USAR Rankings

The model we selected is a penalized logistic regression model using the lme4 package in R. Key Terms:

• Penalized: The penalization makes it so that It takes some time to move very high (or low) on the rankings, so players won’t immediately rocket to the #1 spot after going 1-0.

• Logistic Regression: Statistical method used to predict a binary outcome (Win or Loss). Takes players ratings as inputs and then gives a probability of team 1 winning. Players are ranked based on their estimated effect on winning games. Notably, this does not include point differential, so a 21-10 win gets the same amount of credit as a 21-19 win.

What does this mean:

By default, players come in with an average (100) rating. The model will first predict the outcome of each game based on the players ratings. It then compares those predictions to actual results and calculates the loss (the difference between the prediction and the result). For example if the model predicts team 1 has a 70% chance of winning and they win, the loss is 0.3 (1 - 0.70). If the team two wins, the loss is 0.7 (0.70 - 0). The model then iteratively adjusts players ratings to minimize the differences across all games.

We chose this model over an ELO based model based on comparisons between predictions on 2021 data. Since this model looks at all the data at once, there is no clear formula for how a single game updates the rankings.

All players (both contender and premier) are rated on the same scale and each game is weighted equally. This is due to the long term goal of using the same rating system for players of all levels. In addition, at non-STS events such as those hosted by LROs there are Open divisions that contain a mix of contender and premier players. We see quantifying these games and the potential skill gap between divisions as an important part of our system.

This, however, does not mean a contender win counts the same as a premier win. The strength of your opponent has a big influence on the impact of your win. Beating a team rated much higher than you will most likely increase your rating while beating a team with a much lower rating won’t do much to change your ranking.

We chose a two tournament minimum to try and help the model differentiate between divisions. If a player starts in Contender and plays two tournaments they 1) Qualify at the first tournament and then play premier at the second. The games against the premier players should help place them correctly. 2) They lose games at the first tournament and don’t qualify and then play a second contender tournament. Even if they were to win all the games at the second tournament the loses to at the first should help place them lower. This is not a perfect system however as there are a number of factors that can lead to inaccuracies such as the team they lost to in the first tournament not playing more tournaments and not being bumped down, or the team losing to only highly rated premier teams. The bottom line is the more tournaments and the more games the better.

In addition, as more Open divisions at USAR Sanctioned events occur there will be crucial crossover games to help the rankings accurately rank players.

Player scores are scaled such that an average* player is 100, with higher scores indicating higher player skill.

As a rule of thumb, the model would expect:

• 100-rated players to win about 50% of their games if they were to play with an average partner against two average opponents

• 110-rated players to win about 75% of their games if they were to play with an average partner against two average opponents

• 120-rated players to win about 88% of their games if they were to play with an average partner against two average opponents

• 130-rated players to win about 95% of their games if they were to play with an average partner against two average opponents

The average of a team's Player Scores is a good proxy for team talent. Thus, a team comprised of two 125-rated players should be roughly equal to one comprised of one 100-rated player and one 150-rated player

*Average refers to the average player across all qualified games. For Open, this means all Contender-equivalent and above divisions at USAR Sanctioned Divisions. For Women, this means the top Women's division at USAR Sanctioned Tournaments.

Only USAR Sanctioned tournaments

Pool play, bracket play, and consolation are considered and weighted equally

Rankings are improved when you win games at USAR approved tournaments! (Especially against good competition.)

At this time we are requiring that a player play in at least two sanctioned events to be considered.

Since this is a USAR ranking, only US based players are considered for the rankings.

International players do still have a rating within the model and US players get credit for beating them.

Unfortunately, at this time we are only releasing the top player rankings. We will be including other divisions in the near future.

The rankings system continuously updates player ratings based on W/L record and strength of schedule. Though your W/L record doesn’t change if you don’t play, your strength of schedule still might, as the model updates its understanding of the quality of your opponents. If the team you beat last weekend then goes undefeated this weekend, your rating will likely improve, as your prior win becomes more impressive in hindsight. The reverse can also be true.

Most likely, your partner’s record and strength of schedule when playing without you is more impressive than your record and strength of schedule when playing without them.

The only tournaments considered in rankings are USAR Sanctioned events. Talk to your tournament director, and work with USAR to get your tournament sanctioned so that the results will count!

The score is not currently considered, due to a lack of completeness in score reporting. However, it is incredibly valuable long-term to consistently and accurately report full scores of each game, set, and match played.

For Players:

• Play in USAR events! The more data the better.

• Data hygiene on Fwango

  • Have only two players on your team.

  • Do NOT drop players from your team.

  • Do NOT delete your old teams.

  • Please record all your game scores (not just 1-0). Roundnet Germany has a great explainer about this

For Tournament Directors:

• Get your tournaments sanctioned by USAR

• Data hygiene on Fwango

  • Ensure all registered teams consist of only two players.

  • If a match is a three game series create space for all three scores to be entered (not just 1).

  • Consistently label your all non-bracket stages “Pool Play.”

  • Record injury forfeits as 0 to -1 and non-injury forfeits as 0 to -2.

  • At the end of the day: make sure that all played matches are entered into Fwango and publish final standings.