Swiss Rounds and Tiebreakers

There has been a lot of discussion recently around the Internet about tiebreakers and the Swiss pairings system used at Regionals last month. Today, I want try to help everyone understand how Swiss pairings work (and more importantly where the number of rounds comes from) and what the tiebreakers really are.

First let's address Swiss-style pairings. In any World of Warcraft TCG tournament you will get one point for each match win and no points for each match loss. Each round, players are paired randomly with another player with the same amount of points, e.g. everyone with 3 points will play someone else with 3 points, 2 points plays 2 points, etc. If there are an odd number of players with the most points, one player will be "paired down" meaning they will play someone with the next highest point total. When there are an odd number of players with a certain point total, the highest amount of points always get paired down first. If there are an odd number of players in the tournament, a player with the lowest point total get a bye.

Determining the number of rounds to be played

The easiest way to determine how many rounds is to take the number of entrants and go up to the next number that = 2^x. Whatever x equals is the number of rounds to be played. For instance, if there are 45 players, you would go up to 64 which is 2^6 so there should be 6 rounds. Some organizers don't always follow what should be followed and have adopted their own number of players for each number of rounds. The originial intent of Swiss pairings was to get down to one undefeated player who would be the winner. However, since most card tournaments use the Swiss as a means to get to an 8-man elimination sometimes the numbers are varied. Let's take a quick look at how the Swiss would work for a 64-person tournament. If you're not interested in seeing how this works, scroll down past it.

64 is a power of 2, so we'll be playing 6 rounds in this exercise. Round 1 all players are paired randomly, so we'll have 32 player at 1-0 and 32 at 0-1.
In Round 2, all the 1-0's will play each other and all the 0-1's will play each other. We will have 16 winners in the 1-0 bracket for 16 players at 2-0. The sixteen 1-0 losers will pair up with the 0-1 winners to make 32 1-1's, and there will be 16 losers in the 0-1 bracket for 16 0-2's. So now our standings look like this.
2-0 16 people
1-1 32 people
0-2 16 people
I'm not going to detail every round, but I will show you what the "standings" would look like after each.
Round 3
3-0 8 people
2-1 24 people
1-2 24 people
0-3 8 people
Round 4
4-0 4 people
3-1 16 people
2-2 24 people
1-3 16 people
0-4 4 people
Round 5
5-0 2 people
4-1 10 people
3-2 20 people
2-3 20 people
1-4 10 people
0-5 2 people
Round 6
6-0 1 person
5-1 6 people
4-2 15 people
3-3 20 people
2-4 15 people
1-5 6 people
0-6 1 person.

As you can see, if we were looking for one winner, we would have it as only one person is 6-0. If we were cutting to top 8 we would have close to a clean break here as the one 6-0 and the 6 5-1's would make up 7 of our 8 with one 4-2 getting in. The problem with Regionals was we were playing for top 4. Top 4 is a little messy here after 6 rounds. The 6-0 is obviously in, but then you've got 6 5-1's tiebreaking it out for 3 invites. The 2 possible solutions here are a top 8 cut with a one round playoff, or one extra round of Swiss. UDE chose to play the extra round of Swiss. If you extrapolate out our mock tourney from above you can see that in round 7, the one 6-0 would get paired down, then we would have 2 5-1 vs 5-1 matches and one of the 5-1's would get paired down. Unless the 2 5-1's who are paired up and down respectively both win, we will reach our desired number of invites. If they both win, we will have 5 6-1's battling for 4 slots. Even this one small problem only comes up when the number of players is very near the maximum for the number of rounds.

So, why were so many X-1's left out at Regionals?

The simple answer is not enough TO's ran the extra round of Swiss to ensure the X-1's got their invite. One thing to note about the extra round of Swiss. It is actually slightly more fair to the person who goes undefeated as even if they lose that last extra round, their tiebreakers are all but guaranteed to get them the invite in the rare situation that there is one extra X-1. If there isn't, their last round is basically irrelevent to them and they're not given the opportunity to lose the one round playoff to someone who lost 2 matches on the day.

So now let's talk about tiebreakers. There are 3 tiebreakers. One thing to note before I talk about how the tiebreakers work is that the 1st tiebreaker almost always is the deciding one. I have looked through all the final standings of PC's and many 10K's to see how often the 2nd tiebreaker came into play. No one has ever missed a top 8 based on the SECOND or THIRD tiebreaker, and only one player has ever missed the money based on these tiebreakers. The time they most often come into play is deciding placement in the 30's through the end of the money and even those times are rare. So now that we know that the first tiebreaker is the most important, how exactly do the tiebreakers work?

The first tiebreak is opponent's win/loss sum. What this means is that each for each opponent you played, you take their wins and subtract their losses. This gives you that opponent's sum. You then add the sums of all your opponents. One thing to note here is that no one opponent can contribute worse than -3 to your tiebreak sum. This means if your first round opponent plays all day and loses every match, he is still only a -3 to your sum. The point of this tiebreaker is to determine who played the better opponents during the tournament. If player A and player B are both 6-1, but player A loaded up on people who didn't win very many matches while player B beat several other players in the top 8 then player B's 6-1 is considered better than player A's because he had to beat better opponents to obtain it.
The second tiebreak is an extension of the first. It is your opponents' opponents' win/loss sum. To get this you take the first tiebreak of all your opponents and add them together. What this tiebreaker is saying is your opponents seem to be about the same in quality but let's see who they played to see who's really better.
The third tiebreaker is the sum of the sqaures of the round you lost in. So if you lose in round 1 your third tiebreak gets a 1. Round 2 is worth a 4 and so on. This says the later you lose the better.

There has also been a lot of outcry that Magic's tiebreaker system is better, so let's look at that system quickly and compare it to World of Warcraft. Magic's 1st tiebreaker is opponent's match win %. Essentially the same as opponents win/loss sum. They're both factoring in the quality of your opposition. Since we know that the first tiebreaker is almost always the one that actually breaks ties, in over 90% of scenarios, Magic and World of Warcraft use virtually the same system. Magic's second tiebreaker is where the systems diverge. Magic's second tiebreaker is personal duel win %. Basically, this says "Well your opponents were about the same, so..." and instead of using your opponents' opponents to guage the quality of your tournament work, they say since your opponent were about the same, how bad did you beat them? The third Magic tiebreaker is opponent's duel win %. This one basically says "Ok, your opponents are about equal and you beat them equally bad, but how bad did they beat (or lose to) their opponents?" This one is wildly different than World of Warcraft, but in all the past tournament research I did, I only found a handful of cases in VS. System that went to the third tiebreaker and none in Magic. One thing to remember about WoW is that TO's use the MANTIS software which UDE supplies for all their games. VS. System, Yu-Gi-Oh and WoW all use the same system. Since VS. only plays one game per round, the game win % can't be used in MANTIS.

I hope this helped clear up what happens in a tournament and the likely cause for much of the confusion and tiebreaker madness that occurred at Regionals.