There are two primary reasons for why your GPS will show longer than the official course distance. This is due to how the official measurement is done for certified courses and your GPS accuracy.
Official course measurement: when courses are certified, the path taken is the shortest route possible, tight around any corners, straight through zig-zags on course, etc. This is to ensure that the course run by any racer is never shorter than stated distance. Because you are likely not running the exact same path, perhaps always staying to the right side rather than tight to inside of turns, maybe zig-zagging to pass or be passed by other runners, diverting to use a toilet, etc. your path will be longer than the official course measurement.
GPS accuracy: GPS positioning is typically accurate to with 10 meters (per the Garmin website). What this means is that the strait line you run isn’t straight on GPS, and this can add the distance quickly. There are a couple easy ways to illustrate what this means practically. The first image below is from the 2016 Towpath Half Marathon using GPS… this is the second half of the race on a section (between miles 7 and 12) that is traversed 3 times.. twice going north and once going south. You can see from the map that each time through, the GPS location is very different and quite often well off course.
Another fun example to show GPS inaccuracy is from the track. Two miles on a high school track, all in the inner two lanes, looks anything but consistent!
The bottom line is that your GPS will likely measure a couple percent longer than actual course or run you’re taking. This can easily translate to 0.1-0.3 miles on a half marathon… which would appear to be 3-10 seconds/per mile faster than course time.
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