A guide to USATT ratings

Last updated by Simply Compete Inc. (SC) staff on February 28, 2023

Introduction

The purpose of this document is to capture the mathematical formulae used by USA Table Tennis (USATT) to determine player ratings. USATT uses these ratings to rate players that participate in its sanctioned tournaments and in its league events.

Since 2016, SC has worked with various stakeholders of the table tennis community to systematically capture the details of the rating calculation process as followed by various (differing) implementations (and understandings) in the community. Prior to 2016, these details existed as fragmented knowledge within the community. This document may be the first such document to cohesively define the mathematical formulae involved in the rating calculations in a formal manner with the provided degree of specificity. This document is intended to be a reference for players, parents, coaches, tournament directors, league directors, and anyone else interested in understanding how these ratings are calculated.

The process for calculating ratings of players primarily consists of 4 steps. Each of the 4 steps pass through the match results data from the tournament or the league event under consideration. These 4 steps are sometimes referred to as the 4 passes of the rating processor. In the sections below, we will first describe the process used to identify the initial ratings of the players that participate in the tournament or league event under consideration. We will then describe the 4 passes of the ratings processor in detail.

Initial Rating

The input into the first pass of the ratings processor is the initial rating of the players (for those that have them). The initial rating of a player for a tournament or league event is the rating the player received at the end of the most recent tournament or league event prior to the current tournament or league event. If this is the first tournament or league event the player has ever participated in (based on our records), then the player is deemed to have no initial rating.

Pass 1

In Pass 1, we only consider all the players that come into this tournament or league event with an initial rating while ignoring all the unrated players. If a rated player has a match against an unrated player, then that match result is ignored from the pass 1 calculations as well. We apply the point exchange table shown below to all the matches participated in by the rated players:

Point Spread Expected Result Upset Result
0 - 12 8 8
13 - 37 7 10
38 - 62 6 13
63 - 87 5 16
88 - 112 4 20
113 - 137 3 25
138 - 162 2 30
163 - 187 2 35
188 - 212 1 40
213 - 237 1 45
238 and up 0 50
Point Spread: 0 - 12
Expected Result: 8
Upset Result: 8
Point Spread: 13 - 37
Expected Result: 7
Upset Result: 10
Point Spread: 38 - 62
Expected Result: 6
Upset Result: 13
Point Spread: 63 - 87
Expected Result: 5
Upset Result: 16
Point Spread: 88 - 112
Expected Result: 4
Upset Result: 20
Point Spread: 113 - 137
Expected Result: 3
Upset Result: 25
Point Spread: 138 - 162
Expected Result: 2
Upset Result: 30
Point Spread: 163 - 187
Expected Result: 2
Upset Result: 35
Point Spread: 188 - 212
Expected Result: 1
Upset Result: 40
Point Spread: 213 - 237
Expected Result: 1
Upset Result: 45
Point Spread: 238 and up
Expected Result: 0
Upset Result: 50

Suppose player A has an initial rating of 2000 and player B has an initial rating of 2064, and they played a match against each other. When computing the impact of this match on their rating, the "Point Spread" (as it is referred to in the table above) between these two players is the absolute value of the difference between their initial ratings. When the player with the higher rating wins, presumably the better player won, which is the expected outcome of a match, and therefore the "Expected Result" column applies. If the player with the lower rating wins the match, then presumably this is not expected, and therefore it is deemed as an "Upset Result" and the value from that column in the table above is used. So, in our example of player A vs player B, if player B wins the match, then the expected outcome happens, and 5 points are added to player B's initial rating and 5 points are deducted from player A's initial rating.

Pass 2

The purpose of this pass is solely to determine ratings for unrated players. To do this, we first look at the ratings for rated players that came out of Pass 1 to determine a “Pass 2 Adjustment”. The logic for this is as follows:

  1. We calculate the difference between the Pass 1 Rating and the Initial Rating of the current player. This difference is referred to as the points gained by the player in Pass 1.

  2. For rated players, Pass 1 points gained, are used to calculate the Pass 2 Adjustment in the following way:

    1. If a player gained less than 50 points (exclusive) in pass 1, then we set that player's Pass 2 Adjustment to his/her Initial Rating.
    2. If a player gained between 50 and 74 (inclusive) points in pass 1, then we set the player's Pass 2 Adjustment to his/her Final Pass1 Rating.
    3. If the player has won at least one match, and lost at least 1 match in the tournament or league event, then the player's Pass 2 Adjustment is the average of his/her Final Pass 1 Rating and the average of his/her opponents rating from the best win and the worst loss.
    4. If a player has not lost any of his/her matches in the current tournament or league event, the mathematical median (rounded down to the nearest integer) of all the player's opponents' initial rating is used as his/her Pass 2 Adjustment.
    5. After calculating the Pass 2 Adjustment for all the rated players as described above, we can now calculate the Pass 2 Rating for all the unrated players in this tournament or league event (which is the main purpose of Pass 2). Pass 2 Rating is calculated using the following formula:

