Puzzle ZBIL

During the recent BrainBashers Football Competition, 5 teams were competing.

Each team played each other just once, with 2 points for a win, 1 point for a draw, and 0 points for a loss.

However, the rain damaged the final scoresheet, and this is all that could be read of the final points after all of the matches:
Rugby       6
Grimsby     5
Hereford    4
Lichfield   2
Reading    {?}

Can you work out how many points Reading ended the season with?

workings hint answer print

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