How GP Byes Affect Tiebreakers

The ultimate goal of GP competitors in the Swiss rounds is to make the top 8. In a tournament with at least several hundred players, that is quite an accomplishment. It typically requires going 12-2-1 or better and there's a good chance the last spots come down to tiebreakers, which are determined by averaging the match-win percentage of each opponent a player faces.

Byes are an important part of individual GPs. They are given as a reward to players who have put up good results in the current or previous season, and those in the Hall of Fame. Getting free wins is obviously helpful in getting the kind of record one needs to top 8, but in my opinion there is an underappreciated aspect of byes - they give players a significant advantage in tiebreakers.

How likely are you to make it with a given record?

Before getting into that, let's look at often a player made the top 8, based on how many match points they had in the GP.

As you can see, 12 - 3 is very unlikely to be good enough, 13 - 1 - 1 is a lock and in between you are likely but not certain to make the top 8. Digging into the data a bit deeper, reveals big differences based on the number of byes a player with the record has:

You can see that there's a pretty clear difference between having no byes and at least one. Phrasing it in terms of failing to qualify for the top 8, I think it's particularly striking that 42% of the time (18 of 43) a player went 13 - 2 playing every match they failed to top 8. This happened just 10% of the time (18 out of 174) a player with at least a bye 13 - 2.

Equalizing the opponent pool as much as we can.

A possible explanation for this gap between players with and without a bye is that the players without one might have lost early on, thereby facing weaker opposition at the point those with byes started playing. To neutralize that, let's look only at situations where someone starts out 3 - 0. This guarantees that the players are facing the same pool of players from the fourth match on. As it turns out, this makes things better for the no-bye group, but not by a huge amount. Here is the previous chart, looking only at those with 3 - 0 starts:

Another way to look at this is to go straight to the tiebreakers themselves. Let's look at the match-win percentages of the opponents each round, for all players who started 3 - 0 and went 13 - 2 (it's very similar for players who went 12 - 2 - 1). For each round, the box represents the middle 50% and the lines represent the highest and lowest values.
Looking at round 2, for example, the low is 0.33, which is the lowest possible according to the rules, and the high is 0.71. In other words, the best opponent one of our 3 - 0 to 13 - 2 players faced in round 2 finished with a match-win percentage of 0.71. The top of the box is 0.54 and the bottom 0.375, so half of our group's opponents had a match-win percentage that fell between those, a quarter of them were above 0.54 and a quarter of them were lower than 0.375.

You can see in this graph that the opponents players face in the first couple rounds are significantly worse than those faced by the time the pros enter the field. On one hand, this is pretty obvious - first round players like me tend to be worse than players with byes and the Swiss pairing system means that if you win your first few rounds you'll face better competition. On the other hand, this graph makes it very clear that the tiebreaker system will be biased against players with no byes or even just one.

Depending on your perspective, that may be a good or bad thing. The reason they give byes in the first place is to reward pros and other strong players for their past play, and incentivize people to play in more tournaments. Wizards is obviously aware that giving players free wins will help them over other players, at least in the direct way. Personally, and I'm looking at this from the perspective of someone who has played four GPs to the ultimate medium record of 16 - 16, I think the bye system itself is good, but a player should be able to equal out the advantage the pros get by winning their matches and the tiebreaker system doesn't allow for that. The effect of the byes also seems to break with the underlying logic of the tiebreakers themselves - if two players face identical competition in rounds four through fifteen, and one of them played against three weaker opponents while the other had byes, in what sense has the one with byes made the more difficult or impressive run? I think the best way to improve the system, and make it more fair, would to make a very small change - don't start counting opponents' match-win percentage until round 4. This would still punish players who lose in the first three rounds, while making it a level playing field for all players starting 3 - 0.

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