Sony DSC-H1 high speed shutter question?

when setting mode to high speed shutter, i loose alot of lighting. can
take same environment without flash on auto mode and get picture pretty
bright. environment is indoor gym, daughter playing basketball. in
auto mode getting blurred shots. called sony and they told me i have
to force flash but could not tell me why i loose so much lighting even
on my lcd display and also pictures are also dark other then the person
shooting. the background is really dark and don't like picture. if
anyone can tell me how to increase lighting on high speed shutter mode
other then flash i would appreciate it. don't know why on auto mode, i
have plenty of light in picture without flash and on high speed shutter
mode, i have little light in picture even with flash.

I will first state I am not familar with DSC-H1 high speed shutter
mode, but I can generalize from other cameras.

HSS typically means that I can use a higher shutter speed and still be
able to use flash. There are two problems with that, in your
situation.
1) higher shutter means you need a faster lens aperture to
counterbalance the decrease in light due to shutter speed...but maybe
your lens is as wide open as it can, and the shutter speed is much too
fast for the available light. Result, less light in the photo,
overall.
2) HSS means that the flash outputs many smaller less powerful bursts
of light, rather than one really big burst of light, so that some of
the flash is striking the sensor in all areas. But many smaller less
powerful bursts of light mean that less intense lightis reaching not as
far, leading to only the subject being lit and not the background.