Kingdoms of Men Shooting

I was getting frustrated the other day, as I was trying to sketch out my next few lists of MSU stuff to test, but felt like they were all just terrible.

In my experience with MSU, if you don’t have reliable, efficient, top-notch melee units (which Kingdoms of Men does not), you probably need to invest more in ranged support elements. I was looking at our ranged infantry options, as they are generally our cheapest shooting options, and something I was keen to test them out more... but I was just not thrilled.

Conventional wisdom stated that the bigger the unit, the more damage it would potentially deal (more attacks!), and the more cost-effective magic items (Jar of the 4 winds, or Brew of Keen-Eyeness) would be (since more attacks would be influenced by the item). That made sense. However, taking bigger units is not what MSU is all about, and in some ways, I felt that spending points on these items was throwing good points after bad for KoM.

Conventional wisdom also says that Pierce is a powerful special rule, which we as KoM, do have ready access to. Our Arquebusiers have Pierce -2, which makes them the deadliest of our infantry shooters.

However, the Ranged attack stat for our shooters is 5+ across the board… not great. We’re going to be missing (statistically) 2/3 of our shots, more if the unit is in cover.

It was swiftly becoming a mental quagmire. Our shooters are not accurate, but we can be deadly with our ready access to Pierce, so we want to compensate with more shots, but then we’re spending lots and lots of points….

I decided I was wandering in circles. So I sat down and decided to try my hand at some basic math, to see if I could use numbers to help me identify a “least bad” option for us (not knocking KoM, but we are just human), or highlight anything I may have overlooked or just wasn’t seeing. Uh, strap in, friends. This is a lengthy post.

I was quickly bewildered. I’m no statistician (so apologies, if I misuse any terminology. If you know better, tell me and I can edit the post for correctness.) Eventually, I resorted to my high school physics approach to solving problems, and tried to start oversimplifying as much as humanly possible. 

Thanks, physics!

The first oversimplification I would make, is that I wanted the deadliest units possible. We won’t try to factor in the benefits of having a higher Nerve into these calculations at all.

Part 1: Points per Shot

I started out slow. I knew all shots were not created equal. But... just for curiosity, how many points I would be spending to take each shot?

Bows	Shots	Points	Points per shot
Troop	8	75	9.375
Regiment	10	100	10
Horde	20	165	8.25
Crossbows	Shots	Points	Points per shot
Troop	8	85	10.625
Regiment	10	115	11.5
Horde	20	190	9.5
Arquebusiers	Shots	Points	Points per shot
Troop	8	100	12.5
Regiment	10	135	13.5
Horde	20	225	11.25

Ok, so I remembered basic math. We're off to a good start! The number of shots are equal, so the more expensive weapon option at each level (Arquebusiers) should be paying more per shot at each unit size... which they totally are. 

Additionally, if you are looking for the best “bang for your buck” so-to-speak, the Regiment is the least points efficient option you can pick. If you’re taking a Regiment, you are absolutely taking it for its boosted Nerve value, not the increased damage potential, because at equal points, regiments have fewer attacks than their troop counterparts. Hordes come out on top of everything, though looking at the points per shot, not by as far a margin as I guess I was intuiting. These non-linear unit costs, man…

Part 2: How Many Hits?

I assumed that while the bowmen could hypothetically move, ideally they would not, as they have a decent range, and moving would further reduce their accuracy by 50%. Crossbowmen and Arquebusiers have Reload! so would need to not move in order to shoot… so hey, we'll have everything stand still. We’re doing ok on the oversimplification front so far! More good news is that each unit has the same range, number of attacks, and target roll (5+) needed to hit. Nice. So, across the board, assuming no cover (and no moving), on average:

·         Troops would land 2.66 hits per volley

·         Regiments would land 3.33 hits per volley

·         Hordes would land 6.66 hits per volley

Neat. While the math is easy to follow, I was guess I was surprised at how few shots from a Horde would (statistically) hit. I don’t think I had previously thought the math through before, so it was a kind of stark realization for me. Again, the non-linear unit sizes are messing with my intuition.

