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Mingbo Li

USATT#: 89849

Introduction
This page explains how Mingbo Li (USATT# 89849)'s rating went from 1781 to 1944 at the 888 Table Tennis Grand Opening Team Challenge held on 25 Jun 2021 - 27 Jun 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 Mingbo Li for this tournament.

Initial Rating Pass 1 Pass 2 Pass 3 Final Rating (Pass 4)
1781 1892 1781 1893 1944


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 166 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 888 Table Tennis Grand Opening Team Challenge held on 25 Jun 2021 - 27 Jun 2021 for Mingbo Li, and its source tournament are as follows:
Initial Rating From Tournament Start Day End Day
1781 2021 US National TT Championships California State Qualifier 16 Apr 2021 18 Apr 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 Mingbo Li's match results and applying the point exchange table, gives us the following result:

Mingbo Li's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
180 UPSET 35 Mingbo Li 89849 1781 Amy Zhang 218649 1961
183 UPSET 35 Mingbo Li 89849 1781 Kef Noorani 217865 1964
20 EXPECTED 7 Mingbo Li 89849 1781 Bosman Botha 219904 1761
167 UPSET 35 Mingbo Li 89849 1781 Carlos Alberto Rodriguez 94585 1948
146 EXPECTED 2 Mingbo Li 89849 1781 Anwis Das 98069 1635
31 UPSET 10 Mingbo Li 89849 1781 Minhua Zhu 215008 1812

Mingbo Li's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
150 EXPECTED -2 Man Wai Yeung 96338 1931 Mingbo Li 89849 1781
45 EXPECTED -6 Andy Zhang 216349 1826 Mingbo Li 89849 1781
231 EXPECTED -1 Gabriel Espinosa 93037 2012 Mingbo Li 89849 1781
312 EXPECTED -0 Luis Rodriguez 94586 2093 Mingbo Li 89849 1781
307 EXPECTED -0 Jim Chai 1648 2088 Mingbo Li 89849 1781
190 EXPECTED -1 Johnny Yam 74934 1971 Mingbo Li 89849 1781
268 EXPECTED -0 Giacomo Benincasa 80537 2049 Mingbo Li 89849 1781
378 EXPECTED -0 Kayla Goodwin 92550 2159 Mingbo Li 89849 1781
341 EXPECTED -0 Anastasia Wang 95295 2122 Mingbo Li 89849 1781
165 EXPECTED -2 Yuyang Ying 90630 1946 Mingbo Li 89849 1781
200 EXPECTED -1 Maximilian Kogler 97213 1981 Mingbo Li 89849 1781

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 Mingbo Li 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 Mingbo Li:

Initial Rating Gains/Losses Pass 1 Rating
1781 - 2 + 35 + 35 + 7 - 6 + 35 - 1 + 0 + 2 + 0 - 1 + 0 + 0 + 0 + 10 - 2 - 1 =1892

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[1,166] the index of the player under consideration. i can be as small as 1 or as large as 166 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[1,166] the index of the player under consideration. i can be as small as 1 or as large as 166 for this tournament and the i-th player must be a rated player.
        q q[1,968] the index of the match result under consideration. q can be as small as 1 or as large as 968 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 Mingbo Li is calculated as follows:
        • Given the initial rating of 1781,
        • and the Pass 1 rating of 1892,
        • the Pass 1 gain is 1892 - 1781 = 111.
        • Since the Pass 1 Gain of 111 is greater than 74, and Mingbo Li has won some matches and lost some matches, the Pass 2 Rating is calculated to be the average of the Pass 1 Rating and the average of the Best win and the worst loss:

          1892 + 1964 + 1826 2 2 =1893    (mod 1)


        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 Mingbo Li's matches were against unrated players. So this rule does not apply to him.
    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 Mingbo Li is a rated player, his Pass 2 Adjustment of 1893 will be ignored, along with him Pass 1 Rating of 1892 and his Pass 2 Rating will be set to his initial rating of 1781 with which he 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 Mingbo Li has an initial rating of 1781, he is not an unrated player, and therefore this rule does not apply to him. 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 Mingbo Li's wins and losses and applying the point exchange table, gives us the following result:
    Mingbo Li's Wins
    Winner Loser
    Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
    180 UPSET 35 Mingbo Li 89849 1781 Amy Zhang 218649 1961
    183 UPSET 35 Mingbo Li 89849 1781 Kef Noorani 217865 1964
    20 EXPECTED 7 Mingbo Li 89849 1781 Bosman Botha 219904 1761
    167 UPSET 35 Mingbo Li 89849 1781 Carlos Alberto Rodriguez 94585 1948
    146 EXPECTED 2 Mingbo Li 89849 1781 Anwis Das 98069 1635
    31 UPSET 10 Mingbo Li 89849 1781 Minhua Zhu 215008 1812

