 for  Estee Ackerman

USATT#: 81538

Introduction
This page explains how Estee Ackerman (USATT# 81538)'s rating went from 2035 to 2063 at the US Nationals held on 14 Dec 2015 - 18 Dec 2015. 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 Estee Ackerman for this tournament.

Initial Rating Pass 1 Pass 2 Pass 3 Final Rating (Pass 4)
2035 2011 2035 2035 2063

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 732 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 ${X}_{i}^{3}$, 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 US Nationals held on 14 Dec 2015 - 18 Dec 2015 for Estee Ackerman, and its source tournament are as follows:
Initial Rating From Tournament Start Day End Day
2035 2015 Butterfly Thanksgiving Teams 27 Nov 2015 29 Nov 2015

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

Estee Ackerman's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
190 EXPECTED 1 Estee Ackerman 81538 2035 Jessica Lin 213772 1845
165 EXPECTED 2 Estee Ackerman 81538 2035 Emilie S. Yin 90344 1870
243 EXPECTED 0 Estee Ackerman 81538 2035 Stephanie Chen 88393 1792
165 EXPECTED 2 Estee Ackerman 81538 2035 Emilie S. Yin 90344 1870
243 EXPECTED 0 Estee Ackerman 81538 2035 Stephanie Chen 88393 1792
106 UPSET 20 Estee Ackerman 81538 2035 Emilie Lin 84928 2141
138 EXPECTED 2 Estee Ackerman 81538 2035 Reid Greenspan 18298 1897
33 EXPECTED 7 Estee Ackerman 81538 2035 Pranav Tantravahi 85466 2002
145 EXPECTED 2 Estee Ackerman 81538 2035 Karthik Talluri 89187 1890
47 EXPECTED 6 Estee Ackerman 81538 2035 King Trinh 92546 1988
37 EXPECTED 7 Estee Ackerman 81538 2035 Nathan Lee 92628 1998
352 EXPECTED 0 Estee Ackerman 81538 2035 Ada Zhong 93727 1683
500 EXPECTED 0 Estee Ackerman 81538 2035 Thomas Ha 82297 1535
618 EXPECTED 0 Estee Ackerman 81538 2035 Bernard E. Savitz 49513 1417
375 EXPECTED 0 Estee Ackerman 81538 2035 Hsueh-yen Lin 78058 1660
623 EXPECTED 0 Estee Ackerman 81538 2035 Jamo Parrish 75310 1412
300 EXPECTED 0 Estee Ackerman 81538 2035 Tina Chen 88191 1735
352 EXPECTED 0 Estee Ackerman 81538 2035 Ada Zhong 93727 1683
143 EXPECTED 2 Estee Ackerman 81538 2035 Scott Fong 82954 1892
74 EXPECTED 5 Estee Ackerman 81538 2035 Swathi Giri 89190 1961
182 EXPECTED 2 Estee Ackerman 81538 2035 Miranda Huang 90468 1853
346 EXPECTED 0 Estee Ackerman 81538 2035 Eric W Zheng 96765 1689
190 EXPECTED 1 Estee Ackerman 81538 2035 Jessica Lin 213772 1845
26 UPSET 10 Estee Ackerman 81538 2035 Nelson Yu 65178 2061
213 EXPECTED 1 Estee Ackerman 81538 2035 Jimmy Gao 84654 1822

Estee Ackerman's Losses
Winner Loser
Point Spread Outcome Loss Player USATT # Rating Player USATT # Rating
143 EXPECTED -2 Rachel Jiayu Sung 82232 2178 Estee Ackerman 81538 2035
250 EXPECTED -0 Laura Huang 77689 2285 Estee Ackerman 81538 2035
31 UPSET -10 Ayane Saito 87024 2004 Estee Ackerman 81538 2035
126 UPSET -25 Lavanya Maruthapandian 83894 1909 Estee Ackerman 81538 2035
395 EXPECTED -0 Crystal Wang 77897 2430 Estee Ackerman 81538 2035
61 UPSET -13 Ava Fu 89196 1974 Estee Ackerman 81538 2035
224 EXPECTED -1 Diane Jiang 74742 2259 Estee Ackerman 81538 2035
38 UPSET -13 Adrian Fu 91152 1997 Estee Ackerman 81538 2035
126 UPSET -25 Lavanya Maruthapandian 83894 1909 Estee Ackerman 81538 2035
69 EXPECTED -5 Rishi Balakrishnan 85808 2104 Estee Ackerman 81538 2035

