USATT#: 14272
Initial Rating  Pass 1  Pass 2  Pass 3  Final Rating (Pass 4) 

2106  2158  2106  2169  2167 
Initial Rating  From Tournament  Start Day  End Day 

2106  1998 North American Teams Cham  n/a  29 Nov 1998 
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 
110  EXPECTED  4  Marcos Madrid  14272  2106  Pete May  8146  1996 
366  EXPECTED  0  Marcos Madrid  14272  2106  Ross Novak  8591  1740 
370  EXPECTED  0  Marcos Madrid  14272  2106  Wang Lim  58181  1736 
31  EXPECTED  7  Marcos Madrid  14272  2106  Raymond C. Mack  7967  2075 
202  EXPECTED  1  Marcos Madrid  14272  2106  Jeffrey Lau  18582  1904 
0  0  Marcos Madrid  14272  0  Jung Lee  20463  0  
86  EXPECTED  5  Marcos Madrid  14272  2106  John Jarema  6975  2020 
126  EXPECTED  3  Marcos Madrid  14272  2106  Anthony Wai Hung Kwong  12257  1980 
191  EXPECTED  1  Marcos Madrid  14272  2106  Merr W. Trumbore  10675  1915 
119  EXPECTED  3  Marcos Madrid  14272  2106  Wei Zhang  18436  1987 
136  EXPECTED  3  Marcos Madrid  14272  2106  Andre Scott  49583  1970 
0  0  Marcos Madrid  14272  0  Guy Seltensperger  20372  0  
15  EXPECTED  7  Marcos Madrid  14272  2106  Rafael A. Flores  63553  2091 
240  EXPECTED  0  Marcos Madrid  14272  2106  Brian Farkas  11794  1866 
26  UPSET  10  Marcos Madrid  14272  2106  Samson Dubina  9051  2132 
180  EXPECTED  2  Marcos Madrid  14272  2106  Lennox Douglas  3212  1926 
277  EXPECTED  0  Marcos Madrid  14272  2106  Duc Dinh  18425  1829 
90  EXPECTED  4  Marcos Madrid  14272  2106  Wennin Chiu  15820  2016 
96  EXPECTED  4  Marcos Madrid  14272  2106  William Brown  4476  2010 
54  EXPECTED  6  Marcos Madrid  14272  2106  Lee Bahlman  60104  2052 
277  EXPECTED  0  Marcos Madrid  14272  2106  William Horowitz  60907  1829 
622  EXPECTED  0  Marcos Madrid  14272  2106  Herbert Hodges  12872  1484 
78  UPSET  16  Marcos Madrid  14272  2106  Hiroyuki Hikawa  11762  2184 
414  EXPECTED  0  Marcos Madrid  14272  2106  Alex Groyzburg  13007  1692 
355  EXPECTED  0  Marcos Madrid  14272  2106  Vladimir Gorvits  61620  1751 
38  EXPECTED  6  Marcos Madrid  14272  2106  Kavitha Ganapathy  13118  2068 
5  UPSET  8  Marcos Madrid  14272  2106  JoAnnie Gagnon  2500  2111 
14  EXPECTED  7  Marcos Madrid  14272  2106  Samir Gaagoa  10015  2092 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
66  UPSET  16  Wally Green  10195  2040  Marcos Madrid  14272  2106 
83  UPSET  16  Erica Pilon  2587  2023  Marcos Madrid  14272  2106 
46  UPSET  13  Kelvin Siu  10803  2060  Marcos Madrid  14272  2106 
Initial Rating  Gains/Losses  Pass 1 Rating 

2106 

$=\mathrm{2158}$ 
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 ${\rho}_{\mathrm{i}}^{2}$. 
$i$  $i\in [1,\mathrm{721}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{721}$ for this tournament and the ith player must be a rated player. 
Symbol  Universe  Description 

$i$  $i\in [1,\mathrm{721}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{721}$ for this tournament and the ith player must be a rated player. 
$q$  $q\in [1,\mathrm{6396}]\cap \mathbb{Z}$  the index of the match result under consideration. $q$ can be as small as $1$ or as large as $\mathrm{6396}$ 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 