The purpose of a box jump should be to improve explosive leg power that translates into more explosive athletic movements on the playing field.  The height of the box and the execution of technique are of paramount importance when doing box jumps.  It is always better to use a lower box than a higher box since it will promote better form and reduce injury risks.  I see too many coaches/athletes using 30-42 inch boxes that promote poor form.  Here is what I mean.

The purpose of a box jump is to improve muscle power/elasticity.  If the box is too high, the athlete spends too much time on the ground because they just try to “muscle up” onto the box without a regard for form which reduces muscle elasticity and is counterproductive.  Think lower boxes which promotes a quicker response off the ground, increases muscle elasticity and allows the individual to stay focused on the execution of the jump versus just “trying to get on top of the box” which breaks down their form.  The end result is we get better carryover from training to the playing field.  We have worked with countless elite level athletes over the years using lower boxes for this reason.  The height of the box has to coincide with the athletes strength level and their ability to have a short ground contact time (GCT)  If the athletes strength and power levels are low, always use lower boxes.  If they are more advanced and have years of strength and power training experience under their belt, a higher box can be used but generally speaking, we choose lower boxes in most situations because the results and carryover onto the playing field are greater in our experiences.  Below is a video of collegiate athletes using  4 inch high boxes doing continuous lateral box hops to a long jump.