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Melissa Meschkewitz

USATT#: 1171012

Introduction
This page explains how Melissa Meschkewitz (USATT# 1171012)'s rating went from 670 to 670 at the Barbara Wurster Memorial Open held on 14 May 2021 - 15 May 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 Melissa Meschkewitz for this tournament.

Initial Rating Pass 1 Pass 2 Pass 3 Final Rating (Pass 4)
670 646 670 670 670


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 130 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 Barbara Wurster Memorial Open held on 14 May 2021 - 15 May 2021 for Melissa Meschkewitz, and its source tournament are as follows:
Initial Rating From Tournament Start Day End Day
670 Presper Financial Architects Open 16 Apr 2021 17 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 Melissa Meschkewitz's match results and applying the point exchange table, gives us the following result:

Melissa Meschkewitz's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
52 EXPECTED 6 Melissa Meschkewitz 1171012 670 Anna Chamblee 1169793 618
299 EXPECTED 0 Melissa Meschkewitz 1171012 670 Daniel Chamblee 1169794 371

Melissa Meschkewitz's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
570 EXPECTED -0 David W. Tiche 1170674 1240 Melissa Meschkewitz 1171012 670
164 EXPECTED -2 Adhrit V Kini 1167478 834 Melissa Meschkewitz 1171012 670
521 EXPECTED -0 Nikhil Kori 1157639 1191 Melissa Meschkewitz 1171012 670
849 EXPECTED -0 Istvan Kovacs 93493 1519 Melissa Meschkewitz 1171012 670
616 EXPECTED -0 Laura Paglin 92104 1286 Melissa Meschkewitz 1171012 670
189 EXPECTED -1 Brooks Leonard 85963 859 Melissa Meschkewitz 1171012 670
570 EXPECTED -0 David W. Tiche 1170674 1240 Melissa Meschkewitz 1171012 670
400 EXPECTED -0 Firoz Basheer 1168339 1070 Melissa Meschkewitz 1171012 670
322 EXPECTED -0 Limei Hou 219536 992 Melissa Meschkewitz 1171012 670
113 UPSET -25 Vivaan Chandra 1170374 557 Melissa Meschkewitz 1171012 670
148 EXPECTED -2 Sadhvi Kurra 1169808 818 Melissa Meschkewitz 1171012 670
853 EXPECTED -0 Ryan Day 229653 1523 Melissa Meschkewitz 1171012 670
360 EXPECTED -0 Judah Graber 1170671 1030 Melissa Meschkewitz 1171012 670
713 EXPECTED -0 Brian Dillon 97083 1383 Melissa Meschkewitz 1171012 670
400 EXPECTED -0 Firoz Basheer 1168339 1070 Melissa Meschkewitz 1171012 670
622 EXPECTED -0 Jeffrey K. Newton 47497 1292 Melissa Meschkewitz 1171012 670

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 Melissa Meschkewitz 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 Melissa Meschkewitz:

Initial Rating Gains/Losses Pass 1 Rating
670 + 0 - 2 + 0 + 0 + 0 - 1 + 0 + 0 + 0 + 6 - 25 - 2 + 0 + 0 + 0 + 0 + 0 + 0 =646

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[1,130] the index of the player under consideration. i can be as small as 1 or as large as 130 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[1,130] the index of the player under consideration. i can be as small as 1 or as large as 130 for this tournament and the i-th player must be a rated player.
        q q[1,1103] the index of the match result under consideration. q can be as small as 1 or as large as 1103 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 Melissa Meschkewitz is calculated as follows:
        • Given the initial rating of 670,
        • and the Pass 1 rating of 646,
        • the Pass 1 gain is 646 - 670 = -24.
        • Since the Pass 1 gain of -24 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 Melissa Meschkewitz is 670.

        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 Melissa Meschkewitz'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 Melissa Meschkewitz is a rated player, her Pass 2 Adjustment of 670 will be ignored, along with her Pass 1 Rating of 646 and her Pass 2 Rating will be set to her initial rating of 670 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 Melissa Meschkewitz has an initial rating of 670, 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 Melissa Meschkewitz's wins and losses and applying the point exchange table, gives us the following result:
    Melissa Meschkewitz's Wins
    Winner Loser
    Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
    52 EXPECTED 6 Melissa Meschkewitz 1171012 670 Anna Chamblee 1169793 618
    299 EXPECTED 0 Melissa Meschkewitz 1171012 670 Daniel Chamblee 1169794 371

