Also, it should be noted that HSS is NOT necessary to stop action. That's where you get into Flash Duration. If you use enough power to overpower the sunlight at your given exposure, and your flash duration is short enough to freeze the action, you will freeze it and the shutter speed doesn't matter, except in regard to limiting ambient light.
Here is a shot from last night's rockets game. The team photographer, Bill Baptist is a member here, and he uses strobes set in the ceiling. He could tell you better than me, but I know he uses a shutter speed under 1/300th, while I am using one at 1/800th to stop the same action.
Oklahoma City Thunder vs. Houston Rockets - Photos - February 15, 2012 - ESPN
The thing is, the flash effectively becomes your shutter. And if you pump out enough light to overpower the sun at 1 second and your flash duration is short enough, then you will still freeze the action, even if your shutter speed is 1 second.
BTW, this is one of the things where Paul C Buff's lights fall short. At full power, the AlienBees are only like 1/300th of a second and the Einsteins are only like 1/600th of a second. You need to figure out how much power you will need and what your flash duration will be at each power (know your T.1 and T.5.)