**Introduction**

ΩRank is an iterative algorithm produced by me, Stuart98, used to evaluate the performance of Super Smash Bros. players in tournaments over a given timeframe. ΩRank is the culmination of years of trial and error in producing ranking systems that accurately reflect player results. Past experience by other community members has shown that traditional ladder ranking systems like ELO or Glicko or placement based systems like the Tennis ranking system fail to accurately rank player results in double elimination tournaments. ΩRank evaluates players by giving them points based on who they beat, who they lose to, and who they outplace and are outplaced by over the course of a season. These results are then compared with those of other players to generate each player’s initial score out of 100. After the initial ranking is created, the calculation is repeated using the new score values until the difference in points for every player from one iteration to the next is essentially zero. Simplified versions of the ΩRank algorithm have in the past been used to construct the Wifi Warrior Rank v5-v7.

**Data**

Data for ΩRank is taken directly from smashdata’s database uploads on github. Manual corrections may at times be applied if necessary (such as an unmarked DQ). If a tournament is missing from smashdata due to being private on start.gg or due to being in a challonge bracket, steps will be taken to ensure the tournament is added to smashdata, such as preparing a conversion sheet for processing a challonge bracket into smashdata.

ΩRank calculations are conducted entirely using google sheets. The full ranking spreadsheet will be made available following the release of the ranking.

**Tournaments Evaluated**

ΩRank 2022 used a tournament qualification system similar to the ones once used by the PGRU and other ranking systems for qualifying events, though with some differences. Like the PGRU, tournaments were given point values based on either the total entrant count they had or the level of talent they had at them based on previous rankings. However, instead of only using 50 or 55 players from the previous ranking for evaluating tournaments, the full top 250 from the previous season was used, giving a more accurate picture of the depth of talent at a tournament. Additionally, tournaments in regions with smaller playerbase have a lower threshold for qualification.

Importantly, these qualification point totals were only used to determine if a tournament was eligible for the ranking; they were not used by the ranking itself. How valuable a tournament was on the ranking was instead determined using Retroactive Retiering, where the talent level of competitors at the event was determined based on their performance throughout the entire season.

A handful of tournaments that did not acquire the 300 (225 for regions with a lower qualification threshold) qualification points needed were nonetheless manually qualified based on markedly improved performances of some of their competitors compared to the prior season or a need for additional data on certain players.

**Tournament Tiering**

The weight or value of tournaments in ΩRank is determined via retroactive retiering. Essentially, how valuable a tournament is is based on how all the players in attendance have done over the course of a season, rather than their performance at any time outside of the season. Like the rest of the ranking, this value is iterated upon using the values from the previous iteration. Unlike the old PGR TTS, this calculation considers every relevant player in attendance at an event; thus, an event with few top 20 players and many top 100 players may be equal in value to an event with many top 20 players and few players beyond that. The value of a tournament is used to determine the weight of wins, placements, and losses at the tournament, with larger tournaments having a higher weight. This increase is not linear and is different for various components of a player’s score; for wins, a win on someone at a tournament with a value of 4800 will be worth approximately 2x as much as a win on someone at a tournament with a value of 400, while for losses the difference is just under 6x.

The tiers displayed on the tournament spreadsheet listed further down on this page indicate the rough value of a tournament but are not used by the ranking itself; the exact point values of tournaments after regional multipliers determine the actual value of an event.

**Qualification**

The vast majority of evaluated players are qualified based on the total set wins accumulated at evaluated tournaments. The exact number changes from season to season but is set that between 1,000 and 2,500 players are qualified. For the ΩRank 2022 full year season, that number was 16. Additional players with fewer sets than this may be manually qualified if it is determined that their absence adversely impacts the ranking, such as causing a loss by a top 20 player to be treated as far worse than the winning player’s data would indicate. Six such players were manually qualified for ΩRank 2022. Wins on unqualified players give zero points, and losses to them are based on the winning player’s win rate but are at best treated as a loss to a player with a score of less than 20.

Going forward, metrics will be implemented to identify unqualified players with multiple top 100 wins to make it easier to find those players who should be manually qualified.

**Placements**

Rather than awarding points to players directly for their placement, ΩRank instead awards points based on the players someone outplaced. These points increase based on the degree to which a player outplaced them. Outplacing a player like Tweek is more valuable than outplacing a player like BassMage, and getting 7th at an event a player like Tweek got 33rd at is more valuable than getting 17th at such an event. There are also negative outplacement points, for being outplaced by other players. The penalty for being outplaced by someone increases the lower a player’s score is, and the more they outplace you by. Thus, there’s little penalty for being outplaced by someone like Tweek, while being outplaced by someone not in the top 100 carries a much larger penalty. This penalty increases the larger the score of the player being outplaced.

In order to avoid rewarding empty bracket runs where due to DQs or upsets a player had to beat no strong players to achieve a placement, outplacement points are scaled based on a best win. This means that, for example, a placement of 25th at a tournament with a win on a top 20 player can be worth more than 9th at that tournament with no wins on top 100 players.