    Melissa Meschkewitz's Losses
    Winner Loser
    Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
    570 EXPECTED -0 David W. Tiche 1170674 1240 Melissa Meschkewitz 1171012 670
    164 EXPECTED -2 Adhrit V Kini 1167478 834 Melissa Meschkewitz 1171012 670
    521 EXPECTED -0 Nikhil Kori 1157639 1191 Melissa Meschkewitz 1171012 670
    849 EXPECTED -0 Istvan Kovacs 93493 1519 Melissa Meschkewitz 1171012 670
    616 EXPECTED -0 Laura Paglin 92104 1286 Melissa Meschkewitz 1171012 670
    189 EXPECTED -1 Brooks Leonard 85963 859 Melissa Meschkewitz 1171012 670
    570 EXPECTED -0 David W. Tiche 1170674 1240 Melissa Meschkewitz 1171012 670
    400 EXPECTED -0 Firoz Basheer 1168339 1070 Melissa Meschkewitz 1171012 670
    322 EXPECTED -0 Limei Hou 219536 992 Melissa Meschkewitz 1171012 670
    113 UPSET -25 Vivaan Chandra 1170374 557 Melissa Meschkewitz 1171012 670
    148 EXPECTED -2 Sadhvi Kurra 1169808 818 Melissa Meschkewitz 1171012 670
    853 EXPECTED -0 Ryan Day 229653 1523 Melissa Meschkewitz 1171012 670
    360 EXPECTED -0 Judah Graber 1170671 1030 Melissa Meschkewitz 1171012 670
    713 EXPECTED -0 Brian Dillon 97083 1383 Melissa Meschkewitz 1171012 670
    400 EXPECTED -0 Firoz Basheer 1168339 1070 Melissa Meschkewitz 1171012 670
    622 EXPECTED -0 Jeffrey K. Newton 47497 1292 Melissa Meschkewitz 1171012 670

    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 Melissa Meschkewitz 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 Melissa Meschkewitz in this first part of Pass 3:

    Pass 2 Rating Gains/Losses Pass 3 Part 1 Rating
    670 + 0 - 2 + 0 + 0 + 0 - 1 + 0 + 0 + 0 + 6 - 25 - 2 + 0 + 0 + 0 + 0 + 0 + 0 =646


    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[1,130] the index of the player under consideration. i can be as small as 1 or as large as 130 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 Melissa Meschkewitz is calculated as follows:
        • Given the Pass 2 Rating of 670,
        • and the Pass 3 Part 1 rating of 646,
        • the Pass 3 Part 1 gain is 646 - 670 = -24.
        • Since the Pass 3 Gain of -24 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 Melissa Meschkewitz is 670.

      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. Melissa Meschkewitz's Pass 3 Part 2 Rating came out to 670. Since this value is greater than Melissa Meschkewitz's initial rating of 670, her Pass 3 Adjustment is set to her Pass 3 Part 2 Rating of 670.

      • It is possible for the admin of this tournament to override the Pass 3 Adjustment calculated above with a value they deem appropriate. Melissa Meschkewitz does not have a manually overridden value for her Pass 3 Adjustment, therefore the value remains at 670.
      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 Melissa Meschkewitz's match results and applying the point exchange table, gives us the following result:

Melissa Meschkewitz's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
52 EXPECTED 6 Melissa Meschkewitz 1171012 670 Anna Chamblee 1169793 618
299 EXPECTED 0 Melissa Meschkewitz 1171012 670 Daniel Chamblee 1169794 371

Melissa Meschkewitz's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
570 EXPECTED -0 David W. Tiche 1170674 1240 Melissa Meschkewitz 1171012 670
218 EXPECTED -1 Adhrit V Kini 1167478 888 Melissa Meschkewitz 1171012 670
575 EXPECTED -0 Nikhil Kori 1157639 1245 Melissa Meschkewitz 1171012 670
849 EXPECTED -0 Istvan Kovacs 93493 1519 Melissa Meschkewitz 1171012 670
616 EXPECTED -0 Laura Paglin 92104 1286 Melissa Meschkewitz 1171012 670
582 EXPECTED -0 Brooks Leonard 85963 1252 Melissa Meschkewitz 1171012 670
570 EXPECTED -0 David W. Tiche 1170674 1240 Melissa Meschkewitz 1171012 670
400 EXPECTED -0 Firoz Basheer 1168339 1070 Melissa Meschkewitz 1171012 670
322 EXPECTED -0 Limei Hou 219536 992 Melissa Meschkewitz 1171012 670
120 EXPECTED -3 Vivaan Chandra 1170374 790 Melissa Meschkewitz 1171012 670
148 EXPECTED -2 Sadhvi Kurra 1169808 818 Melissa Meschkewitz 1171012 670
853 EXPECTED -0 Ryan Day 229653 1523 Melissa Meschkewitz 1171012 670
413 EXPECTED -0 Judah Graber 1170671 1083 Melissa Meschkewitz 1171012 670
713 EXPECTED -0 Brian Dillon 97083 1383 Melissa Meschkewitz 1171012 670
400 EXPECTED -0 Firoz Basheer 1168339 1070 Melissa Meschkewitz 1171012 670
622 EXPECTED -0 Jeffrey K. Newton 47497 1292 Melissa Meschkewitz 1171012 670

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 Melissa Meschkewitz 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 Melissa Meschkewitz:

Pass 3 Rating Gains/Losses Pass 4 Rating
670 + 0 - 1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 6 - 3 - 2 + 0 + 0 + 0 + 0 + 0 + 0 =670

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