Part 3: Average “Deadliness”

Since the number of shots/hits would be the same, I figured that the Arquebusiers would be the most killy unit type (dealing the most wounds), and the Horde of Arquebusiers, the most killy ranged infantry unit overall. That was actually correct. Phew. My intuition is correct there! Piercing is no joke folks. 

	Defense 3+	Defense 4+	Defense 5+	Defense 6+
Bowmen Troop	1.7777777778	1.3333333333	0.8888888889	0.4444444444
Bowmen Reg.	2.2222222222	1.6666666667	1.1111111111	0.5555555556
Bowmen Horde	4.4444444444	3.3333333333	2.2222222222	1.1111111111
Crossbow Troop	2.2222222222	1.7777777778	1.3333333333	0.8888888889
Crossbow Reg.	2.7777777778	2.2222222222	1.6666666667	1.1111111111
Crossbow Horde	5.5555555556	4.4444444444	3.3333333333	2.2222222222
Arquebus. Troop	2.2222222222	2.2222222222	1.7777777778	1.3333333333
Arquebusier Reg.	2.7777777778	2.7777777778	2.2222222222	1.6666666667
Arquebus. Horde	5.5555555556	5.5555555556	4.4444444444	3.3333333333

Part 4: Efficiency and mitigating excessive pierce

you may have noticed Crossbows Hordes and Arquebusier Hordes tie in their deadliness against units with Defense 3+. So in that one instance, the Arquebusiers aren't the most efficient tools use of points.

That "overkill" intrigued me, so I tried to take one more step in this exercise, and circle back to looking at how points factor in compared to deadliness, to see if there were any sweet spots for unit deadliness. This table takes the unit points and divides it by the corresponding number above. A lower number is therefore better, as you're spending fewer points to deal that anticipated damage.

  

	Defense 3+	Defense 4+	Defense 5+	Defense 6+
Bowmen Troop	42.1875	56.25	84.375	168.75
Bowmen Regiment	45	60	90	180
Bowmen Horde	37.125	49.5	74.25	148.5
Crossbow Troop	38.25	47.8125	63.75	95.625
Crossbow Regiment	41.4	51.75	69	103.5
Crossbow Horde	34.2	42.75	57	85.5
Arquebusier Troop	45	45	56.25	75
Arquebusier Regiment	48.6	48.6	60.75	81
Arquebusier Horde	40.5	40.5	50.625	67.5

Part 5: Findings

Well... generally speaking:

• Arquebusiers are the deadliest option for ranged infantry... which should be a no brainer, as they have Pierce -2, the best of these options. What surprised me is that they came out as being the most points efficient way to deal damage of these options too. I would have assumed that we would pay a little premium for the extra oompf (meaning they might not be be best choice in every situation), but point for point they appear to be our best investment for infantry shooters.
• Taking Hordes of our infantry shooters is the most points-efficient way to take our shooters (most shots per points spend and most expected damage for points spent, compared to the same unit type of different  sizes).
• Troops are the second best choice if you are looking for points efficiency. Going big seems to be mathematically encouraged, and you pay a little extra for the extra drop/deployment/unit, as it gives you more options in game (splitting fire among two targets, for instance).
• Unless you really really really want that extra nerve, avoid regiments.
• As for dealing with your opponent... these are the most points efficient ranged infantry options to take against units with these defenses.

	Best	2nd Best	3rd Best
Defense 3+	Crossbow Horde	Bowmen Horde	Crossbow Troop
Defense 4+	Arquebusier Horde	Crossbow Horde	Arquebusier Troop
Defense 5+	Arquebusier Horde	Arquebusier Troop	Crossbow Horde
Defense 6+	Arquebusier Horde	Arquebusier Troop	Arquebusier Regiment

I gotta say, I was surprised by what I found.

I should also say, that I'm fighting off a cold. If someone notices any math errors, please speak up and I can amend the post. Thanks!