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Natalie Chan

USATT#: 198840

Introduction
This page explains how Natalie Chan (USATT# 198840)'s rating went from 2122 to 2145 at the 2021 US National Table Tennis Championships held on 4 Jul 2021 - 9 Jul 2021. These ratings are calculated by the ratings processor which goes through 4 passes over the match results data for a tournament. The following values are produced at the end of each of the 4 passes of the ratings processor for Natalie Chan for this tournament.

Initial Rating Pass 1 Pass 2 Pass 3 Final Rating (Pass 4)
2122 2133 2122 2122 2145


You can click here to view a table of all the resultant values from each of the 4 passes (and the initial rating) of the ratings processor for all of the 486 players in this tournament. Sections below for further details on the initial rating and the 4 passes of the ratings processor.

Note: We use mathematical notation to express the exact operations carried out in each pass of the ratings processor below. Whenever you see a variable/symbol such as for example Xi3, we are following the convention that the superscript part of the variable (in this case "3") indicates an index (such as in a series), and it should not be misconstrued to be an exponent (which is how it is used by default).

Initial Rating
The initial rating of a player for a tournament is the rating the player received at the end of the most recent tournament prior to the current tournament. If this is the first tournament the player has ever participated in (based on our records), then the player has no initial rating.

The initial rating for 2021 US National Table Tennis Championships held on 4 Jul 2021 - 9 Jul 2021 for Natalie Chan, and its source tournament are as follows:
Initial Rating From Tournament Start Day End Day
2122 888 Table Tennis Grand Opening Team Challenge 25 Jun 2021 27 Jun 2021

Click here to view the details of the initial ratings for all the players in this tournament.

Pass 1 Rating
In Pass 1, we only consider all the players that come into this tournament 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

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 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 therfore 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 watch, then the expected outcome happens, and 5 points are added to player B's rating and 5 points are deducted from player A's rating. Looking at Natalie Chan's match results and applying the point exchange table, gives us the following result:

Natalie Chan's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
101 EXPECTED 4 Natalie Chan 198840 2122 Stephen Yatvitskiy 94739 2021
463 EXPECTED 0 Natalie Chan 198840 2122 Catherine Palm 220024 1659
231 EXPECTED 1 Natalie Chan 198840 2122 Wayne A. Carney 508 1891
75 UPSET 16 Natalie Chan 198840 2122 Emily Quan 202992 2197
57 EXPECTED 6 Natalie Chan 198840 2122 Purvi Soni 98261 2065
446 EXPECTED 0 Natalie Chan 198840 2122 Alicia Yu 217211 1676
269 EXPECTED 0 Natalie Chan 198840 2122 Aarthi Loganathan 217446 1853
286 EXPECTED 0 Natalie Chan 198840 2122 Carmen Yu 217532 1836
32 EXPECTED 7 Natalie Chan 198840 2122 Kylie Hei Man Lam 97471 2090
197 EXPECTED 1 Natalie Chan 198840 2122 Riley Marie Esquejo 94652 1925
447 EXPECTED 0 Natalie Chan 198840 2122 Andrea Tang 202987 1675
191 EXPECTED 1 Natalie Chan 198840 2122 Aishi Dassarma 96618 1931
340 EXPECTED 0 Natalie Chan 198840 2122 Dariah Feng 224231 1782
1327 EXPECTED 0 Natalie Chan 198840 2122 Anya Shanbhag 1171127 795
168 EXPECTED 2 Natalie Chan 198840 2122 Anushka Oak 73408 1954
99 EXPECTED 4 Natalie Chan 198840 2122 Alyssa Jian Kang 212231 2023
223 EXPECTED 1 Natalie Chan 198840 2122 Aria Shi 222815 1899
1378 EXPECTED 0 Natalie Chan 198840 2122 Valerie Rolph 212221 744

Natalie Chan's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
297 EXPECTED -0 Sarah Isabel Jalli 94697 2419 Natalie Chan 198840 2122
387 EXPECTED -0 Amy Wang 76235 2509 Natalie Chan 198840 2122
489 EXPECTED -0 Lily Zhang 31126 2611 Natalie Chan 198840 2122
57 EXPECTED -6 Priyan Jindal 90352 2179 Natalie Chan 198840 2122
131 EXPECTED -3 Rachel Wang 96633 2253 Natalie Chan 198840 2122
81 UPSET -16 Tiffany Lam 96513 2041 Natalie Chan 198840 2122
35 EXPECTED -7 Yishiuan Lin 230429 2157 Natalie Chan 198840 2122

You can click here to view a table of outcomes and points gained/lost from all the matches with all the players in this tournament.

