USATT#: 1819
 Coach Level: National
Initial Rating  Pass 1  Pass 2  Pass 3  Final Rating (Pass 4) 

2497  2487  2497  2497  2513 
Initial Rating  From Tournament  Start Day  End Day 

2497  PCTTC Open  n/a  16 Nov 2003 
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 
216  EXPECTED  1  Han Xiao  1819  2497  Eyal Adini  27633  2281 
299  EXPECTED  0  Han Xiao  1819  2497  Steve M. Berger  42840  2198 
155  EXPECTED  2  Han Xiao  1819  2497  Barry Dattel  5221  2342 
266  EXPECTED  0  Han Xiao  1819  2497  H. Richard Hicks  6642  2231 
395  EXPECTED  0  Han Xiao  1819  2497  Anthony Wai Hung Kwong  12257  2102 
406  EXPECTED  0  Han Xiao  1819  2497  David Liu  22988  2091 
95  EXPECTED  4  Han Xiao  1819  2497  Hui Yuan Liu  2369  2402 
327  EXPECTED  0  Han Xiao  1819  2497  Henry Mccoullum  8191  2170 
22  EXPECTED  7  Han Xiao  1819  2497  Jiachen David Wang  999  2475 
171  UPSET  35  Han Xiao  1819  2497  Barney J. Reed  44775  2668 
76  UPSET  16  Han Xiao  1819  2497  Atanda Musa  13648  2573 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
255  UPSET  50  Courtney Roberts  56320  2242  Han Xiao  1819  2497 
128  EXPECTED  3  Faazil Kassam  14212  2625  Han Xiao  1819  2497 
57  EXPECTED  6  Yuxiang Li  21400  2554  Han Xiao  1819  2497 
56  UPSET  13  Renata Peluchova  22035  2441  Han Xiao  1819  2497 
221  EXPECTED  1  Pradeeban PeterPaul  2023  2718  Han Xiao  1819  2497 
229  EXPECTED  1  David YongXiang Zhuang  58322  2726  Han Xiao  1819  2497 
217  EXPECTED  1  Lin Zhigang  779  2714  Han Xiao  1819  2497 
Initial Rating  Gains/Losses  Pass 1 Rating 

2497 

$=\mathrm{2487}$ 
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 ${\rho}_{\mathrm{i}}^{2}$. 
$i$  $i\in [1,\mathrm{772}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{772}$ for this tournament and the ith player must be a rated player. 
Symbol  Universe  Description 

$i$  $i\in [1,\mathrm{772}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{772}$ for this tournament and the ith player must be a rated player. 
$q$  $q\in [1,\mathrm{6866}]\cap \mathbb{Z}$  the index of the match result under consideration. $q$ can be as small as $1$ or as large as $\mathrm{6866}$ 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 