18 mph avg is fantastic.
I have started biking 8 months my self after about 8 years of not being in the saddle and I can manage 17 - 18mph avg on my Cannondale CAAD8 and 14 - 15mph on my Cannondale BadBoy 26''. I put it down to my big muscular leg from playing front row in Rugby.
I have no help really but what help me was to spin my legs faster in a lower gear "Higher Cadence" I tend to aim for 80 - 90 rpm. I was finding it hard even with my massive leg that if I used High Gearing "50 - 60 rpm" my legs would start to get painfully and would take forever for them to recover thus slowing me down.