Common "rule" is that, on full frame, a picture can be taken handheld at a shutter speed of 1 sec/focal length in mm. Meaning, most shots will be acceptable. Look into camera shake. Every movement, unless you make nice circular movements, has a start, middle and end. At the ends of a pendular movement the speed is zero. When you take several shots you will end up with a very blurred one, taken in the middle of the movement, a frozen one, taken at a turning point of the movement and probably one in between these. The shutter speeds mentioned in the question to me are very short for action. In my pictures I like to show movement thus I use shutter speeds 10 times the rule. Meaning 1/30 for 300mm. At these speeds I find IS help full. At shorter speeds the IS will not be very help full, meaning not very visible, and with longer exposure times the IS will come short.
For action shots I use the speed I need to show the action how I like. Meaning, as example, the prop of an airplane makes a full circle during the shot. I do not care what this speed is in relation to "formulas". I use what I need. If I adjust something it will be the support or the number of shots needed to get the shot I want to end up with.