I’ve seen it in every movie, video game and documentary that involves throwing a grenade. The thrower always has a stiff throwing arm and swings his arm above his head to throw the grenade. Why not throw it like a baseball? I’d imagine you could throw it farther and much more accurately this way.
I volunteer at the National Army Museum in London and as part of the WW1 centenary celebrations we did a lot of object handling sessions and one object was a dead Mills Bomb.
This was the first hand grenade to use a pull out pin to prime it before throwing and was the most widely used hand grenades by the Allies during WW1. British soldiers were explicitly taught to throw the Mills Bomb in an action like throwing a cricket ball which would have been familiar to many British men at the time so the throwing action you have seen may in part be due to this.
Also remember that when throwing a grenade you not want it to fly like ball. You need to lob it up and over and then drop straight down into an enemy position such as a trench or shell scrape. The straight arm action, if the grenade is released at the right point creates this type of flight path. As far as I know (I am British and have never played baseball!) the baseball style throw has the ball fly straight forward in a flat trajectory.
Additionally, from what I can see the dynamic whole body movement of a baseball throw wouldn't work that well for a soldier encumbered by kit or lying/crouching in an awkward position. If all you have to move is your arm then you can launch a grenade from most positions which for a soldier is usually lying prone or on one knee. During a fire fight soldiers are usually only standing upright while advancing to contact (running towards the people firing at them while another soldier provides covering fire) or when in cover. Otherwise they are trained to be take a knee or lie flat on their belt buckle to reduce the target they present.
Thanks for the thorough response! I was actually watching a YouTube documentary about the Mills Bomb when I was reminded of my question. Funny you brought up the Mills Bomb right after I had learned about it. Cheers from the U.S.
So, here's a cracking couple of pages from Small Arms Training Volume 1 Pamphlet no 13 Grenade, dated 1942:
http://josephs-militaria-and-homefront-collection.co.uk/gt2126.jpg
The main point is to reinforce from the amazing answer you've already received is that the intention is to throw the grenade from cover most often targeting someone in cover:
"Practice squad in throwing from different types of cover, e.g. a bank, trench, etc. The thrower's position must be modified to suit the height of the cover available, which may neccessitate kneeling or lying as well as standing."
Emphasising the point that you stay in cover, throwing a grenade 'like a baseball' would generally mean exposing yourself to potential fire coming from the window/door etc you're targetting.
