[Editor’s Note– This may not be the kind of article most people would browse through between rounds on MTGO or while watching TV. That said, the information provided here may well improve your tournament finishes more than any other articles you read this year. Though it may seem a little dense in the math dept., we feel the knowledge it contains is invaluable to players, and it is something that players ask about at every tournament. In short: it pays to know this (literally).]
In case anyone reading is unfamiliar with who I am, my name is Eli Kassis. I have been playing competitive magic for over 18 years. I had the idea to write this article because I frequently find myself at events with players asking for tie-breaker advice the final round before the Top 8 the event. I also have encountered many misconceptions from players who happened to be my opponents which led them to erroneous conclusions which in turn negatively affected my options. Once I am across the table from them they tend to be a bit too skeptical of what I am saying to believe me, so why not get ahead of the curve, explain it all out here and then just show them the link with my smart phone at the next event to clear things up? I thought it would help give perspective to the readers to start with a short true/false test to point out a lot of the misconceptions players have with regards to how this process works. Obviously your reading this article for your own benefit to learn so if you want to cheat and look at the answers below that’s your prerogative. In explained the answer to each question I am also including the information that I am trying to get across.
True or False:
1) The larger the number of people in an event (i.e. the greater the # of rounds) the more your game (NOT Match) win percentage and/or your past opponents game win percentage will matter.
2) The formula for the number of rounds in an event is X # of rounds = Y (The # of participants) / 2 to the X = Y is as close to but < 1.
3) If you are in 9th place in the standings going into the last round and you win your match you will almost always make the top 8.
4) It is completely possible to know for sure, at the beginning of an event, if an X-2 record can make the top 8 with a large turnout (>100 People).
5) A bye can hurt your tiebreakers.
6) If I play a friend in the early rounds of an event we should intentionally draw to prevent either of us from receiving a loss.
7) If my record is X-1 with 2 rounds left to go and a record of X-1-1 is what is needed to make the top 8, then my goal is to win this round and then hopefully draw with my last opponent into the top 8.
8 ) Even though there is a multitude of possibilities that draws bring into the equation, the final math breakdown of how many people are in each record bracket can provide us with many definite conclusions.
9) Losing in the first round of an event pretty much guarantee’s that you will have poor tie-breakers.
10) If I start off 0-2 in a 7, 8, or 9 round event and the math tells me that 1 X-2 can make the top 8. It doesn’t make sense for me to stay in and try to battle back.
Now I am going to post the answers for you and give a little explanation of why that is the case. I will try to be as descriptive as possible and remain understandable, but math is a subject some people get and other do not. If you don’t follow the math just remember this rule of thumb of the statement that is being made: you do not have to understand why as long as you know the right answer… Depending on your level of expertise and tournament experience you may be surprised by some or many of these answers. I would say if you got all 10 correct you probably don’t need to be reading this article (and you probably don’t seek out my advice at tournaments either… thank you). If you missed a few than you are likely good enough that you could use any edge to help push you over the top and this article is actually perfectly suited for you.
Let’s start at the top.
1) The answer is False. The reason is simple, Wizards uses 3 scores as tie-breaker scores. The first and most important category is your opponents’ MATCH win percentage. If that number equals that of the person you are in a tied with, than it goes to your second tie-breaker, your GAME win percentage. If you still do not have someone that stands out than the third tie-breaker is used which is your opponents GAME win percentage. The 2nd and 3rd tie-breakers [are usually irrelevant]. When an event has gone on for 6 or more rounds the number of opponents you’ve had as well as they number of different possibilities with which they’ve performed over the course of the day is extremely variable. The more rounds in the event, the more outcome possibilities exist. This makes it extremely improbable that any two players with have an identical percentage and need to use a second tie-breaker. Does this mean it doesn’t happen? No, but it is statistically insignificant.
2) This answer is True. Wizards uses as system that says 5-8 players is 3 rounds, 9-16 players is 4 rounds, and up and up. Multiplying the total number of players by 2 each time adding a round. This is meant to distinguish one 1st place at the end of a Swiss format tournament. It just so happens that most Magic events have adopted the Top 8 format to add an extra level of play so that you can still win a tournament even having lost a match in the Swiss.
3) This answer is False. You might think it’s ridiculous to imagine that you could win and not advance in the rankings, but in many tournaments 1st-8th are a full win ahead of 9th place. Since they are exactly 8 and the Top 8 is needed they will all be paired against each other as an even number in the same bracket and they will all draw to reserve their spot in the top 8. This does not always happen, but it’s frequent enough not to believe in the misconception that just because your 9th means you have a chance.
4) This answer is True. This explanation may be the most complex, but try to follow it as it’s a very useful predictive tool for tournaments.
If there are 8 players in an event, after 1 round there will be 4 winners (1-0) and 4 losers (0-1), in round 2 the winners will play the winners and the losers the losers, obviously. So after round two there will be 2 (2-0’s) 4 (1-1’s) and 2 (0-2’s). After a third round with everyone getting paired the same way there will be 1 (3-0) 3 (2-1’s) 3 (1-2’s) and 1 (0-3). A mathematician developed a triangle that helps to put it in a better context, it looks something like this.
