Have Dev's ever seen an Olympic javelin throw or Baseball outfielder do a big throw? They leap/jump into their throws
Not really, maybe their body inertia brings them off the ground after the throw but thats about it. Trust me they are still grounded when releasing said throw, if they weren't they would have shit for power/distance
As an actual thrower for track I can safely say that jumping does make you throw farther, and also using strech reflexes helps a lot too.
So you're telling us all that your coach tells you to jump during or after your throw? lol right, also you're talking about running and throwing not standing still and throwing, big difference.
But being limber does help, it helps generate leverage from your bodies many lever systems. Length factors in as well. As the longer your levers are the more distance they will travel(mostly in arc formation, like a circle), which usually equals higher velocity/speed. Flexibility allows your levers to travel farther.
This is the reason why the flamberge does more damage than a katana. Sure the katana is faster but is also slower. Using a 2 lever system, with one being your arm and the other being the sword, we can determine that the flamberge will have a higher actual swing speed than the katana. Note there must be a balance though as too long is bad. A baseball bat, sword, track javelin, boxers punch etc etc all have found their balance. You want maximum length and weight that user can handle to achieve maximum power/speed.
Length of the levers * distance traveled * using set force = swing speed
(not an actual equation lol but it' something similar)
Edit: longest edit ever