The "Outcome" column above, shows whether the match had an expected (player with the higher rating wins the match) or an upset (player with the higher rating loses the match) outcome. Based on this outcome, and using both the player's initial rating, we apply the point exchange table from above and show the ratings points earned and lost by Natalie Chan in the "Gain" column. Matches are separated out into two tables for wins and losses where points are gained and lost respectively. We get the following math to calculate the Pass 1 Rating for Natalie Chan:

Initial Rating Gains/Losses Pass 1 Rating
2122 + 4 + 0 + 1 + 16 + 0 + 6 + 0 + 0 + 0 - 6 - 3 + 0 + 0 + 7 + 1 + 0 + 1 + 0 + 0 + 2 - 16 - 7 + 4 + 1 + 0 =2133

You can click here to view a table of pass1 calculations for all the rated players in this tournament.

Pass 2 Rating
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 an “Pass 2 Adjustment”. The logic for this is as follows:

  1. We calculate the points gained in Pass 1. Points gained is simply the difference between the Pass 1 Rating and the Initial Rating of a player:

    ρi2 = Pi1 - Pi0
    where,

    Symbol Universe Description
    Pi0 Pi0+ the initial rating for the i-th player. We use the symbol P and the superscript 0 to represent the idea that we sometimes refer to the process of identifying the initial rating of the given player as Pass 0 of the ratings processor.
    Pi1 Pi1+ the Pass 1 rating for the i-th player.
    ρi2 ρi2 the points gained by the i-th player in this tournament. Note here that we use the superscript 2 to denote that this value is calculated and used in Pass 2 of the ratings processor. Further, ρi2 only exists for players who have a well defined Pass 1 Rating. For Players with an undefined Pass 1 Rating (unrated players), will have an undefined ρi2.
    i i[1,486] the index of the player under consideration. i can be as small as 1 or as large as 486 for this tournament and the i-th player must be a rated player.

  2. For rated players, Pass 1 points gained, ρi2, is 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 a player gains 75 or more points (inclusive) in pass 1, then the following formula applies:
      • If the player has won at least one match, and lost at least 1 match in the tournament, 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, represented using the formula below:

        αi2 = Pi1 + Bi + Wi 2 2

        where αi2 is the Pass 2 Adjustment for the current player, Pi1 is the Pass 1 Rating, Bi is the rating of the highest rated opponent against which the current player won a match, and Wi is the rating of the lowest rated opponent against which the current player lost a match.
      • If a player has not lost any of his/her matches in the current tournament, the mathematical median (rounded down to the nearest integer) of all of the player's opponents initial rating is used as his/her Pass 2 Adjustment:

        αi2 = {Pk0}

        where Pk0 is the initial rating of the player who was the i-th player's opponent from the k-th match.
        Symbol Universe Description
        i i[1,486] the index of the player under consideration. i can be as small as 1 or as large as 486 for this tournament and the i-th player must be a rated player.
        q q[1,3230] the index of the match result under consideration. q can be as small as 1 or as large as 3230 for this tournament and the q-th match must be have both rated players as opponents.
        g g[1,5] the g-th game of the current match result under consideration. q can be as small as 1 or as large as 5 for this tournament assuming players play up to 5 games in a match.
        Pk0 Pk0+ initial rating of the i-th player's opponent from the k-th match.


      • Therefore, the Pass 2 Adjustment for Natalie Chan is calculated as follows:
        • Given the initial rating of 2122,
        • and the Pass 1 rating of 2133,
        • the Pass 1 gain is 2133 - 2122 = 11.
        • Since the Pass 1 gain of 11 is less than 50, the Pass 2 Rating (also referred to as Pass 2 Adjustment) is reset back to the initial rating.
        • Therefore the Pass 2 Adjustment for Natalie Chan is 2122.

        You can click here to view a table of Pass 2 Adjustments for all the rated players in this tournament.

  3. 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 (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 click here to view these players who received a 1200 Pass 2 Rating. Not all of Natalie Chan's matches were against unrated players. So this rule does not apply to her.
    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) as defined by this formula here:

