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It really depends on what kind of runner you are honestly. If you run just for the pure pleasure of it and you don't care about the data, a GPS is like a waste of money, but if you're serious about improving your times or you want to track your routes, it's pretty useful because it gives you the precise distance and speed in real time, stuff that your phone might not be able to do well if you keep it in your pocket. Most of the runners I know use it mainly so they don't get lost and to see how long they've been running, and it's convenient because you don't have to carry your phone around. But honestly, if you're just starting out now, you could also wait a bit and save up, it's not like having the watch is going to change your performance on its own.
It depends on what kind of runner you are. If you're serious about running and want to track your progress, a GPS is pretty useful. It gives you the exact distance, your pace, elevation... stuff that you can't always capture well with your phone or a regular app, especially if you're in an urban area with buildings all around. Personally I need it because I never know if I actually did the kilometers I think I did, and it's also useful for switching up your routes without getting lost. But if you're just running to get some exercise, like 3-4 times a week in the park doing the same loop, honestly you don't need it. A free app on your phone does the job.
The important thing is that it's reliable. Some cheap watches lose signal, especially if you're running between trees or narrow streets. I've seen some that get the distance pretty wrong, which is frustrating when you want to track your progress. A decent Garmin or an Apple Watch work well, but they cost a lot. If you're just starting out, I'd try with your smartphone first, see how it goes.
Another thing: GPS eats up a ton of battery. If you're running for half an hour maybe it's fine, but if you do long distances you gotta remember to charge it a lot. It bugs me having another device on my wrist when I've already got my guitar waiting for me at home, but I get that for people who are serious about running it's worth it.
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