I made this research for a Hive Workshop modder Lord Perenolde II(
https://www.hiveworkshop.com/members/lordperenoldeii.123823/ ), who is making an ambitious bid to transpose the Warcraft II campaign to Warcraft III. Earlier he adapted Warcraft I for the same game, and the two of us worked together a lot in uncovering the game mechanics of Warcraft I, especially in regards to damage calculation. I was also asked to help around Warcraft II, in particular about how splash damage mechanics work(primarilly for catapults and ships), and since there's some interesting stuff in here, I thought I might share these here. I really recommend reading the comprehensive Battle.net strategy guide(
http://classic.battle.net/war2/basic/combat.shtml ) for explaining how the basic combat mechanics work, although sadly that site did not provide any insight to the intricacies of splash damage.
Catapults/Ballistas: Catapults affect 9 squares every strike, where central square suffers full damage, while the surrounding 8 squares suffer damage reduced by 75%. Each of the 9 squares generates a random numeric value independent from one another, meaning that a strong full damage value does not necessarilly mean the surrounding squares will have proportionally strong values. I have made a chart with 5 strike samples which demonstrates how the splash damage values are all arbitrary, but consistently never break outside of the 12.5-25% damage potential:
Battleships/Juggernauts and Destroyers: When it comes to ships with cannons, their splash damage is more directed. When they shoot horizontally or vertically(or close to it), they deal a 6-square damage grid, and when they shoot diagonally, they deal a 4-square damage grid(and they all deal high damage!). However, for some reason which I can't figure out, ships do not consistently do these directed splash strikes. Sometimes they do the 9-square grid just like catapults, and I can't tell if there are any conditions that must be met, such ship trajectory, target distance, angle, position, sprite etc. I tried everything but just can't get consistent results. About half the time I get the 9-square grid, and other times I get the directed grid, and this might be either some sort of bug or a very obtuse condition within the game code, and I have no idea why anyone would put this intentionally.
Submarines/Turtles: They don't deal splash damage, but direct damage particular to a target unit.
Cannon towers: Cannon towers strike the same way ships do, which is 4-square AoE diagonally, 6-square horizontally/vertically. Unlike ships, however, they don't seem to suddenly deal the strange 9-square grid like it happens with ships, so they are thankfully consistent in that manner.
That's all I've uncovered, and I thought this information might be important enough to post it to the forums. If you've got any other interesting findings regarding splash damage and how it's calculated, feel free to respond!