Conversation so far:
Where did Billy Southworth go to school?
CANNOTANSWER.
When did he start playing?
At the age of 19, he signed a contract with the Portsmouth team in the Ohio State League.
How long did he play for them?
He joined the Cleveland Indians in 1913, but only appeared in one game, entering as a replacement on defense.
Did he play for anyone else?
The elder Southworth returned to the Cleveland Indians in 1915 and appeared in 60 games.
When did he start coaching instead of playing?
Southworth suffered a 1927 rib injury that limited his playing time.
The Cardinals' leadership began to look for a role for Southworth beyond his playing career.
Did he end up playing for any other teams other than the ones mentioned before?
He played for the Birmingham Barons in 1917 and part of 1918.
Did he play with anyone else that was famous?
CANNOTANSWER.
What was his career like, how well did he do as a player?
Southworth played more regularly in 1919, appearing in 121 games and leading the league with 14 triples.
Did he do better in the beginning of his career versus the end?
In 1926, Southworth's offensive production increased and he finished the season with a .320 batting average.

Question: What was his batting average towards the end?
Self-contained rewrite: What was Billy Southworth's batting average towards the end?