**Wins**

How valuable a win is depends on two primary factors: the score of the player the win is on, and the value of the event the win happened at. Wins on players with a score of zero give no points; wins on players with scores above zero give points based on the score at a non-linear rate, such that a win on a player with a score of 100 (the #1 player) might be worth nearly 15 times that of a player with a score of 50 (the #50 player). This is then scaled based on the tier of the tournament attended, with wins at the largest of events being worth as much as twice as much as wins at smaller events.

Additionally, to reward players with a breadth of wins on multiple similarly skilled players compared to players with many wins on a single player, as well as to diminish the impact of a single win on a player that someone has many losses to, there is an additional multiplier based on the total number of sets between two players, such that each additional set between two players reduces the value of every set between them. Also, additional win points are rewarded depending on the volatility of a player, or the difference between their best wins and worst losses, with wins on low volatility players being worth more than similarly ranked high volatility players.

**Losses**

Losses are evaluated primarily based on the score of the losing player, the difference in scores between the winning player and the losing player, and the value of the tournament the loss happened at. Losing to someone with a higher score than you will cause a small malus in points; losing to someone with a much lower score than you will cause a much larger loss of points.

There is an additional multiplier based on the score of the losing player, such that higher ranked players (who have more points to begin with) lose more points to a loss to a player with a score a given number of points below them than a player with a lower score. For example, a player with a score of 70 will lose approximately 45% more points for a loss to a player with a score of 50, compared to how many points a player with a score of 50 would lose for taking a loss to a player with a score of 30.

Like wins, losses are scaled based on the size of the tournament they occurred at, with losses at more valuable tournaments counting for more. In order to avoid punishing players for attending regionals, losses use a much steeper scaling than wins, such that a loss at a tournament with a value of 4800 is approximately 6x as punishing as a loss at a tournament with a value of 400.

In order to prevent regional multipliers from counterproductively causing players in that region from being worse off due to their losses hurting them more, there is a multiplier to mitigate the effect of regional multipliers on losses, such that they still hurt a bit more than if the multiplier were not in effect but not to the extent that they would otherwise.

Like wins, the impact of a loss to a player is reduced based on the total number of sets between two players. If you lose to a player ranked far below you that you have beaten many times, the large number of sets between the two players means the impact of the loss is reduced.

**Overall Multipliers**

After all of a player’s outplacement, win, and loss points have been summed, their points are then given punitive or bonus multipliers based on their consistency and peaks throughout the season. The scores of their peak win (scaled to give a bonus for higher level wins) as well as their a weighted (based on tournament value) average peak win for each event they attended with skilled players (defined as events with players equal or better to that of their third best win in attendance) and their weighted average worst loss at each event they attended are calculated. For events at which a player did not lose, their worst loss at the event is treated as having a score of the best player they beat, plus 20.

After these three numbers have been calculated, a regression for each number is calculated to determine what each player’s peak win, average peak win, and average worst loss should be given their own score. The actual values are then divided by the predicted values to determine if a player should be given a bonus or penalty. For each result, total points are multiplied by around 2^result (capping at 2^2). The effect of this is that players with few, strong results are given a bonus, while players with many, weaker results are given a penalty.

Additionally, to encourage a certain level of attendance, players with fewer than four logged tournaments are subjected to a penalty based on their total number of tournaments attended, such that a player with 3 tournaments logged will receive a 0.91x multiplier, and a player with 1 tournament logged will receive a 0.75x multiplier. This only affects these players’ ranking score; their score used in win and loss calculations ignores the low attendance multiplier, so players are not punished for wins or losses against players with low attendance.

**Score**

After a player’s total points have been calculated, their score will be calculated based on their points, the points of the #1 player, and the points of the #50 player. Scores are logarithmically scaled, such that the player with the most points will always have a score of 100.0 and the player with the 50th most points will always have a score of 50.0. Note that the publicly ranked 50th player might have a score of lower than 50.0 if there were top 50 players who were attendance cuts, suspended, or banned from the ranking.

**Bans, Suspensions, and Attendance Cuts**

Players who have the results to be ranked in the top 100 may still be excluded from it if they fit into one of three categories:

1. Players who are serving an indefinite ban from their local scene and/or from majors are excluded from the ranking entirely and will not be mentioned on playercards or blurbs.

2. Players who are serving temporary bans with defined expiry dates, or who are known to be under active investigation for serious misconduct are suspended from the rankings. They are not ranked themselves, but may be mentioned on playercards or blurbs.

3. Players who failed to meet the minimum attendance requirement of 3 tournaments (including 2 majors) or 4 tournaments (including one major) are excluded from the top 100, but are still given playercards and blurbs if their results placed them in the top 100.

Players in all 3 categories are treated as top 100 wins or losses for a player if the algorithm put them within the top 100, so the number of players who count as top 100 wins or losses is slightly more than 100.