      Pi2 = Bi2 + Wi2 2

      where Pi2 is the Pass 2 Rating for the i-th player, Bi2 is the largest Pass 2 Adjustment (best win) of the opponenet against whom the i-th player won a match, and Wi2 is the smallest Pass 2 Adjustment (worst loss) of the opponent against whom the i-th player lost a match.
    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:
      Pi2 = Bi2 + k=0Mi-1 I(Bi2-αk2)
      where the function I(x) is defined as, \begin{equation} I(x)=\left\{ \begin{array}{ll} 10, & \text{if}\ x >= 1, x <= 50 \\ 5, & \text{if}\ x >= 51, x <=100 \\ 1, & \text{if}\ x >= 101, x <= 150 \\ 0, & \text{otherwise} \end{array}\right. \end{equation}
      where,
      Symbol Universe Description
      Pi2 Pi2+ the pass 2 rating, of the i-th player in this tournament only applicable to unrated players, where Pi0 is not defined
      Bi2 Bi2+ the largest of the Pass 2 Adjustments of opponents of the i-th player against whom he/she won a match.
      αk2 αk2+ the Pass 2 Adjustment of the player who was the opponent of the i-th player in the k-th match
      I(x) I:+ a function that maps all integers to one of the values from -- 0, 1, 5, 10.
      Mi Mi+ total number of matches played by the i-th player in this tournament
      k k[0,Mi-1]+ The index of the match of the i-th player ranging from 0 to Mi-1
    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 formula:
      Pi2 = Wi2 + k=0Mi-1 I(Wi2-αk2)
      where I(x) is defined above and,

      Symbol Universe Description
      Pi2 Pi2+ the pass 2 rating, of the i-th player in this tournament only applicable to unrated players, where Pi0 is not defined
      Wi2 Wi2+ the smallest of the Pass 2 Adjustments of opponents of the i-th player against whom he/she lost a match.
      αk2 αk2+ the Pass 2 Adjustment of the player who was the opponent of the i-th player in the k-th match
      I(x) I:+ a function that maps all integers to one of the values from -- 0, 1, 5, 10.
      Mi Mi+ total number of matches played by the i-th player in this tournament
      k k[0,Mi-1]+ The index of the match of the i-th player ranging from 0 to Mi-1
    5. For the rated players, all the work done in Pass 1 and Pass 2 to undone and they have their ratings reset back to their initial ratings while the unrated players keep their Pass 2 Adjustment as their final Pass 2 Rating. Since Natalie Chan is a rated player, her Pass 2 Adjustment of 2122 will be ignored, along with her Pass 1 Rating of 2133 and her Pass 2 Rating will be set to her initial rating of 2122 with which she came into this tournament.


Click here to see detailed information about the Pass 2 Ratings of all the other players in this tournament.

Pass 3 Rating
Any of the unrated players who have all wins or all losses are skipped in Pass 3. Since Natalie Chan has an initial rating of 2122, she is not an unrated player, and therefore this rule does not apply to her. You can click here to view list of all the players that are skipped in this Pass 3.

Pass 3 Rating is calculated using 2 steps described below:
  1. In the first part of Pass 3, we apply the point exchange table described in Pass 1 above except this time by using all the players' Pass 2 Ratings. Looking at Natalie Chan's wins and losses and applying the point exchange table, gives us the following result:
    Natalie Chan's Wins
    Winner Loser
    Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
    101 EXPECTED 4 Natalie Chan 198840 2122 Stephen Yatvitskiy 94739 2021
    463 EXPECTED 0 Natalie Chan 198840 2122 Catherine Palm 220024 1659
    231 EXPECTED 1 Natalie Chan 198840 2122 Wayne A. Carney 508 1891
    75 UPSET 16 Natalie Chan 198840 2122 Emily Quan 202992 2197
    57 EXPECTED 6 Natalie Chan 198840 2122 Purvi Soni 98261 2065
    446 EXPECTED 0 Natalie Chan 198840 2122 Alicia Yu 217211 1676
    269 EXPECTED 0 Natalie Chan 198840 2122 Aarthi Loganathan 217446 1853
    286 EXPECTED 0 Natalie Chan 198840 2122 Carmen Yu 217532 1836
    32 EXPECTED 7 Natalie Chan 198840 2122 Kylie Hei Man Lam 97471 2090
    197 EXPECTED 1 Natalie Chan 198840 2122 Riley Marie Esquejo 94652 1925
    447 EXPECTED 0 Natalie Chan 198840 2122 Andrea Tang 202987 1675
    191 EXPECTED 1 Natalie Chan 198840 2122 Aishi Dassarma 96618 1931
    340 EXPECTED 0 Natalie Chan 198840 2122 Dariah Feng 224231 1782
    1327 EXPECTED 0 Natalie Chan 198840 2122 Anya Shanbhag 1171127 795
    168 EXPECTED 2 Natalie Chan 198840 2122 Anushka Oak 73408 1954
    99 EXPECTED 4 Natalie Chan 198840 2122 Alyssa Jian Kang 212231 2023
    223 EXPECTED 1 Natalie Chan 198840 2122 Aria Shi 222815 1899
    1378 EXPECTED 0 Natalie Chan 198840 2122 Valerie Rolph 212221 744

    Natalie Chan's Losses
    Winner Loser
    Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
    297 EXPECTED -0 Sarah Isabel Jalli 94697 2419 Natalie Chan 198840 2122
    387 EXPECTED -0 Amy Wang 76235 2509 Natalie Chan 198840 2122
    489 EXPECTED -0 Lily Zhang 31126 2611 Natalie Chan 198840 2122
    57 EXPECTED -6 Priyan Jindal 90352 2179 Natalie Chan 198840 2122
    131 EXPECTED -3 Rachel Wang 96633 2253 Natalie Chan 198840 2122
    81 UPSET -16 Tiffany Lam 96513 2041 Natalie Chan 198840 2122
    35 EXPECTED -7 Yishiuan Lin 230429 2157 Natalie Chan 198840 2122

    You can click here to view a table of outcomes and points gained/lost from all the matches with all the players in this tournament for Pass 3 Part 1.

