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Why do you assume your iPhone X is correctly capturing measurements? All GPS devices are incorrect to some extent. As to the half marathon, did she run the tangents right and exact to every turn? Did she not weave around any runners? Because races are measured by a wheel to the tightest tangent and the straightest line and they’re not certified based on GPS. I have been running for 24 years and never once has a half marathon/marathon (of which I’ve run over a dozen) come out to 13.1 or 26.2 on a GPS watch—because of those factors.

Maybe the watch is wrong. Hard to know without a 3rd device to use as a proxy. Either way -- one of the two is off by a sizable distance for our hike. A 0.3 mile discrepancy for a hike under 2 miles is enormous.
 
Maybe the watch is wrong. Hard to know without a 3rd device to use as a proxy. Either way -- one of the two is off by a sizable distance for our hike. A 0.3 mile discrepancy for a hike under 2 miles is enormous.

A quick a google search actually turns up a lot of discussion on problems with GPS accuracy with the iPhone X.

https://discussions.apple.com/thread/8377639

I’ve run the same running routes for years—a decade actually—and gone through 3 Garmin watches, and my Apple Watch matches up exactly with all of those mile markers. Again, many factors can affect GPS with any device, but in my experience with several GPS devices, the AW is just as accurate.
 
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Maybe the watch is wrong. Hard to know without a 3rd device to use as a proxy. Either way -- one of the two is off by a sizable distance for our hike. A 0.3 mile discrepancy for a hike under 2 miles is enormous.
Your wife's AW is probably correct. She ran a 1/2 marathon that recorded 13.25 miles. That's a 1.1% discrepancy. That's pretty good even without considering the impossibility of actually hitting every tangent on the course.

Here's what I would do to check to see if it's truly the watch or the X that is the problem. Map a course using runmyroute.com. It uses google map information and for the most part it's dead accurate. Walk the same course that you mapped with the X and the AW. Then compare which device is closer to the google data.

Alternatively, find an outdoor track at a high school or middle school that is out in the open. Walk the inside lane for 4 to 8 laps. See which device is closest to 1 and 2 miles. I would suggest walking instead of running to get more GPS data points.

Lastly, I was having problems with the accuracy of my AW S2 about 8 months ago. On courses that I ran using my iPhone5, I was pretty spot on compared to google maps. Then when I got my AW, I used NRC and if I started a run with the phone (iPhone 6 at this point), the miles were correct. If I started the run with the AW, the miles were overstated by 10 to 15%. I solved the problem by fixing the permissions for motion tracking and/or unpairing the AW. Now, it's dead on accurate no matter if I start the run using the phone or the watch.
 
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