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My last track days were the first ones I even tried to determine my lap times. More out of a curiosity thing than any other. I still feel like I have a lot of room for improvement so the timing gives me a benchmark on roughly where I stand. I haven't started racing the clock yet, and probably won't for a while.
That having been said, chasing other riders that are slightly faster has helped me increase my corner speed and move my braking points closer to the corner. Generally speaking I feel that if the other rider can do it, my bike can do it. I just need to build the confidence and skills so that I can do it too.
I've done quite a few track days this year, and a few last year. Until my last track day I really never found myself riding at a similar pace to another rider for more than a lap or so. I think as I'm getting faster I'm starting to run into more riders of similar abilities and I'm trying to find ways to use them to further my learning. I've been having fun with it and really enjoying riding with you all.