USATT Ratings Explainer

Rating Explainer Pass 3 Rating

Alexey Andreev

USATT#: 219319

1613 1713

MDTTC June Open
17 Jun 2022 - 18 Jun 2022

Pass 3 Rating

Any of the unrated players who have all wins or all losses are skipped in Pass 3. Since Alexey Andreev has an initial rating of 1613, he is not an unrated player, and therefore this rule does not apply to him. You can view a list of all the players that are skipped in this Pass 3 in a table toward the bottom of this web page.

Pass 3 Rating is calculated using the steps described below:

In the first part of Pass 3, we apply the point exchange table described in Pass 1 except this time by using all the players' Pass 2 Ratings. Looking at Alexey Andreev's wins and losses and applying the point exchange table, gives us the following result:

Alexey Andreev's Wins

			Winner			Loser
Point Spread	Outcome	Gain	Player	USATT #	Rating	Player	USATT #	Rating
273	UPSET	50	Alexey Andreev	219319	1663	George Nie	71290	1936

Alexey Andreev's Losses

			Winner			Loser
Point Spread	Outcome	Loss	Player	USATT #	Rating	Player	USATT #	Rating
443	EXPECTED	-0	Allan Anzagira	218469	2106	Alexey Andreev	219319	1663
539	EXPECTED	-0	Vikash Sahu	28377	2202	Alexey Andreev	219319	1663

You can view a table of outcomes and points gained/lost from all the matches with all the players in this tournament for Pass 3 Part 1 toward the end of his web page.

The "Outcome" column above, shows whether the match had an expected (player with the higher rating wins the match) or an upset (player with the higher rating loses the match) outcome. Based on this outcome, and using both the player's Pass 2 Rating, we apply the point exchange table from above and show the rating points earned and lost by Alexey Andreev in the "Gain" column. Matches are divided up into two tables for wins and losses where points are "Gain"ed for the wins and "loss"ed for losses. Putting all the gains and losses together, we get the following math to calculate the rating for Alexey Andreev in this first part of Pass 3:

Pass 2 Rating	Gains/Losses	Pass 3 Part 1 Rating
1613	+ 0 + 50 + 0	= 1663

You can view a table of these calculations for all the players in this tournament toward the end of this web page.

Given the Pass 3 Part 1 rating calculated above, the second part of Pass 3 looks very similar to the part of Pass 2 that deals with rated players where we calculate their Pass 2 Adjustment.

First, we calculate the points gained in Pass 3 Part 1. Points gained is simply the difference between the Pass 3 Part 1 Rating and the Pass 2 Rating of a player:

ρ_{i}^{3} = p_{i}^{3} - P_{i}^{2}

where,

Symbol	Universe	Description
$P_{i}^{2}$	$P_{i}^{2} \in ℤ^{+}$	the Pass 2 Rating for the $i$ -th player.
$p_{i}^{3}$	$p_{i}^{3} \in ℤ^{+}$	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.
$ρ_{i}^{3}$	$ρ_{i}^{3} \in ℤ$	the points gained by the $i$ -th player in this tournament in Pass 3.
$i$	$i \in [1, 107] \cap ℤ$	the index of the player under consideration. $i$ can be as small as $1$ or as large as $107$ for this tournament.

Pass 3 points gained, ρi3, is then used to calculate the Pass 3 Part 2 Rating in the following way:
1. If a player gained less than 50 points (exclusive) in Pass 3 Part 1, then we set that player's Pass 3 Part 2 Rating to his/her Pass 2 Rating.
2. If a player gained between 50 and 74 (inclusive) points in Pass 3 Part 1, then we set the player's Pass 3 Part 2 Rating to his/her Pass 3 Part 1 Rating.
3. If a player gains 75 or more points (inclusive) in Pass 3 Part 1, then the following formula applies:
  - If the player has won at least one match, and lost at least 1 match in the tournament, then the player's Pass 3 Part 2 Rating is the average of his/her Pass 3 Part 1 Rating and the average of his/her opponents rating from the best win and the worst loss, represented using the formula below:
    
    $α_{i}^{3} = ⌊ \frac{p_{i}^{3}+\frac{B_{i}^{3}+W_{i}^{3}}{2}}{2} ⌋$
    
    where $α_{i}^{3}$ is the Pass 3 Part 2 Rating for the current player, $p_{i}^{3}$ is the Pass 3 Part 1 Rating, $B_{i}^{3}$ is the rating of the highest rated opponent against which the current player won a match, and $W_{i}$ is the rating of the lowest rated opponent against which the current player lost a match.
  - If a player has not lost any of his/her matches in the current tournament, the mathematical median (rounded down to the nearest integer) of all the player's opponents' ratings is used as his/her Pass 3 Part 2 Rating:
    
    $α_{i}^{3} = ⌊\tilde{{p_{k}^{3}}}⌋$
    
    where $p_{k}^{3}$ is the Pass 3 Part 1 Rating of the i-th player's opponent from the k-th match.
  - Therefore, the Pass 3 Part 2 Rating for Alexey Andreev is calculated as follows:
    - Given the Pass 2 Rating of 1613,
    - and the Pass 3 Part 1 rating of 1663,
    - the Pass 3 Part 1 gain is 1663 - 1613 = 50.
    - Since the Pass 3 Gain of 50 is between 50 and 74 (inclusive), the Pass 3 Part 2 Rating is set to be the Pass 3 Part 1 Rating.
    - Therefore the Pass 3 Part 2 Rating for Alexey Andreev is 1663.
  The Pass 3 Part 2 rating ends up becoming the final Pass 3 rating (also referred to as the Pass 3 Adjustment) except as follows:
  - In the cases where the Pass 3 Part 2 rating is less than the players' initial rating $P_{i}^{0}$ , the Pass 3 rating is reset back to that players initial rating. Alexey Andreev's Pass 3 Part 2 Rating came out to 1663. Since this value is greater than or equal to Alexey Andreev's initial rating of 1613, his Pass 3 Adjustment is set to his Pass 3 Part 2 Rating of 1663.