How can I create a recursive query over a column that has gaps?

Question

I've adapted the recursive query from here in order to calculate ELO ratings (like in chess) from a list of game outcomes on-the-fly.

Given a table of games like:

id | home_player | away_player | home_score | away_score |
|--|-------------|-------------|------------|------------|
1  | 1           | 2           | 21         | 18         |
2  | 2           | 3           | 14         | 21         |
3  | 1           | 3           | 12         | 21         |
5  | 3           | 2           | 21         | 8          |

I want to construct a table of ELO ratings for each player after each game has been played, like this:

| current_game_number | player_id | previous_elo | new_elo |
|---------------------|-----------|--------------|---------|
| 0                   | 1         | 1000         | 1000    |
| 0                   | 2         | 1000         | 1000    |
| 0                   | 3         | 1000         | 1000    |
| 1                   | 3         | 1000         | 1000    |
| 1                   | 2         | 1000         | 984     |
| 1                   | 1         | 1000         | 1016    |
| 2                   | 1         | 1016         | 1016    |
| 2                   | 2         | 984          | 969     |
| 2                   | 3         | 1000         | 1015    |
| 3                   | 3         | 1015         | 1031    |
| 3                   | 2         | 969          | 969     |
| 3                   | 1         | 1016         | 1000    |

I can get most of the way there with this recursive query:

WITH RECURSIVE p(current_game_number) AS (
  SELECT
    0               AS id,
    id as player_id,
    1000.0 :: FLOAT AS previous_elo,
    1000.0 :: FLOAT AS new_elo
  FROM players
  UNION ALL
  (
    WITH previous_elos AS (
        SELECT *
        FROM p
    )
    SELECT
      games.id,
      player_id,
      previous_elos.new_elo AS previous_elo,
      round(CASE WHEN player_id NOT IN (home_player, away_player)
        THEN previous_elos.new_elo
            WHEN player_id = home_player
              THEN previous_elos.new_elo + 32.0 * ((CASE WHEN home_score > away_score THEN 1 ELSE 0 END) - (r1 / (r1 + r2)))
            ELSE previous_elos.new_elo + 32.0 * ((CASE WHEN away_score > home_score THEN 1 ELSE 0 END) - (r2 / (r1 + r2))) END)
    FROM games
      JOIN previous_elos
        ON current_game_number = games.id - 1
      JOIN LATERAL (
           SELECT
             pow(10.0, (SELECT new_elo
                        FROM previous_elos
                        WHERE current_game_number = games.id - 1 AND player_id = home_player) / 400.0) AS r1,
             pow(10.0, (SELECT new_elo
                        FROM previous_elos
                        WHERE current_game_number = games.id - 1 AND player_id = away_player) / 400.0) AS r2
           ) r
        ON TRUE
  )
) SELECT * FROM p;

However, If there is a gap in the game ID sequence, as in the example table above, the query stops at the gap and doesn't continue to calculate ELOs. I would like to support gaps so that games can be deleted and concurrent inserts are supported.

I'm lost as to how to extend the query to "skip gaps" in the id sequence. My hunch is it would require changing the recursive join to skip the gaps:

FROM games
  JOIN previous_elos
    ON current_game_number = games.id - 1

Does anyone have a suggestion to fix this? Any help is very appreciated!

Please see this SQLFiddle which is populated with the schema and sample data.

Answer 1

To avoid gaps use additional CTE:

WITH re_enumerated_games AS 
( SELECT ROW_NUMBER() OVER (ORDER BY id) id,
         id real_game_id,
         home_player,
         away_player,
         home_score,
         away_score 
   FROM games ),