Some more clarification:

backoff.init is applied on an network error. If connection was active, but connection gets lost or some other protocol/network error occurs, beats will disconnect and use backoff.init. After backoff.init, beats try to reconnect. If the reconnect fails, the backoff is increased exponentially up to backoff.max. After successful reconnect, the backoff timer is reset. On next network error, backoff will start with again with backoff.init.

A (initial) connection error is just one potential error among others.

@urso I'm trying to get all these details into the paragraph without making it too long. Does this work?

The number of seconds to wait before trying to reconnect to Elasticsearch after
a network error. After waiting `backoff.init` seconds, {beatname_uc} tries to
reconnect. If the attempt fails, the backoff timer is increased exponentially up
to `backoff.max`. After a successful connection, the backoff timer is reset. The
default is 1s.

I've left the following sentence out because it restates the previous sentence: "On next network error, backoff will start with again with backoff.init."

@dedemorton SGTM