      1. If all of the matches of an unrated player are against other unrated players, then the Pass 2 Rating for that player is simply set to 1200. You can view these players who received a 1200 Pass 2 Rating toward the end of this web page.
      2. For unrated players with wins and losses, where at least 1 of the opponents has an initial rating, the Pass 2 Rating is the average of the best win and the worst loss (using the Pass 2 Adjustment of all rated players).
      3. For unrated players with all wins and no losses, where at least 1 of the opponents has an initial rating, the Pass 2 Rating is calculated using the following formula:
        1. We first calculate the points difference between the best win and the worst loss of all the current player's opponents, where the best win is the highest Pass 2 adjustment rating of the opponent against whom the player has won a match, and the worst loss is the lowest Pass 2 adjustment rating of the opponent against whom the player has lost a match in the tournament or league event under consideration.
        2. For each of the opponents' difference between best wins and worst losses, if the difference is between 1 and 50 (inclusive) then an intermediate value of 10 is assigned; if the difference is between 51 and 100 (inclusive) then an intermediate value of 5 is assigned; if the difference is between 101 and 150 (inclusive) then an intermediate value of 1 is assigned; otherwise the intermediate value of 0 is assigned.
        3. All of the intermediate values described in the step above get added to the current player's best win (which is the highest Pass 2 Adjustment of the opponent against whom the current player won a match in the current tournament or league event) and that value is deemed the Pass 2 Rating for the current player.
      4. For unrated players with all losses and no wins, where at least 1 of the opponents has an initial rating, the Pass 2 Rating is calculated using the following step:
        1. We first calculate the points differences between the current player's worst loss, which is the lowest Pass 2 Adjustment of the opponent against whom the player has lost a match in the current league or tournament rating, and the Pass 2 Adjustments of all the opponents for the tournament or league event under consideration.
        2. For each of the differences described in the step above, if the difference is between 1 and 50 (inclusive) then an intermediate value of 10 is assigned; if the difference is between 51 and 100 (inclusive) then an intermediate value of 5 is assigned; if the difference is between 101 and 150 (inclusive) then an intermediate value of 1 is assigned; otherwise the intermediate value of 0 is assigned.
        3. The Pass 2 Rating is determined by adding the sum of the intermediate values calculated in the step above to the current player's worst loss.

Pass 3

Any of the unrated players who have all wins or all losses are skipped in Pass 3. Pass 3 Rating is calculated using the steps described below:

  1. In the first part of Pass 3, we apply the point exchange table described in Pass 1 except this time by using all the players' Pass 2 Ratings. This rating will be referred to as the the Pass 3 Part 1 rating.
  2. Given the Pass 3 Part 1 rating calculated above, the second part of Pass 3 looks very similar to the part of Pass 2 that deals with rated players where we calculate their Pass 2 Adjustment.
    1. First, we calculate the points gained in Pass 3 Part 1. Points gained is simply the difference between the Pass 3 Part 1 Rating and the Pass 2 Rating of a player.
    2. Pass 3 points gained is then used to calculate the Pass 3 Part 2 Rating in the following way:
      1. If a player gained less than 50 points (exclusive) in Pass 3 Part 1, then we set that player's Pass 3 Part 2 Rating to his/her Pass 2 Rating.
      2. If a player gained between 50 and 74 (inclusive) points in Pass 3 Part 1, then we set the player's Pass 3 Part 2 Rating to his/her Pass 3 Part 1 Rating.
      3. If a player gains 75 or more points (inclusive) in Pass 3 Part 1, then the following formula applies:
        1. If the player has won at least one match, and lost at least 1 match in the tournament or league event, then the player's Pass 3 Part 2 Rating is the average of his/her Pass 3 Part 1 Rating and the average of his/her opponents rating from the best win and the worst loss.
        2. If a player has not lost any of his/her matches in the current tournament or league event, the mathematical median (rounded down to the nearest integer) of all the player's opponents' ratings is used as his/her Pass 3 Part 2 Rating.
      4. The Pass 3 Part 2 rating ends up becoming the final Pass 3 rating (also referred to as the Pass 3 Adjustment) except as follows:
        1. In the cases where the Pass 3 Part 2 rating is less than the players' initial rating Pi0, the Pass 3 rating is reset back to that players initial rating.
        2. It is possible for the admin of this tournament or league event to override the Pass 3 Adjustment calculated above with a value they deem is appropriate.

Pass 4

Pass 4 is the final pass of the rating processor. In this pass, we take the adjusted ratings (Pass 3 Adjustment) of all the rated players, and the assigned ratings of unrated players (Pass 2 Rating), and apply the point exchange table to the match results based on these ratings to arrive at a final rating.