Define This: Tiebreakers

In this new set of chapters on Define This, Moudou will be going into more specific notions of the vocabulary. While some words are easy to define, some have a sturdy theoretical background, or are simply not easy to describe as such. After going through CA and QA, he now works with some very mathematical notions to break some ties.

The Different Levels

Math Board

Let's get some context first.

Once an event begins, be it the Players' Championship or your FNM, everyone participating is entitled to win the thing. This is the basis of any competitive play. If it weren't the case, it wouldn't be half as attractive, now would it? However, it also means that someone has to win it all. And sometimes, things are not easy to settle with a basic system.

Standings from Barcelona RPTQ

These are the rankings before the last round of my RPTQ in Barcelona (thanks to the judges for allowing this to be posted online to illustrate the article ). As you can see, there are several columns, tons of small numbers, but no ties. So, let's dig in.

Match Points and Match Win Percentage

This might seem obvious, but the very first tiebreaker between you and the guy sitting next to you is the amount of matches you win. A victory will give you 3 match points, a draw will give you one, a loss will give you none. This is not very different from most sports (football, handball, rugby, etc.), so it's pretty easy to keep in mind.

From this amount, you can calculate the Match Win Percentage (MWP) using the formula down below:

MWP = Match Points / (3 x Number of rounds)

Things get tricky when several players have the same amount of match points. So, let's dig into the first "real" tiebreaker.

Opponents' Match Win Percentage

When two players have the same amount of match points (and thus the same MWP), the logic is that the one who has played against the best players should be rewarded for having the same number of wins than the other in spite of the added difficulty. If player A's opponents have done better than player B's opponents, the conclusion is that A was a better player than B because he had the same score against better opponents.

In order to quantify that a bit more (because you can't just go around saying things like "I feel you didn't play very worthy opponents, so bad luck you're not going into Top 8 despite having the requisite amount of match wins"), we calculate the average on A's (and B's, distinctly of course) opponents' MWP. This is the Opponents' Match Win Percentage, or OMW%.

A's OMW% = average (A's Opponents' MWP)

Do note that there are a couple of points that affect the calculation:

  • Byes do not count for the calculation of OMW%
  • Opponents with MWP under 33% are counted as having an MWP of 33%

These two points are mostly in place to avoid some corky calculations during the early rounds of an event, where some fatally end up with zero points without it being very representative of anything.

Player's Game Win Percentage

If A and B have the same number of match wins as well as the same OMW% (which can easily happen if they had the same result on their round 1 match for instance), we look at how they dominated their matches. Basically, we look at how easily they won or how bad they got crushed. To represent this, we look at how many games they won and lost, as opposed to how many matches were won or lost. We simply calculate their Player's Game Win Percentage (PGW%) as the ratio of games won over games played.

PGW% = Games Won / Games Played

Basically, winning your first match 2-0 will give you 3 Match Points, an OGW% of 33% and a PGW% of 100%, whereas if you had won 2-1 you would have 3 Match Points and an OGW% of 33% as well, but a PGW% of 67%.

Opponents' Game Win Percentage

I think you're getting the gist of it: if two players have identical match points, OMW% and PGW%, we go to the OGW%, which is the average PGW% of a player's opponents. It's as "simple" as that.

How does it affect your event?

Math Meme

As I mentioned in the intro, many players do not know or understand how tiebreakers are treated. I have seen a lot of seasoned PPTQ players in Paris to whom I had to explain the system, even though they were actually running through said system twice a weekend. There is nothing wrong with not understanding the basics of course, this is just in case you're interested in going a little deeper than the basics. It's always useful to have a small insight into when you can offer an intentional draw (ID) to get into that op 8.

Here is a non-exhaustive list of things you should keep in mind during your next sanctioned event:

  • Byes are really good: A bye is a victory you get without playing your match. So obviously, you get 3 free match points, that's pretty neat in and of itself. This can happen in several situations (odd number of participants for example). But wait, there's more! Since a bye does not count in your OMW%, it basically behaves as an opponent winning all his matches, meaning your OMW% (your first tiebreaker, very relevant) is improved by that much.
  • Your opponents' results matter, regardless of your results against them. It is a common belief that the results of those you lose to matters more than those you beat. We have clearly seen this is not true. This originates from the fact that you "know" that the ones you beat have at best your MWP (which is of course not true at all) whereas the people you lose to can in turn lose everything and damage your OMW or just as well improve it if they keep winning. That is not true.
  • It is generally better to lose late than early. I deliberately place this point after the previous one because you shouldn't give in too much into beliefs and shortcuts. However, it is true that if you win against someone, their MWP will not improve. The more you win, the more you will face people with impressive MWP, as you will be paired against people with the same number of match points. If you lose early, your opponents' MWP will be lower... at the time you face them. Do keep in mind that things can evolve a lot depending on the stage of the event, which is another reason to not lose to early on.

Conclusion

We're done for the month! I hope you guys learned something interesting today, and I do hope that you can use that knowledge to your benefit next time you try to figure out if double-draw-into-top-8 is a good plan or not. The solution might be a lot easier than you'd think:

Will Ferell Meme

As usual, I can only encourage you to ask your vocabulary questions. No question is sillier than not asking it and then later saying something stupid. So please, ask away, comment, ask on Facebook, Twitter, feel free to let me know where (if) I was wrong! I still have not quite settled on what I'll go through next time, but we'll figure it out. You also can help me out by asking for new notions to dig into

La bise!

Opinions expressed in this article are those of the author and not necessarily Cardmarket.

2 Comments

Moudou(2019-01-30 15:10)

Hi there Rofellos !

That's a very interesting question you ask. And to be honest, I'm not sure.

One thing is for sure : your match-win-percentage is not affected. You still have the same amount of match points whether your previous opponent are DQed or not.

As for the following tiebreakers, I am unsure. I do believe that a DQed player is not accounted in any way in the tournament : no PW or Pro Points, no mention on the rankings, etc. Going by that logic, they are not taken into account when calculating your opponents MW%, thus effectively counting as a bye (against which you might have lost).

While I believe this to be what happens, I have found no written evidence for this. I have asked several judges and other communities but no-one seems to know for sure. I guess nobody wants to hear about people being DQed :)

Rofellos(2019-01-28 21:04)

Hi,

How does a DQ affect the Tiebreakers of the DQ'ed player's opponents? Lets say in an eight people-Booster Draft i suffer losses in the first two rounds ending in a Bye in round three. During round three my first and second match's opponents are paired against each other and are both engaging in wagering about the result of the Match between the two players with each six points.
How do my tie breakers evolve when both players are DQ'ed from the Draft? Do they rise or fall?

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