Meaning of, "Baseball is the only field of endeavor where a man can succeed three times out of ten and be considered a good performer," Ted...

What Ted Williams is talking about here is a baseball
statistic called batting average.  For a long time, batting average was seen as the best
way to decide if someone was a good hitter.

A player's
batting average is determined by taking the number of hits they get (in a season or a
career) and dividing it by the number of at bats they get.  If a person gets 3 hits in
10 at bats, their batting average is .300.  This is considered to be a very good
average.  Ted Williams was the last player to hit better than .400 for a whole season
and that was in 1941.

What Williams was saying in this
quote is that baseball is an inherently difficult or even frustrating sport.  A batter
who fails 7 times out of 10 is a good batter.  Imagine if you failed 7 of 10 classes in
school.  Or imagine if a doctor failed to cure 7 of 10 patients who came to
them.

So this is a statement about how difficult and
frustrating baseball is, at least from the perspective of a
hitter.