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 Estee Ackerman 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 Estee Ackerman:

Initial Rating Gains/Losses Pass 1 Rating
2035 + 1 + 2 - 2 + 0 + 0 - 10 - 25 + 0 + 2 + 0 + 20 - 13 - 1 + 2 + 7 + 2 + 6 + 7 + 0 + 0 - 13 + 0 + 0 + 0 + 0 + 0 + 2 - 25 + 5 + 2 + 0 + 1 - 5 + 10 + 1 $=\mathrm{2011}$

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:

${\rho }_{i}^{2}={P}_{i}^{1}-{P}_{i}^{0}$
where,

 Symbol Universe Description ${P}_{i}^{0}$ ${P}_{i}^{0}\in \mathrm{{ℤ}^{+}}$ 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. ${P}_{i}^{1}$ ${P}_{i}^{1}\in \mathrm{{ℤ}^{+}}$ the Pass 1 rating for the $i$-th player. ${\rho }_{i}^{2}$ ${\rho }_{i}^{2}\in ℤ$ 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, ${\rho }_{i}^{2}$ 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 ${\rho }_{i}^{2}$. $i$ $i\in \left[1,\mathrm{732}\right]\cap ℤ$ the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{732}$ for this tournament and the i-th player must be a rated player.

2. For rated players, Pass 1 points gained, ${\rho }_{i}^{2}$, 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:

$\mathrm{{\alpha }_{i}^{2}}=⌊\mathrm{\frac{\mathrm{{P}_{i}^{1}}+\mathrm{\frac{\mathrm{{B}_{i}}+\mathrm{{W}_{i}}}{2}}}{2}}⌋$

where ${\alpha }_{i}^{2}$ is the Pass 2 Adjustment for the current player, ${P}_{i}^{1}$ is the Pass 1 Rating, ${B}_{i}$ is the rating of the highest rated opponent against which the current player won a match, and ${W}_{i}$ 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:

$\mathrm{{\alpha }_{i}^{2}}=\mathrm{⌊\stackrel{\sim }{\mathrm{\left\{\mathrm{{P}_{k}^{0}}\right\}}}⌋}$

where ${P}_{k}^{0}$ is the initial rating of the player who was the i-th player's opponent from the k-th match.
Symbol Universe Description
$i$ $i\in \left[1,\mathrm{732}\right]\cap ℤ$ the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{732}$ for this tournament and the i-th player must be a rated player.
$q$ $q\in \left[1,\mathrm{5029}\right]\cap ℤ$ the index of the match result under consideration. $q$ can be as small as $1$ or as large as $\mathrm{5029}$ for this tournament and the q-th match must be have both rated players as opponents.
$g$ $g\in \left[1,5\right]\cap ℤ$ 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.
${P}_{k}^{0}$ ${P}_{k}^{0}\in \mathrm{{ℤ}^{+}}$ initial rating of the i-th player's opponent from the k-th match.

• Therefore, the Pass 2 Adjustment for Estee Ackerman is calculated as follows:
• Given the initial rating of 2035,
• and the Pass 1 rating of 2011,
• the Pass 1 gain is 2011 - 2035 = -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 Estee Ackerman is 2035.

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 Estee Ackerman'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:

$\mathrm{{P}_{i}^{2}}=⌊\mathrm{\frac{\mathrm{{B}_{i}^{2}}+\mathrm{{W}_{i}^{2}}}{2}}⌋$

