Ok, first thing first, we need to clarify the definitions from the beginning. What do you mean by underarm? This:
(https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTWugZbzHjJLiMkMZzar9FcpG5xg_-TPZ0tvqqmK39zkmpkfMdV)
Or this:
(http://www.europabarbarorum.com/p/art/EB-art-IG_noble_hoplite.jpg)
?
Because, I've seen people refering to the latter as over-arm, while other, when saying over-arm, are talking about this:
(http://1.bp.blogspot.com/-zBodTfmlLHE/UJD92f5ZamI/AAAAAAAAHJg/y8JnJ3_m6Uo/s1600/hoplite+phalanx.jpg)
Now, I'm not an expert in ancient greek warfare, neither did I read a lot of books about this matter, so my opinion is built only in what I think makes most sense and, therefore, I don't hold to it like the ultimate truth about hoplite warfare.
First of all, let's note that the great majority of the mods use the over-arm (I'm talking about the one showed in the third picture). This is probably due to the fact that Europa Barbarorum's team decided for it in their mod. Seeing as they're considered the Holy Bible of historicity, it's only natural that the other modders followed their steps. From what I understand, Europa Barborum's team decision was largely due to Peter Connolly's studies, in which he concluded that an over-arm thrust is stronger than an underarm one. Recently, Storm of Spears, a Christopher Matthew’s book, was published, in which tha author apparently (never read it) disproves Connoly's theories and reachs the conclusion that the overhand position was only used to throw the spear and that the underarm thrust it's more powerful than the over-arm counterpart.
Personally, I think that this "which thrust is stronger" discussion is silly. The ancient greeks did not had the current machinery that allow us to conclude that the x thrust it's N stronger than y. Probably, they thought: "Oh well, it seems that this thrust is slightly better than the other". My point being that the peak force of the thrust was not the most important thing an hoplite had in mind in the hour to choose his stance.
This leads us to the question: "What's the most important thing to bear in mind when you're choosing your position?". I would say: "Survivability", in other words, the stance that gives you more chances of surviving. That's why I think the over-arm grip was mainly used, because it allowed you to stay in formation, with your shield interlapped with the man in your side, thus boosting your chance of survival, while you can't do this using the underarm grip without hurting the man behind you. Now, that's not to say that the underarm stance was never used, I'm sure with was used many times, but, while staying in formation, I believe the overarm grip ruled.
Well, it depends of the time, really. In the Hellenistic era, the classical hoplite formula was outdated, and, therefore, more loosened formations were developed. The hoplites were no longer the main line, but had the job of flanking the enemy, while the phanlanx pinned them down. This type of warfare required lighter armour and a looser formation, resulting in the Ekdromoi. The classical phalanx, from the Peloponesian War, for example, was a pretty closely ranked formation, though, similar to this:
(http://unconstrainedsophistory.files.wordpress.com/2012/02/20120222-165009.jpg)
True, but with overarm you have the possibility of pointing the spear more towards the ground, making that the opposite point would be over that man's head, the one that is behind you, when you pulled it backwards. Like this:
(http://1.bp.blogspot.com/-zeXNhw4-vDw/T_GxV5AruSI/AAAAAAAAAWs/hyiRmPoPaFs/s1600/Classical+Greek+Hoplites.jpg)
I found this:
(https://imagizer.imageshack.us/v2/500x342q90/541/9p19.jpg)(http://s30.postimg.org/x8d4cayb5/underarm_thrust.jpg)
Here's some pics:
(http://www.thesundaytimes.co.uk/sto/multimedia/archive/00006/dani_tribe_6971a.jpg)(http://static.environmentalgraffiti.com/sites/default/files/images/http-inlinethumb02.webshots.com-46081-2799678740105101600S600x600Q85.img_assist_custom-600x372.jpg)(http://2.bp.blogspot.com/-_wz13rrKLx0/UFG0uxWph_I/AAAAAAAABqo/koQkhAY0wWA/s640/0_5b7aa_ab5a3ec_orig.jpg)(http://image.shutterstock.com/display_pic_with_logo/595873/595873,1323296482,2/stock-photo-new-guinea-indonesia-december-unidentified-warriors-of-a-papuan-tribe-in-traditional-clothes-90350869.jpg)(http://i.telegraph.co.uk/multimedia/archive/01109/zulu-460_1109277c.jpg)
I agree with you, though. While in formation, some kind of over-the-shield stance must have been used. When not in formation, underhand seems more effective than overhand.
Agreed, but, once again, in an hoplite formation, this type of underhand would be completely impossible:
(https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTWugZbzHjJLiMkMZzar9FcpG5xg_-TPZ0tvqqmK39zkmpkfMdV)
Only this stance could be used:
(https://imagizer.imageshack.us/v2/500x342q90/541/9p19.jpg)
As any historian knows, the ultimate conclusion for any highly debated subject is:
(http://www.fromquarkstoquasars.com/wp-content/uploads/2014/01/aliens-meme.jpeg)