noun syntax

Using expressions (nouns) in which verbs and adjectives are nounified
Represents "S + V" or "S + be verb + adjective".
Translate nouns as verbs.
Translate nouns that can be verbs back into verbs.

his(S) love(V) of Ichiro(O).
his love for Ichiro.
Change to He love Ichiro.

The fact of his success in Japan.
Change the noun success to the verb succeed.
Since there is only his (possessive) when thinking about who succeeded, change his to he (nominative).
He succeeds in Japan.
(Reason: Japanese is a verb-centered language (action-centered). English is a noun-centered language.)
Yuki was surprised at Darvish's sudden arrival.
Darvish's sudden arrival.
→Darvish(S) arrived(O) suddenly(M).

Application

education(V) by coach(S) of player(O).
Replace education with the verb educate.
From the by, we infer that the coach is the actor.
(Similar to how by expresses the actor in the passive voice)
You can see that it is a noun construction with children as the object.
Educating coaches to players.