where ${P}_{i}^{2}$ is the Pass 2 Rating for the i-th player, ${B}_{i}^{2}$ is the largest Pass 2 Adjustment (best win) of the opponenet against whom the i-th player won a match, and ${W}_{i}^{2}$ 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 $I\left(x\right)$ 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
${P}_{i}^{2}$ ${P}_{i}^{2}\in \mathrm{{ℤ}^{+}}$ the pass 2 rating, of the i-th player in this tournament only applicable to unrated players, where ${P}_{i}^{0}$ is not defined
${B}_{i}^{2}$ ${B}_{i}^{2}\in \mathrm{{ℤ}^{+}}$ the largest of the Pass 2 Adjustments of opponents of the i-th player against whom he/she won a match.
${\alpha }_{k}^{2}$ ${\alpha }_{k}^{2}\in \mathrm{{ℤ}^{+}}$ the Pass 2 Adjustment of the player who was the opponent of the i-th player in the k-th match
$I\left(x\right)$ $I:ℤ↦\mathrm{{ℤ}^{+}}$ a function that maps all integers to one of the values from -- 0, 1, 5, 10.
${M}_{i}$ ${M}_{i}\in \mathrm{{ℤ}^{+}}$ total number of matches played by the i-th player in this tournament
k $k\in \mathrm{\left[0,\mathrm{{M}_{i}}-1\right]\cap {ℤ}^{+}}$ The index of the match of the i-th player ranging from 0 to ${M}_{i}-1$
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 $I\left(x\right)$ is defined above and,

Symbol Universe Description
${P}_{i}^{2}$ ${P}_{i}^{2}\in \mathrm{{ℤ}^{+}}$ the pass 2 rating, of the i-th player in this tournament only applicable to unrated players, where ${P}_{i}^{0}$ is not defined
${W}_{i}^{2}$ ${W}_{i}^{2}\in \mathrm{{ℤ}^{+}}$ the smallest of the Pass 2 Adjustments of opponents of the i-th player against whom he/she lost a match.
${\alpha }_{k}^{2}$ ${\alpha }_{k}^{2}\in \mathrm{{ℤ}^{+}}$ the Pass 2 Adjustment of the player who was the opponent of the i-th player in the k-th match
$I\left(x\right)$ $I:ℤ↦\mathrm{{ℤ}^{+}}$ a function that maps all integers to one of the values from -- 0, 1, 5, 10.
${M}_{i}$ ${M}_{i}\in \mathrm{{ℤ}^{+}}$ total number of matches played by the i-th player in this tournament
k $k\in \mathrm{\left[0,\mathrm{{M}_{i}}-1\right]\cap {ℤ}^{+}}$ The index of the match of the i-th player ranging from 0 to ${M}_{i}-1$
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 Estee Ackerman is a rated player, her Pass 2 Adjustment of 2035 will be ignored, along with her Pass 1 Rating of 2011 and her Pass 2 Rating will be set to her initial rating of 2035 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 Estee Ackerman has an initial rating of 2035, 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 Estee Ackerman's wins and losses and applying the point exchange table, gives us the following result:
Estee Ackerman's Wins
Winner Loser
Point Spread Outcome Gain Player USATT # Rating Player USATT # Rating
190 EXPECTED 1 Estee Ackerman 81538 2035 Jessica Lin 213772 1845
165 EXPECTED 2 Estee Ackerman 81538 2035 Emilie S. Yin 90344 1870
243 EXPECTED 0 Estee Ackerman 81538 2035 Stephanie Chen 88393 1792
165 EXPECTED 2 Estee Ackerman 81538 2035 Emilie S. Yin 90344 1870
243 EXPECTED 0 Estee Ackerman 81538 2035 Stephanie Chen 88393 1792
106 UPSET 20 Estee Ackerman 81538 2035 Emilie Lin 84928 2141
138 EXPECTED 2 Estee Ackerman 81538 2035 Reid Greenspan 18298 1897
33 EXPECTED 7 Estee Ackerman 81538 2035 Pranav Tantravahi 85466 2002
145 EXPECTED 2 Estee Ackerman 81538 2035 Karthik Talluri 89187 1890
47 EXPECTED 6 Estee Ackerman 81538 2035 King Trinh 92546 1988
37 EXPECTED 7 Estee Ackerman 81538 2035 Nathan Lee 92628 1998
352 EXPECTED 0 Estee Ackerman 81538 2035 Ada Zhong 93727 1683
500 EXPECTED 0 Estee Ackerman 81538 2035 Thomas Ha 82297 1535
618 EXPECTED 0 Estee Ackerman 81538 2035 Bernard E. Savitz 49513 1417
375 EXPECTED 0 Estee Ackerman 81538 2035 Hsueh-yen Lin 78058 1660
623 EXPECTED 0 Estee Ackerman 81538 2035 Jamo Parrish 75310 1412