Many Tweeters follow the way Twitter has it setup for us to respond to our followers and therefore we do so accordingly, not much thought goes into the way we respond so much so as we would to how we respond.
As you are aware when you tweet something it can go out to the masses, it does not necessarily remain disclosed to those who have chosen to follow you, in fact you may even notice that when receiving a response it may be from someone you have never had the pleasure of tweeting with before. This is due to the non-restrictions an @mention or @reply unknowingly can cause.
Due to the way Twitter has it set-up to make responding to others easier we tend to follow suit and respond after any @mentions or @replys instead of before, this is a convenient form of responding to people directly but it limits your response to be seen by the masses.
Some may ponder as to why they would want their responses seen by the masses on Twitter and that is a legitimate question worth answering. Of course not all of your responses to others need to be seen but in some cases it is worth letting others know about your Twitter conversations simply to show that you are real and that you most certainly interact.
Showing you are real and are an interactive account sounds perhaps like an odd point to prove, however with the many accounts on Twitter that happens to be spammy or not real, you want to show your authentication as often as you can.
Responding to an @mention or @reply before their Twitter names will allow more people to see your tweets, hence your engagement. This then can lead to more responses depending on the type of tweet as well as possibly more followers.
Certainly it is up to you to make your account as appealing as possible and the more you find a niche the better your Twitter experience will be, but if you want others to begin seeing you outside of waiting for a retweet, than adding responses prior to the twitter names will help you do just that.
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