Monday, November 23, 2015

Loser's Advantage in Byed Brackets

After the most recent Brutality event, I had a very valuable question asked about how Power Ranking points are distributed via a double elimination bracket. WARNING: bracket science incoming, read at your own risk.

If you have a double elimination bracket that is not full, you have to use "Byes". These are automatic wins for whomever is placed against them. Traditionally, these byes go to the strongest players in the bracket. Hence the reason I use Power Rankings to rate players who attend my monthly event series. It helps me determine who "deserves" the byes in the most objective way possible. The person with the most points receives the first bye, and then the person with the second most points, and so on. Ties in points can make this allocation tricky.

Okay, that sounds good. But wait, what about when those "Byes" go to the Loser's Bracket after Winner's Round 1? Well, what happens is that these byes can do one of two things: they can face each other (which is uncommon), and then a "Bye" advances to Loser's Round 2 - or - two "Byes" enter Loser's Round 1 and give two lucky players a free pass to Loser's Round 2. In the first example, that very lucky player would earn a trip to Loser's Round 3. The second example is preferable, because these two players effectively split the benefit of having byes in the bracket instead of one player reaping all the reward.

Take a look at the image below. You see the top two seeds, Player 1 and Player 2 in blue. You see the Byes in red. You see the potentially "lucky" players, those who can benefit from the byes, in green.

This means that those players who play against other players in Loser's Round 1, and win, can end up with the same final placement, and points earned, as one of the "lucky" players who got a free pass to Loser's Round 2. How is this possible?

Take a look at the following image. You will notice that Player 3, who is now highlighted in purple, has a record of 1 win - 1 loss. Now, look at Player 11, in green. Player 11 has a record of 0 win - 1 loss, but is already in Loser's Round 2! Player 3 had to earn a win in order to make it into Loser's Round 2, where Player 11 did not. This shows the power of the loser's advantage in byed brackets.
Look at the next image. You will notice that both Player 3, in purple, and Player 11, in green, have been eliminated from the tournament in Loser's Round 2. For a basic double elimination bracket, this means that Player 3 and Player 11 both share 13th Place, and earn the same number of ranking points. This happens even though Player 3's record, 1-2, is better than Player 11's record, 0-2.

This is what makes double elimination brackets structurally inferior to round robin brackets in terms of determining the most accurate placements. However, as you know, a round robin bracket takes forever. It requires more time and more setups in order to run effectively. Eventually, running a round robin of more than 6-7 people can become a huge mess if not properly supported. So, the FGC has historically used double elimination as the standard tournament format to help mitigate time, setup, and support staff constraints. Unfortunately, double elimination brackets, when forced to implement "Byes", have the problem I described above.

But wait, there is hope! As I was responding to the original question that inspired this post, I realized that I can help mitigate the problem of "Byes" giving an advantage to "lucky" players. You noticed I kept using the word "lucky". Well, it does not have to be that way. I noticed that Challonge may not show the "Byes", but it is predictable in how it assigns them and predictable in who it gives the Loser's Round 2 advantage to. I can use this knowledge to purposefully use the Power Rankings and make sure that only certain players may end up with that Loser's Round 2 advantage.

From now on, I will purposefully use the Power Rankings to put the players with the lowest number of points in the positions that may result in a Loser's Round 2 advantage. Why not the players with higher rankings? Good question! The reason is that the purpose of seeding goes beyond assigning "Byes". Seeding is also meant to separate the strongest players from each other, so that they do not eliminate each other from the bracket early on. If they do, then a less skilled player may have an "easy bracket", and get a higher placement that is not an accurate reflection of skill level. Think of seeding, used this way, as a contrived method to get the same kind of results that a round robin bracket would provide.

So, this means that only the weakest players will get the Loser's Round 2 advantage. Strong players will still be separated from each other in the bracket, and the balance of all these decisions is a strong response to a bracket structure (double elimination) that is not perfect. To be clear, even without "Byes" a double elimination bracket is still not as accurate as a round robin bracket. "Byes" just make the job more difficult. Seeding still exists, and there are still problems with seeding. No one is ever completely happy (me included) and bracket science is sometimes bracket art. I do my best to keep my subjective opinion of players' skill levels out of the bracket creation process.

I am, and always will be, an open book on these kinds of issues. So please never hesitate to ask me anything about my events, and big thanks to the person who brought this up. I am glad that someone else was paying as close attention as I do! Anyone is welcome to contact me at: powerupfighters"at"gmail"dot"com
Nathan Shields PowerUp Founder

Fighting game enthusiast, martial artist, and teacher. Nathan Shields ran three regional events, two of which were part of the Road to EVO Championships in 2011 and 2012. He continues to run local FGC events and supervise the growth of his scene and the PowerUp brand.

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