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However Dominions also has a bunch of units purely for flavor because it makes sense lorewise that they exist and I love the series for that.
That's one of the reasons why units with multiple attacks due to having more than two arms, being ambidextrous, etc are highly valuable as they, most often, offer different damage outputs due to fielding different kind of weapons.
Firstly, a lot of Ulm's variation comes from regular infantry vs black plate infantry. The difference there is 4 protection points.
This is not at all intuitive, but 22 protection is more than twice as good as 18 protection, due to the DRN system. If your eating a strength 19 attack as Ulm, the infantry get injured 46% of the time they get hit, while black plate infantry get hurt only 18% of the time. If your eating a more realistic 13 damage attack, from say... a militia's spear, before any penalties or defense apply, the regular infantry is hurt only 11% of the time... while the black plate infantry is hurt 5% of the time.
So in a sense, the difference of 4 points in that case is they will in most circumstances, when facing pure damage, take 50% less damage, which due to the Lanchester square law and the fact that Ulm has troops that hit like trucks, allows black plate troops to dominate the battlefield.
Once you understand how big a 4 protection swing is, the reason weapons matter makes sense too: A hammer or morningstar is 18 or 17 damage, so you probably hurt most humanoid targets that aren't Ulm themselves... but if you want to crack harder targets like armored giants or certain monsters, the maul or even hailberd lets you not just do more damage (probably killing most lightly armored humans in a single blow pretty much every time) but damaging stuff like heavy cavalry consistently, and damaging buffed armored giants at all. A lot of things that are not at all threatened by humans with one handed weapons face an extreme risk vs Ulm with hammers.
Spears and shields have their own unique offensive and defensive bonuses.
Shields are a form of layered defense as they allow Ulm infantry to both have high defense values (effectively 17, which compared to an average soldier's attack skill of 10 is very poor odds of beating, based on DRN, even with an attack bonus weapon like a sword), which lets them parry most blows. The opponent then needs to do damage through the 17 protection of the shield and then through the 23 protection of the black plate. Suffice to say, nothing is getting through that that isn't something that ignores protection entirely, or is an very specialized tool, meaning that this layered defense makes Ulm infantry with shields extremely hard to kill by humans unless they are very fatigued. Even giants can struggle to hurt them, so while they give up the terrifying lethality of hammer troops, they hold the line extremely well. Combined with the fact that this allows defense against ranged attacks at all, and that makes shielded Ulm troops the best human line holders in the game.
Spears offer a different form of layered defense: Making an attack against a spearman requires a morale test against a 'fake' attack the spearman makes against the defender, if they have a longer weapon than you. This test isn't terribly hard in most circumstances, but considering how hard it is to hurt Ulmish infantry at all, even cutting down the attacks made against them by a fraction is a lot. This makes spearmen sort of a compromise between mauls and shields, as they will take less attrition in melee while still packing a weapon that can do a lot of damage easily.
For the classic sword vs. hammer barbarians the sword is almost entirely better (though rarely the bashing damage might be a big advantage) but costs significantly more resources so maximizing recruitment may require some compromise depending on the province.
It's very intuitive that spears are longer than swords, for example. Likewise, it's intuitive that flails get a bonus attack against shields, that crossbows are more powerful but slower to fire than standard bows and that blunt weapons cause more damage to skeletons than piercing weapons.
That's all that's really needed for someone who's just trying to learn the ropes of Dominions.
Can other players do better relying on a more thorough understanding of the mechanics? Absolutely. But is it necessary to do well against standard AI or in casual MP games? Not really!
Similarly, you can find a lot of people who will point to a specific weapon and say "and this is why I recruit exactly this guy out of these options". Weapon variety is sometimes a subtle difference, and sometimes it's a Flail.
I find that a big hurdle to a lot of people learning Dom is this specific fact, as the non-linear difference in outcomes from stats due to DNR is integral to almost every interaction. The fact that subtle troop stat differences lead to such different outcomes is very central to what makes Dominions dominions, and more importantly for learning how troops work, makes its counters harder than most other strategy game counters: in something like starcraft even though marines are very hard countered by carriers, the carriers are going to take losses vs a sufficient stack of marines. In Dominions, a few heavy cavalry units can take on a fairly arbitrary amount of basic troops with no casualties.
The short version wouldn't be 'its intuitive that spears are longer than swords' but probably 'a difference in 2 on stats is very big, and a difference in 4 is nearly overwhelming.'
Spears being long is also very counterintuitive, specifically because a spear's length doesn't impact the game in any way besides hitting certain sized units in certain body parts, dual wielding, and morale interactions, so explaining that (even on a surface level) is pretty important, because it doesn't grant the things you would actually expect a spear to grant you.
Specifically, you kind of need to explain that spears are about fighting low morale units safely, as the main thing you would expect spears to be good for, which is being a second line of troops, doesn't work at all.
I have taught 6 people to play dominions and every single person has tried to put long spears behind shield troops because that is literally how they were used historically.
That's interesting! I would not have thought of that.
In something like D&D or Warhammer, most rolls are a single die against a flat target. In Dominions you're rolling opposed sets of 2d6, so you're rolling more dice and comparing the highest - and then doing that across battles of dozens or hundreds of units. Averages win out a LOT more than most other systems.
So yes, small-seeming stat differences of 2 points can be very important.
I did forget about parrying! That still serves a similar purpose of spears being an anti chaff unit though!
You can do that with some nations in COE