How-to implement an entity with an unknown maximum number of attributes?
You could do this. It would allow good performance for normal duration games, while allowing you to also store long running games.

CREATE TABLE InningRuns (
    GameId INT NOT NULL REFERENCES [...],
    Team CHAR(4) NOT NULL, --'Home','Away'
    Inning1 TINYINT, --Seeing how more than 255 runs are not really possible in an inning
    Inning2 TINYINT,
    [...],
    Inning9 TINYINT,
    ExtraInnings XML | TINYINT[] | VARBINARY | ETC., --Use to hold any runs in extra innings.
    PRIMARY KEY (GameId, Team)
)


You could further normalize and have a row for each unique combination of game, team, &amp; inning. This would allow you as many innings as the InningId datatype would allow.

CREATE TABLE InningRuns (
    InningRunId INT IDENTITY PRIMARY KEY,
    GameId INT NOT NULL REFERENCES [...],
    Team CHAR(4) NOT NULL, --'Home','Away'
    InningId TINYINT, --Seeing how more than 255 innings might be excessive
    Runs TINYINT,
    UNIQUE (GameId, Team, InningId)
)


Edit: I know PostgreSQL uses Sequences instead of IDENTITY, I don't recall the correct syntax off hand, so translate accordingly.