ELO Formula in SQL Query - tsql

Question

This isn't my original query, it's one posted by a gentleman at http://elliot.land/. This is the script for the ELO Rating system. Problem with me is, I've tried and tried, but I don't know how to convert this POSTGRESQL (RECURSIVE) to TSQL (CTE). Anyone can help me with the conversion?
This is the data:
CREATE TABLE plays (
game_number INT NOT NULL, -- must be consecutive and start at 1!
p1name VARCHAR(255) NOT NULL, -- first player
p1score FLOAT NOT NULL, -- 0 or 1
p2name VARCHAR(255) NOT NULL, -- second player
p2score FLOAT NOT NULL -- 0 or 1
);
INSERT INTO plays VALUES
(1, 'Elliot', 0, 'Brendan', 1),
(2, 'Bob', 1, 'Brendan', 0),
(3, 'Bob', 1, 'Elliot', 0),
(4, 'Jane', 1, 'Bob', 0),
(5, 'Bob', 0, 'Brendan', 1),
(6, 'Jane', 1, 'Elliot', 0);
Here is the Formula where I need help with the conversion:
WITH RECURSIVE p(current_game_number) AS (
WITH players AS (
SELECT DISTINCT p1name AS player_name
FROM plays
UNION
SELECT DISTINCT p2name
FROM plays
)
SELECT
0 AS game_number,
player_name,
1000.0 :: FLOAT AS previous_elo,
1000.0 :: FLOAT AS new_elo
FROM players
UNION ALL
(
WITH previous_elos AS (
SELECT *
FROM p
)
SELECT
plays.game_number,
player_name,
previous_elos.new_elo AS previous_elo,
round(CASE WHEN player_name NOT IN (p1name, p2name)
THEN previous_elos.new_elo
WHEN player_name = p1name
THEN previous_elos.new_elo + 32.0 * (p1score - (r1 / (r1 + r2)))
ELSE previous_elos.new_elo + 32.0 * (p2score - (r2 / (r1 + r2))) END)
FROM plays
JOIN previous_elos
ON current_game_number = plays.game_number - 1
JOIN LATERAL (
SELECT
pow(10.0, (SELECT new_elo
FROM previous_elos
WHERE current_game_number = plays.game_number - 1 AND player_name = p1name) / 400.0) AS r1,
pow(10.0, (SELECT new_elo
FROM previous_elos
WHERE current_game_number = plays.game_number - 1 AND player_name = p2name) / 400.0) AS r2
) r
ON TRUE
)
)
SELECT
player_name,
(
SELECT new_elo
FROM p
WHERE t.player_name = p.player_name
ORDER BY current_game_number DESC
LIMIT 1
) AS elo,
count(CASE WHEN previous_elo < new_elo
THEN 1
ELSE NULL END) AS wins,
count(CASE WHEN previous_elo > new_elo
THEN 1
ELSE NULL END) AS losses
FROM
(
SELECT *
FROM p
WHERE previous_elo <> new_elo
ORDER BY current_game_number, player_name
) t
GROUP BY player_name
ORDER BY elo DESC;