4 4 (Results after Round 1)
/ \ / \
2 4 2 (Round 2)
/ \ / \ / \
1 3 3 1 (Round 3)
This triangle puts the explanation in diagram form, as long as you know how to read it. Results after round 1 show you the same thing we told you above, 4 people will be 1-0 and 4 people will be 0-1. After the 3rd round we see again that there will be 1 (3-0) 3 (2-1’s) 3 (1-2’s) and 1 (0-3). Now as I state in Question #8, that the possibility of a tie-breaker may complicate the results. Let me elaborate. This triangle can be used for many functions. You may notice in round 3 that the left side mirrors the right side is bisected down the middle. This allows us to establish several truths based on the diagram. If this were a tournament with a larger attendance then we would also have more rounds to follow. You would also encounter the dilemma that this triangle would have had with a 4th round thrown in the mix. How do you split an odd # (1,3,5 etc.) into two equal halves? Simple answer is you don’t. Before you start you choose 1 direction (East or West) of the triangle to always round up on and the other direction to round down on. Since we are bisecting the triangle down the middle and we have added odd numbers into the equation we will no longer have identical halves. Since we do not care how the bottom half of a tournament is doing we can ignore all the data of those who have performed less than 50% and instead use the data of the other half as something else more interpretive. The figure furthest from the center will now typically denote the undefeated players. If a Swiss style performs as its supposed to and the Swiss rounds are over you will typically see a 1 in this slot as 1 person should be solely undefeated. However, as we all know there are many intentional draws in the last round or two of a tournament. We will get to that in a moment. The next number over (closer to the center) denotes the player that is X-1, then X-2 and so on and so forth (until you reach the middle). Since you are always rounding in the same direction, one side of the bisected triangle’s numbers will be greater than the others. This creates what I like to term a “Best-Case Scenario” and a “Worst-Case Scenario”. I’ve termed them Best-Case and Worst-Case because depending on where you stand and what you are trying to accomplish one of the scenarios will be more favorable to you than the other. This is extremely relevant because the more unfavorable scenario demonstrates the worst things can get. So if your plan can handle things in the worst case scenario than you are sure to succeed because that is as bad as it gets. If your plan requires the best-case scenario to be present then cross your fingers. Players drawing in an event lead to circumstances that make the results fall somewhere between the best-case and worst-case scenario. So we can still interpret what we may need and the best we can hope for from the data. This all becomes very relevant if you ever go to one of those tournaments that do not put out standings until the last round. Even more so as most tournament organizers have adopted a style of posting it for a few minutes, you get to fight a crowd of people trying to do the same thing (look at the same small piece of paper) and then they take it away from you even though you would like more time to confirm your conclusions (Anyone else’s head hurt yet?). I promise that was the most confusing answer/explanation.
5) The answer is False. A bye is always a good thing and especially if it’s in round 1. Why? Because a bye is awarded to the person lowest on the totem pole and in round 1 everyone is equal so not only are you not lowest on the totem pole but you also got the free win. Tie-breakers are calculated based upon your opponents win percentages and since the chances of getting a bye are random and there’s no fair system of incorporating a bye’s tie-breaker standings you are simply awarded 100% opponent match win percentage from the bye. Meaning it is the best possible situation because you functionally beat them and they did not lose any other matches.
6) The answer is False. Real simple, a win gives you 3 points and the loser 0, a draw gives you each 1 point for a total of 2. If your goal is the overall success than you want to maximize the points you both earn with a win instead of a draw. Do what the pro’s do, agree to a prize split of some percentage of your winnings (it does not have to be half!) and play it out like men.
7) The answer is False. This may have stumped most players, even veterans because it is a tactic I often advise people to take that is often overlooked. Ask any long-term player how many times they have gotten to the final round and came up against an opponent who refused to draw or could not draw. Whether they played down or ran up against someone looking to dream crush. If you are certain you need a win and a draw why not get two chances to draw by asking your 2nd to last round opponent to draw then playing out your last round? As an additional benefit you’ll get paired against someone with a worse record which means they also may be easier to beat. A couple downsides to keep in mind: you may run out of time in your final round and two draws will kill you, so if you play slow don’t use this method. Secondly, you will play a person with a worse record in the last round so if you are looking to battle with tie-breakers to squeeze into the top 8 this may not help as much as going about it the traditional way.
8 ) This answer is True. I explained it very thoroughly in the explanation of question 4 so reference that if you have any questions.
9) This answer is True. If you follow out a triangle (from Question # 4) down the path of someone who has lost in the first round and then keeps on winning you may also notice the trajectory that will send all of your opponents. Your 2nd round opponent will now be 0-2, third round opponent 1-2, and so on and so forth. In a 1 day event that is crippling to your tiebreakers. Over a longer tournament like a Grand Prix that can be brought closer when there is an even greater number of rounds because there is much ground to covers but you will still be hurting for tie-breaker points come final standings.
10) This answer is True. As I have just stated in the explanation to Question # 9 losing in the first round means your breakers will be hurting, losing in the first two rounds means your breakers will be abysmal and you are guaranteed that if any of the X-2’s don’t make top 8 than they sure will be you. However, if your goal is to get Planeswalker points or you feel like playing for playing sake then by all means don’t let me stop you.
I’ll stop here as I am sure anyone still reading has probably used up all their patience by now. Rest assured there is more info and nuances into calculating and predicting tournament outcomes, but this article is as good of a start as any towards catching you up to the rest of the competitive field.