USATT#: 73290
Initial Rating  Pass 1  Pass 2  Pass 3  Final Rating (Pass 4) 

2621  2623  2621  2621  2623 
Initial Rating  From Tournament  Start Day  End Day 

2621  Westchester May 2021 Little Open  29 May 2021  30 May 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 
178  EXPECTED  2  Juan Liu  73290  2621  Jiaqi Lin  230877  2443 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
Initial Rating  Gains/Losses  Pass 1 Rating 

2621 

$=\mathrm{2623}$ 
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 ${\rho}_{\mathrm{i}}^{2}$. 
$i$  $i\in [1,4]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $4$ for this tournament and the ith player must be a rated player. 
Symbol  Universe  Description 

$i$  $i\in [1,4]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $4$ for this tournament and the ith player must be a rated player. 
$q$  $q\in [1,2]\cap \mathbb{Z}$  the index of the match result under consideration. $q$ can be as small as $1$ or as large as $2$ 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 
178  EXPECTED  2  Juan Liu  73290  2621  Jiaqi Lin  230877  2443 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
Pass 2 Rating  Gains/Losses  Pass 3 Part 1 Rating 

2621 

$=\mathrm{2623}$ 
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. 
$i$  $i\in [1,4]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $4$ for this tournament. 
Winner  Loser  

Point Spread  Outcome  Gain  Player  USATT #  Rating  Player  USATT #  Rating 
178  EXPECTED  2  Juan Liu  73290  2621  Jiaqi Lin  230877  2443 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
Pass 3 Rating  Gains/Losses  Pass 4 Rating 

2621 

$=\mathrm{2623}$ 