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Ilija Lupulesku

USATT#: 4011 | Coach Level: National

Introduction
This page explains how Ilija Lupulesku (USATT# 4011)'s rating went from 2739 to 2750 at the 2002 US National Championships held on - 22 Dec 2002. 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 Ilija Lupulesku for this tournament.

Initial Rating Pass 1 Pass 2 Pass 3 Final Rating (Pass 4)
2739 2750 2739 2739 2750


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 677 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 2002 US National Championships held on - 22 Dec 2002 for Ilija Lupulesku, and its source tournament are as follows:
Initial Rating From Tournament Start Day End Day
2739 Stiga N.A. Teams Championships n/a 1 Dec 2002

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 Ilija Lupulesku's match results and applying the point exchange table, gives us the following result:

Ilija Lupulesku's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
2 EXPECTED 8 Ilija Lupulesku 4011 2739 David Yong-Xiang Zhuang 58322 2737
320 EXPECTED 0 Ilija Lupulesku 4011 2739 Han Xiao 1819 2419
521 EXPECTED 0 Ilija Lupulesku 4011 2739 Thor J. Truelson 27830 2218
249 EXPECTED 0 Ilija Lupulesku 4011 2739 De C. Tran 44945 2490
127 EXPECTED 3 Ilija Lupulesku 4011 2739 Eric Owens 31196 2612
310 EXPECTED 0 Ilija Lupulesku 4011 2739 Sean Patrick O'Neill 8840 2429
310 EXPECTED 0 Ilija Lupulesku 4011 2739 Sean Patrick O'Neill 8840 2429
628 EXPECTED 0 Ilija Lupulesku 4011 2739 Donald B. Hayes 50664 2111
518 EXPECTED 0 Ilija Lupulesku 4011 2739 Tri H. H. Dinh 49435 2221
393 EXPECTED 0 Ilija Lupulesku 4011 2739 Barry Dattel 5221 2346

Ilija Lupulesku's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating

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 Ilija Lupulesku 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 Ilija Lupulesku:

Initial Rating Gains/Losses Pass 1 Rating
2739 + 8 + 0 + 0 + 0 + 3 + 0 + 0 + 0 + 0 + 0 =2750

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[1,677] the index of the player under consideration. i can be as small as 1 or as large as 677 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[1,677] the index of the player under consideration. i can be as small as 1 or as large as 677 for this tournament and the i-th player must be a rated player.
        q q[1,3657] the index of the match result under consideration. q can be as small as 1 or as large as 3657 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 Ilija Lupulesku is calculated as follows:
        • Given the initial rating of 2739,
        • and the Pass 1 rating of 2750,
        • the Pass 1 gain is 2750 - 2739 = 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 Ilija Lupulesku is 2739.

        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 Ilija Lupulesku'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 Ilija Lupulesku is a rated player, his Pass 2 Adjustment of 2739 will be ignored, along with him Pass 1 Rating of 2750 and his Pass 2 Rating will be set to his initial rating of 2739 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 Ilija Lupulesku has an initial rating of 2739, 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 Ilija Lupulesku's wins and losses and applying the point exchange table, gives us the following result:
    Ilija Lupulesku's Wins
    Winner Loser
    Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
    2 EXPECTED 8 Ilija Lupulesku 4011 2739 David Yong-Xiang Zhuang 58322 2737
    320 EXPECTED 0 Ilija Lupulesku 4011 2739 Han Xiao 1819 2419
    521 EXPECTED 0 Ilija Lupulesku 4011 2739 Thor J. Truelson 27830 2218
    249 EXPECTED 0 Ilija Lupulesku 4011 2739 De C. Tran 44945 2490
    127 EXPECTED 3 Ilija Lupulesku 4011 2739 Eric Owens 31196 2612
    310 EXPECTED 0 Ilija Lupulesku 4011 2739 Sean Patrick O'Neill 8840 2429
    310 EXPECTED 0 Ilija Lupulesku 4011 2739 Sean Patrick O'Neill 8840 2429
    628 EXPECTED 0 Ilija Lupulesku 4011 2739 Donald B. Hayes 50664 2111
    518 EXPECTED 0 Ilija Lupulesku 4011 2739 Tri H. H. Dinh 49435 2221
    393 EXPECTED 0 Ilija Lupulesku 4011 2739 Barry Dattel 5221 2346

    Ilija Lupulesku's Losses
    Winner Loser
    Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating