Does anyone know of open data sets about running behavior/running activity. I'd love to find some where there are histories for individual runners, but even data about large numbers of runners (distance, pace, location, you name it) would be interesting. I would prefer the data to be about amateurs runners, if that is possible. I haven't found anything yet, but I'm not an expert in this field. Thanks for any suggestions.
ARRS - the Association of Road Runner Statisticians seems like the best place for you to start; there's a lot of data that sounds to me to be exactly what you want.
IAAF, the international association of athletics federations has some interesting data too. here's one example for road running marathon records for senior men outdoor:
OSM hosts GPS traces for various activities. If you find a couple of frequent uploaders, you can then get a history. This would be more likely for jogging, rather than timed races.
and for example these tags (WATCH OUT: tags are case sensitive)
Bulk GPS traces are here: https://planet.openstreetmap.org/gps/