2016 was a breakthrough year for the competitive Super Smash Bros 4 scene. The community coalesced around a universal ruleset and the metagame began to stabilize, especially since the last balance patch was released in May 2016.
There has been some debate on how well players performed relative to each other in that hectic period. The most widely-accepted rankings published by Panda Global takes into account a player’s tournament placements and set wins and losses. (Their full methodology can be found here.)
I propose a simpler ranking method that is based only on tournament placements and is as objective as possible. Last month on the frontpage of Hacker News, there was an article by Simon Tatham on ranking countries’ medal results in the 2008 Olympics by defining a partial order among countries and visualizing it with a Hasse diagram, a directed acyclic graph. He defined the problem as follows:
- We must consider more medals to be better than fewer, other things being equal. If country A has at least as many gold, at least as many silver and at least as many bronze as country B, then we must surely consider it to have done at least as well.
- We must consider the higher medals to be better than the lower. If country C has one more silver than country D but one fewer bronze, we must surely consider it to have done unambiguously better by any sensible ranking, because it has the score country D would have had if one of their bronze medallists had done a little better and won silver instead.
So we want to say that one country has done strictly better than another if the medal score of the latter can be transformed into the former by a sequence of medal additions and medal upgrades. A bit of thought shows that this is exactly equivalent to defining a partial order on triples of medals, in which a triple (G,S,B) is considered at least as good as another triple (g,s,b) if and only if it satisfies the three conditions
- G ≥ g
- G + S ≥ g + s
- G + S + B ≥ g + s + b
Being an avid fan of competitive Smash Bros, I wondered if this method could apply to major Smash Bros tournaments to obtain a results-based ranking of the top professional Smashers’ performance. Each player could be considered a country, each tournament could be considered an Olympic event, each top 3 placement at a major or supermajor tournament could be considered its corresponding Olympic medal.
Obtaining the Hasse Diagram
First, I obtained a list of major and super-major Smash Bros tournaments in 2016 from Liquipedia and collected the top 3 placements from each tournament.
|Tournament||1st 🥇||2nd 🥈||3rd 🥉|
|Shots Fired 2||Nairo||Mr. R||Tweek|
|Get On My Level 2016||Ally||ZeRo||Larry Lurr|
|2GGT: KTAR Saga||Pink Fresh||Marss||VoiD|
|Super Smash Con 2016||Nairo||Dabuz||Mr. R|
|2GGT: Abadango Saga||ZeRo||Larry Lurr||Nairo|
|The Big House 6||ZeRo||ANTi||Komorikiri|
|UGC Smash Open||ZeRo||Abadango||ESAM|
|2GGT: ZeRo Saga||MKLeo||Larry Lurr||VoiD|
Then, I wrote a Python script that took in these results, converted them into a list of tuples representing placement frequencies, and applied the partial order to each pair of unique tuples to obtain this resulting diagram.
To nobody’s surprise, ZeRo crushed everyone else, winning six out of the fourteen majors and supermajors in 2016. Ally came in second, closely beating Nairo who came in third.
Below Nairo, the diagram becomes a bit messy. Remember that an arrow pointing from node A to node B means that A unambiguously beats B. This is the case if there exists a path from A to B, too. For example, Nairo unambiguously beats Larry Lurr and Dabuz, but the same can’t be said for Abadango and ANTi versus Larry Lurr and Dabuz.
Some might think that the Hasse diagram might be wrong on some examples: “Pink Fresh (one 1st place) should definitely beat VoiD (two 3rd places)! If we award five points for each 1st place, three points for each 2nd place, and one point for each 3rd place, Pink Fresh would have five points to VoiD’s two.” But according to the Hasse diagram’s partial order, this comparison is subjective. What if VoiD had six 3rd place performances in 2016 instead of just two? According to that scoring scheme, VoiD would beat Pink Fresh on points. Therefore, this comparison and similar ones, too, should be more nuanced and holistic.
How Does It Compare to the Official Rankings?
The most authoritative list that I could find ranking the players in this time period is PGR v2. It only covers tournaments from May 2016 through December 2016, a subset of the tournaments that we just considered. There were 20 players represented in the top 3 placements at all major and supermajor tournaments in 2016 and as a result appear in the diagram. Here are their rankings in PGR v2:
|Player||PGR v2 Rank|
The order of the players according to the Hasse ordering doesn’t exactly match with Panda Global’s list, but it’s pretty close. The highest ranked players in PGR v2 who didn’t place in the top 3 of a 2016 major or supermajor tournament are Mr. E (18th), KEN (19th), and Captain Zack (20th).
This comparison reveals some shortcomings. Because there were only 20 players represented in the diagram, it missed some solid players like Mr. E, KEN, and Captain Zack—players who didn’t place in the top 3 at any major/supermajor tournament in 2016, but otherwise performed well against the 20 players represented.
Overall, I think this is an interesting take on ranking professional Smash players as objectively as possible in a game that was (and still is) young and whose metagame was evolving at a breakneck speed.
I am quite surprised that the results I got were mostly in agreement with a more thorough ranking methodology that Panda Global used, even though it didn’t account for head-to-head matchups or top players’ ability to attend tournaments. The competitive Smash Bros 4 scene has only grown since last year with more big tournaments and more up-and-coming players, so I will get around to analyzing more recent tournaments with this approach.