Assuming the characters before the date in the filename are always the same length and all of your rasters are together in the same folder, see if this prints out the raster file names for each day that exists in the filename dates.
import arcpy
from collections import defaultdict
def main():
raster_dir = r"D:\NASA\Data\SMAP\2014\Processed"
arcpy.env.workspace = raster_dir
raster_days = defaultdict(list)
for r in arcpy.ListRasters():
raster_days[r[15:23]].append(r)
for date, rasters in raster_days.items():
print(date)
for r in rasters:
print("\t{}".format(r))
if __name__ == '__main__':
main()
This creates a dictionary where the key is a date string (YYYYMMDD) and the value is a list of raster filenames that all have that date. If that works, you should be able to use this dictionary to calculate your statistics however you want.
EDIT:
Fixed typo on raster_days variable name in for loop.