Why would they need to make a jump check? Diopsid's are insectile, meaning they have 6 limbs. 4 are for holding weapons, 2 are for walking. No jumping needed.

Now, if the OPs friends' PC is making a lot of jump checks, there is a good chance he has the Battle Jump regional feat from Unapproachable East. That would double ALL damage, including Str damage. If the PC was Battle Jumping with a 1handed weapon, that would result in double Str damage as the end result. It would also result in double weapon damage and double all-other-static-bonuses as well. Battle Jump is a 1st level feat, and thus accessable at ECL2, unlike its big brother Leap Attack, which is not.