    Mingbo Li's Losses
    Winner Loser
    Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
    150 EXPECTED -2 Man Wai Yeung 96338 1931 Mingbo Li 89849 1781
    45 EXPECTED -6 Andy Zhang 216349 1826 Mingbo Li 89849 1781
    231 EXPECTED -1 Gabriel Espinosa 93037 2012 Mingbo Li 89849 1781
    312 EXPECTED -0 Luis Rodriguez 94586 2093 Mingbo Li 89849 1781
    307 EXPECTED -0 Jim Chai 1648 2088 Mingbo Li 89849 1781
    190 EXPECTED -1 Johnny Yam 74934 1971 Mingbo Li 89849 1781
    268 EXPECTED -0 Giacomo Benincasa 80537 2049 Mingbo Li 89849 1781
    378 EXPECTED -0 Kayla Goodwin 92550 2159 Mingbo Li 89849 1781
    341 EXPECTED -0 Anastasia Wang 95295 2122 Mingbo Li 89849 1781
    165 EXPECTED -2 Yuyang Ying 90630 1946 Mingbo Li 89849 1781
    200 EXPECTED -1 Maximilian Kogler 97213 1981 Mingbo Li 89849 1781

    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 Mingbo Li 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 Mingbo Li in this first part of Pass 3:

    Pass 2 Rating Gains/Losses Pass 3 Part 1 Rating
    1781 - 2 + 35 + 35 + 7 - 6 + 35 - 1 + 0 + 2 + 0 - 1 + 0 + 0 + 0 + 10 - 2 - 1 =1892


    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[1,166] the index of the player under consideration. i can be as small as 1 or as large as 166 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 Mingbo Li is calculated as follows:
        • Given the Pass 2 Rating of 1781,
        • and the Pass 3 Part 1 rating of 1892,
        • the Pass 3 Part 1 gain is 1892 - 1781 = 111.
        • Since the Pass 3 Gain of 111 is greater than 74, and Mingbo Li has won some matches and lost some matches, the Pass 3 Part 2 Rating is calculated to be the average of the Pass 3 Part 1 Rating and the average of the Best win and the worst loss:

          1892 + 1964 + 1826 2 2 =1893.5


      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. Mingbo Li's Pass 3 Part 2 Rating came out to 1893. Since this value is greater than Mingbo Li's initial rating of 1781, his Pass 3 Adjustment is set to his Pass 3 Part 2 Rating of 1893.

      • It is possible for the admin of this tournament to override the Pass 3 Adjustment calculated above with a value they deem appropriate. Mingbo Li does not have a manually overridden value for his Pass 3 Adjustment, therefore the value remains at 1893.
      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 Mingbo Li's match results and applying the point exchange table, gives us the following result:

Mingbo Li's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
68 UPSET 16 Mingbo Li 89849 1893 Amy Zhang 218649 1961
71 UPSET 16 Mingbo Li 89849 1893 Kef Noorani 217865 1964
143 UPSET 30 Mingbo Li 89849 1893 Bosman Botha 219904 2036
55 UPSET 13 Mingbo Li 89849 1893 Carlos Alberto Rodriguez 94585 1948
258 EXPECTED 0 Mingbo Li 89849 1893 Anwis Das 98069 1635
81 EXPECTED 5 Mingbo Li 89849 1893 Minhua Zhu 215008 1812

Mingbo Li's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
38 EXPECTED -6 Man Wai Yeung 96338 1931 Mingbo Li 89849 1893
46 EXPECTED -6 Andy Zhang 216349 1939 Mingbo Li 89849 1893
209 EXPECTED -1 Gabriel Espinosa 93037 2102 Mingbo Li 89849 1893
200 EXPECTED -1 Luis Rodriguez 94586 2093 Mingbo Li 89849 1893
195 EXPECTED -1 Jim Chai 1648 2088 Mingbo Li 89849 1893
78 EXPECTED -5 Johnny Yam 74934 1971 Mingbo Li 89849 1893
237 EXPECTED -1 Giacomo Benincasa 80537 2130 Mingbo Li 89849 1893
266 EXPECTED -0 Kayla Goodwin 92550 2159 Mingbo Li 89849 1893
229 EXPECTED -1 Anastasia Wang 95295 2122 Mingbo Li 89849 1893
114 EXPECTED -3 Yuyang Ying 90630 2007 Mingbo Li 89849 1893
88 EXPECTED -4 Maximilian Kogler 97213 1981 Mingbo Li 89849 1893

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 players' Pass 3 Adjustment, we apply the point exchange table from above and show the ratings points earned and lost by Mingbo Li in the "Gain" and "Loss" columns. 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 4 Rating for Mingbo Li:

Pass 3 Rating Gains/Losses Pass 4 Rating
1893 - 6 + 16 + 16 + 30 - 6 + 13 - 1 - 1 + 0 - 1 - 5 - 1 + 0 - 1 + 5 - 3 - 4 =1944

You can click here to view a table of Pass 4 calculations for all the players in this tournament.