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In the old, pre-garmin days, I was a pretty good judge of pace. Since getting my first garmin in 1999, I found myself obsessing for a few years. I've gone back to running by perceived effort and my times are almost back to where they were a decade ago. (Probably coincidence).
I still wear the garmin though so I can geek out when I get home. If I'm racing well, I don't have time to look at it, if I'm not running well I might sneak a peak to try to maintain pace. I never set a beep though, I think that is bad manners in races, although fine in training. As for those who have beeping garmins but are listening to their ipods - don't take me there!
A couple of years ago I ran an off-road race where watches and garmins were banned. All runners were aked to predict their finish time. I finished 8 seconds faster than I had predicted and won a bottle of fizz for being the closest to my time. Once you know your body You don't really need the technology!
I'm with Jonny. I wear my Garmin all the time, on the basis that you can't really have too much information to geek over afterwards (should you want to). However, I lost my HR chest strap a couple of weekends ago (left it at a race HQ I suspect), and it's kind of prompted me to generally rethink my "feedback during races" strategy. I'm not a slave to the Garmin anyway, but I ran a pretty decent race on Saturday being a lot more conscious of perceived effort, almost as if it was nice not to have the distraction of something else to tell you (supposedly) how hard you're working. I still had info re: splits, pace etc. to hand, but I only ever glanced at the Garmin occasionally to see how far there was left to go. (They don't have mile markers at the National Road Relays and I'd never done the long leg before!)
I may well go Garmin-less for a few shorter races over the Summer, see how liberating it feels.