USATT#: 222229
Initial Rating  Pass 1  Pass 2  Pass 3  Final Rating (Pass 4) 

1640  1646  1640  1640  1646 
Initial Rating  From League  Event Date 

1640  AZ PTTC Monday  19 Mar 2018 
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 
29  EXPECTED  7  Andrew Ramirez  222229  1640  Kraig Murray  221332  1611 
388  EXPECTED  0  Andrew Ramirez  222229  1640  Saul Mendoza  220196  1252 
46  EXPECTED  6  Andrew Ramirez  222229  1640  Roberto R. Saria  62622  1594 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
19  EXPECTED  7  Nathan A Crabtree  95450  1659  Andrew Ramirez  222229  1640 
Initial Rating  Gains/Losses  Pass 1 Rating 

1640 

$=\mathrm{1646}$ 
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 league event. 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 ${\rho}_{\mathrm{i}}^{2}$. 
$i$  $i\in [1,\mathrm{21}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{21}$ for this league event and the ith player must be a rated player. 
Symbol  Universe  Description 

$i$  $i\in [1,\mathrm{21}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{21}$ for this league event and the ith player must be a rated player. 
$q$  $q\in [1,\mathrm{43}]\cap \mathbb{Z}$  the index of the match result under consideration. $q$ can be as small as $1$ or as large as $\mathrm{43}$ for this league event 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 league event 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 league event 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 league event 
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 league event 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 league event 
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 
29  EXPECTED  7  Andrew Ramirez  222229  1640  Kraig Murray  221332  1611 
388  EXPECTED  0  Andrew Ramirez  222229  1640  Saul Mendoza  220196  1252 
46  EXPECTED  6  Andrew Ramirez  222229  1640  Roberto R. Saria  62622  1594 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
19  EXPECTED  7  Nathan A Crabtree  95450  1659  Andrew Ramirez  222229  1640 
Pass 2 Rating  Gains/Losses  Pass 3 Part 1 Rating 

1640 

$=\mathrm{1646}$ 
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 league event in Pass 3. 
$i$  $i\in [1,\mathrm{21}]\cap \mathbb{Z}$  the index of the player under consideration. $i$ can be as small as $1$ or as large as $\mathrm{21}$ for this league event. 
Winner  Loser  

Point Spread  Outcome  Gain  Player  USATT #  Rating  Player  USATT #  Rating 
29  EXPECTED  7  Andrew Ramirez  222229  1640  Kraig Murray  221332  1611 
388  EXPECTED  0  Andrew Ramirez  222229  1640  Saul Mendoza  220196  1252 
46  EXPECTED  6  Andrew Ramirez  222229  1640  Roberto R. Saria  62622  1594 
Winner  Loser  

Point Spread  Outcome  Loss  Player  USATT #  Rating  Player  USATT #  Rating 
19  EXPECTED  7  Nathan A Crabtree  95450  1659  Andrew Ramirez  222229  1640 
Pass 3 Rating  Gains/Losses  Pass 4 Rating 

1640 

$=\mathrm{1646}$ 