    The "Outcome" column above, shows whether the match had an expected (player with the higher rating wins the match) or an upset (player with the higher rating loses the match) outcome. Based on this outcome, and using both the player's Pass 2 Rating, we apply the point exchange table from above and show the rating points earned and lost by Natalie Chan in the "Gain" column. Matches are divided up into two tables for wins and losses where points are "Gain"ed for the wins and "loss"ed for losses. Putting all the gains and losses together, we get the following math to calculate the rating for Natalie Chan in this first part of Pass 3:

    Pass 2 Rating Gains/Losses Pass 3 Part 1 Rating
    2122 + 4 + 0 + 1 + 16 + 0 + 6 + 0 + 0 + 0 - 6 - 3 + 0 + 0 + 7 + 1 + 0 + 1 + 0 + 0 + 2 - 16 - 7 + 4 + 1 + 0 =2133


    You can click here to view a table of these calculations for all the players in this tournament.

  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:

      ρi3 = pi3 - Pi2
      where,

      Symbol Universe Description
      Pi2 Pi2+ the Pass 2 Rating for the i-th player.
      pi3 pi3+ the Pass 3 Part 1 rating for the i-th player. (Note that since this is an intermediate result, we are using a lower case p instead of the upper case P that we use to indicate final result from each pass of the ratings processor.
      ρi3 ρi3 the points gained by the i-th player in this tournament in Pass 3.
      i i[1,486] the index of the player under consideration. i can be as small as 1 or as large as 486 for this tournament.

  3. Pass 3 points gained, ρi3, 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:
      • If the player has won at least one match, and lost at least 1 match in the tournament, 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, represented using the formula below:

        αi3 = pi3 + Bi3 + Wi3 2 2

        where αi3 is the Pass 3 Part 2 Rating for the current player, pi3 is the Pass 3 Part 1 Rating, Bi3 is the rating of the highest rated opponent against which the current player won a match, and Wi is the rating of the lowest rated opponent against which the current player lost a match.
      • If a player has not lost any of his/her matches in the current tournament, the mathematical median (rounded down to the nearest integer) of all of the player's opponents rating is used as his/her Pass 3 Part 2 Rating:
        αi3 = {pk3}

        where pk3 is the Pass 3 Part 1 Rating of the i-th player's opponent from the k-th match.

      • Therefore, the Pass 3 Part 2 Rating for Natalie Chan is calculated as follows:
        • Given the Pass 2 Rating of 2122,
        • and the Pass 3 Part 1 rating of 2133,
        • the Pass 3 Part 1 gain is 2133 - 2122 = 11.
        • Since the Pass 3 Gain of 11 is less than 50, the Pass 3 Part 2 Rating is reset back to the Pass 2 Rating.
        • Therefore the Pass 3 Part 2 Rating for Natalie Chan is 2122.

      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:
      • 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. Natalie Chan's Pass 3 Part 2 Rating came out to 2122. Since this value is greater than Natalie Chan's initial rating of 2122, her Pass 3 Adjustment is set to her Pass 3 Part 2 Rating of 2122.

      • It is possible for the admin of this tournament to override the Pass 3 Adjustment calculated above with a value they deem appropriate. Natalie Chan does not have a manually overridden value for her Pass 3 Adjustment, therefore the value remains at 2122.
      You can click here to view a table of Pass 3 Part 2 Ratings for all the players in this tournament along with any manually overridden values.

Pass 4 Rating
Pass 4 is the final pass of the ratings processor. In this pass, we take the adjusted ratings (Pass 3 Adjustment) of all the rated players, and the assigned rating 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. Looking at Natalie Chan's match results and applying the point exchange table, gives us the following result:

Natalie Chan's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
101 EXPECTED 4 Natalie Chan 198840 2122 Stephen Yatvitskiy 94739 2021
308 EXPECTED 0 Natalie Chan 198840 2122 Catherine Palm 220024 1814
231 EXPECTED 1 Natalie Chan 198840 2122 Wayne A. Carney 508 1891
75 UPSET 16 Natalie Chan 198840 2122 Emily Quan 202992 2197