USATT#: 212153
Initial Rating  Pass 1  Pass 2  Pass 3  Final Rating (Pass 4) 

2217  2232  2217  2217  2234 
Initial Rating  From Tournament  Start Day  End Day 

2217  Westchester 2021 June Open  26 Jun 2021  27 Jun 2021 
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 
Winner  Loser  

Point Spread  Outcome  Gain  Player  USATT #  Rating  Player  USATT #  Rating 
416  EXPECTED  0  Lucy Chen  212153  2217  Ronald Meeks  82089  1801 
165  EXPECTED  2  Lucy Chen  212153  2217  Kayla Goodwin  92550  2052 
222  EXPECTED  1  Lucy Chen  212153  2217  Jacob Lee  215212  1995 
73  UPSET  16  Lucy Chen  212153  2217  Jeff Ruiz  93102  2290 
201  EXPECTED  1  Lucy Chen  212153  2217  John P. P. Ochsner  5004  2016 
283  EXPECTED  0  Lucy Chen  212153  2217  Alex Luo  202029  1934 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
94  EXPECTED  4  Stanley Hsu  97890  2311  Lucy Chen  212153  2217 
188  EXPECTED  1  Alex Averin  81774  2405  Lucy Chen  212153  2217 
Initial Rating  Gains/Losses  Pass 1 Rating 

2217 

$=\mathrm{2232}$ 
Symbol  Universe  Description 
${P}_{\mathrm{i}}^{0}$  ${P}_{\mathrm{i}}^{0}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  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. 
${P}_{\mathrm{i}}^{1}$  ${P}_{\mathrm{i}}^{1}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  the Pass 1 rating for the $i$th player. 
${\rho}_{\mathrm{i}}^{2}$  ${\rho}_{\mathrm{i}}^{2}\in \mathbb{Z}$  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, ${\rho}_{\mathrm{i}}^{2}$ 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 ${\rho}_{\mathrm{i}}^{2}$. 
$i$  $i\in [1,\mathrm{486}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{486}$ for this tournament and the ith player must be a rated player. 
Symbol  Universe  Description 

$i$  $i\in [1,\mathrm{486}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{486}$ for this tournament and the ith player must be a rated player. 
$q$  $q\in [1,\mathrm{3230}]\cap \mathbb{Z}$  the index of the match result under consideration. $q$ can be as small as $1$ or as large as $\mathrm{3230}$ for this tournament and the qth match must be have both rated players as opponents. 
$g$  $g\in [1,5]\cap \mathbb{Z}$  the gth 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. 
${P}_{\mathrm{k}}^{0}$  ${P}_{\mathrm{k}}^{0}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  initial rating of the ith player's opponent from the kth match. 
Symbol  Universe  Description 

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

${P}_{\mathrm{i}}^{2}$  ${P}_{\mathrm{i}}^{2}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  the pass 2 rating, of the ith player in this tournament only applicable to unrated players, where ${P}_{\mathrm{i}}^{0}$ is not defined 
${W}_{\mathrm{i}}^{2}$  ${W}_{\mathrm{i}}^{2}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  the smallest of the Pass 2 Adjustments of opponents of the ith player against whom he/she lost a match. 
${\alpha}_{\mathrm{k}}^{2}$  ${\alpha}_{\mathrm{k}}^{2}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  the Pass 2 Adjustment of the player who was the opponent of the ith player in the kth match 
$I\left(x\right)$  $I:\mathbb{Z}\mapsto \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  a function that maps all integers to one of the values from  0, 1, 5, 10. 
${M}_{\mathrm{i}}$  ${M}_{\mathrm{i}}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  total number of matches played by the ith player in this tournament 
k  $k\in \mathrm{[0,\mathrm{{M}_{\mathrm{i}}}1]\cap {\mathbb{Z}}^{\mathrm{+}}}$  The index of the match of the ith player ranging from 0 to ${M}_{\mathrm{i}}1$ 
Winner  Loser  

Point Spread  Outcome  Gain  Player  USATT #  Rating  Player  USATT #  Rating 
416  EXPECTED  0  Lucy Chen  212153  2217  Ronald Meeks  82089  1801 
165  EXPECTED  2  Lucy Chen  212153  2217  Kayla Goodwin  92550  2052 
222  EXPECTED  1  Lucy Chen  212153  2217  Jacob Lee  215212  1995 
73  UPSET  16  Lucy Chen  212153  2217  Jeff Ruiz  93102  2290 
201  EXPECTED  1  Lucy Chen  212153  2217  John P. P. Ochsner  5004  2016 
283  EXPECTED  0  Lucy Chen  212153  2217  Alex Luo  202029  1934 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
94  EXPECTED  4  Stanley Hsu  97890  2311  Lucy Chen  212153  2217 
188  EXPECTED  1  Alex Averin  81774  2405  Lucy Chen  212153  2217 
Pass 2 Rating  Gains/Losses  Pass 3 Part 1 Rating 

2217 

$=\mathrm{2232}$ 
Symbol  Universe  Description 
${P}_{\mathrm{i}}^{2}$  ${P}_{\mathrm{i}}^{2}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  the Pass 2 Rating for the $i$th player. 
${p}_{\mathrm{i}}^{3}$  ${p}_{\mathrm{i}}^{3}\in \mathrm{{\mathbb{Z}}^{\mathrm{+}}}$  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. 
${\rho}_{\mathrm{i}}^{3}$  ${\rho}_{\mathrm{i}}^{3}\in \mathbb{Z}$  the points gained by the $i$th player in this tournament in Pass 3. 
$i$  $i\in [1,\mathrm{486}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{486}$ for this tournament. 
Winner  Loser  

Point Spread  Outcome  Gain  Player  USATT #  Rating  Player  USATT #  Rating 
416  EXPECTED  0  Lucy Chen  212153  2217  Ronald Meeks  82089  1801 
165  EXPECTED  2  Lucy Chen  212153  2217  Kayla Goodwin  92550  2052 
222  EXPECTED  1  Lucy Chen  212153  2217  Jacob Lee  215212  1995 