The best replacement for running shorts is compression shorts.

The best alternatives to running shorts are rated as following:
★★★★★  compression shorts
★★★★  training shorts
★★★  basketball shorts

Your alternative for running shorts is not listed? Suggest!
Speaking about running shorts, one probably shouldn't forget about underwear.

Other search terms related to running shorts and their ratings are:
★★★★★ underwear
You have in mind a companion for running shorts and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of running shorts in all years. Click on graph for more.
running shorts
compression shorts
training shorts