If we imagine ourselves in the scene in which the witness speaks with a firm and confident voice saying "that is the man I saw", the most probable thing is that it convinces us because she is very sure of herself, the witness does not doubt it for a moment, she/he is stating it.
The word <u>averred</u> can be replaced by <u>stated</u> since they have the same meaning. Other synonims can be claim, declare or affirm.
