether they can draw.

Step 1 – What do the pairings for this round look like?

  • 22 versus 21
  • 22 versus 21
  • 21 versus 21
  • 21 versus 21
  • 19 versus 19

As I mentioned directly above this section, the top three tables can safely draw while the bolded tables (placed seventh through tenth in standings going into this round) must play it out in order to Top 8.

Quotes

My quotes section will never be as good as Ted Knutson's (I also don't include any cheesecake, so meh) as the purpose of this section, for me, is to give some images or tidbits of conversation that I find amusing and/or funny. Some of them tend to be inside jokes, but if this section really bothers you, skip it or pretend it's not here. It's also short since I accidentally deleted the folder where I was collecting them . . . sad face!

<@Zapgaze> so I just found out nina simone is a woman

[04:41:33] <@garetjax> how many diff languages did robot swear in?

[04:41:51] <@Robot> english and portuguese only

Chris Mascioli

chrism315 on modo

@dieplstkson twitter (follow me, <3) dieplstks.blogspot.com

Comments

comments