Monday, November 7, 2016

On Battle Rating

I was working out wages on a unit of goblin spider-riders when my willingness to deal with wages as a wargamey balancing factor finally broke down.  I eventually came to the conclusion that Battle Rating is the next best thing, and decided to work out BRs for the units I developed previously.  Since I am interested in BR for this purpose of balancing armies for Battles, I eliminated references to the unrounded number of attacks, and replaced them with the rounded number of attacks (because that is the stat that will matter in play).  I also rounded to increments of 0.25 instead of 0.5 for finer granularity.

From Mercenaries of the Vale of Traitors:
  • Norse Reavers: 1.25
    • This seems about right; they're light infantry, but they're decent light infantry
    • Veterans: 1.75
  • Norse Huskarls: 1.75
    • Again, pretty reasonable - they're mediocre heavy infantry
    • Veterans: 2.5
  • Norse Skoglanders: 1.75
    • The main reason these are cheaper than longbowmen is that their AC is lower, and the BR formula weights that pretty heavily.
    • Veterans: 2.75-3, depending on pricing of special cover ability
  • Skami Skirmishers: 1.25
    • Veterans: 2.5
  • Skami Hunters: 0.75
    • AC 1 is super cheap.  At AC0, units get BR 0...  who needs armor, really?
    • Veterans: 1.5
  • War Mastadons: 9.25
    • Compared to cataphracts at BR7.5, mastadons are slower, have higher AC, and do a ton more damage on the charge.  Seems fairly reasonable.
  • Orcs: per DaW:C, p68
  • Iron Face Glaives: 4
    • Hobgoblin heavy infantry with AC5 instead of 3 and corresponding speed decrease, reasonable rating increase
  • Iron Face Archers: 6
    • Hobgoblin longbowmen with AC5 instead of 3, again we see the weight put on AC
  • Dwarven Spearmen: 4
    • Seeing some inconsistency here; when I run the stock Dwarven Heavy Infantry A through my spreadsheet, I get 3.5 instead of 3 (per Campaigns).  Heavy Infantry B is also at 3.5, but C is at 2.5 (lower damage), and D is at 2 (lower damage and lower AC).  So Campaigns' BRs took sort of the middle of that range, and then mine are basically the best stock Dwarf Heavy Infantry but with higher AC, ergo more expensive.  OK.
  • Dwarven Crossbowmen: 9
    • Campaigns has Dwarven Crossbowmen at BR 3.5, but with AC4 instead of 6, and 2 melee attacks instead of 3.  Even taking unrounded values into account, I still get BR 6 for Campaigns' dwarven crossbowmen.  Comparing them to human crossbowmen at BR3, they have 1.33x as many HP and 1.5x as much ranged attack power, so twice as expensive is not deeply unreasonable.  Comparing them to Elven Longbowmen at BR7, they're slightly weaker in several ways (slower, lower HP, fewer melee attacks, higher THAC0).  So I feel like BR 3.5 is probably substantially undervaluing stock dwarf crossbowmen, and then I went and put them in plate, which explains how I got from 6 to 9.  Whether they're actually worth 9 is another question; if you have 17 BR to spend, is four units of dwarven spearmen vs two units of spearmen and one of crossbowmen a reasonable fight?  This might be a particularly unfavorable scenario for the crossbowmen, though...

From Dwarf Units:
  • Furies (calculated with UHP 10 and ML6 representing their special abilities):
    •  Greataxe:1.75
      • with throwing axes: 2
    • Axe+shield:2.25
      • with throwing axes: 3
    • Two axes:1.5
      • with throwing axes: 2
    • Getting the low-AC discount again.
  • Musketeers: maybe I'll dig out Guns of War later and see what it says about firearm unit BR, if anything
  • War Machine, assuming Morale +2: 
    • No entry for War Machine movement type in the BR rules
    • If treating as Loose Mounted (can withdraw from attacks), 16
    • If Formed Mounted (can't withdraw), 10
    • I know for sure I'd rather have a Formed Mounted War Machine than a company of dwarven crossbowmen, because the war machine has a very good chance of destroying the crossbowmen in three rounds of fire or less, without having its paint scratched.

So I think one takeaway from this is that the BR system has a couple of holes in it.  One of these is low-AC units.  Command and Control aside, I'd much rather have two AC1 units than an equivalent AC2 unit, but the BR system estimates their worth to be equal (nevermind AC0 units; that's some Eurisko there).  The only time AC2 is twice as durable as AC1 is if your opponent is at 18+ THAC0.  On the flip side, at 12+ THAC0, which is pretty close to DaW humans, AC8 is actually eight times as durable as AC1.  This falls rapidly as THAC0 improves, and as disorder, flanking, and charge bonuses pile on in the decisive melee.  On the flip side, it seems that the early/ranged phase of the game has more AC-increasers / attack penalties available: volleying overhead, the Defend action, and cover.  It'd be interesting to run a couple of games and keep track of all of the to-hit numbers that come up, to get a reasonable statistical sample and figure out how much better different armor classes actually are in practice.

Likewise, the current formulae do not take into account THAC0 at all.  Four attacks are four attacks, whether they're from a human pike phalanx at THAC0 11+ or a 20HD war machine at THAC0 -3+.

The weight put on charge-maximum melee damage is also interesting.  A unit which can make four melee attacks a turn is rated the same as one which can make two per turn, but gets a bonus hoof attack and a point of bonus lance damage on a charge.  So that's kinda weird and potentially exploitable.  It makes some sense though, because charges to flanks and rear of already-damaged units are when decisive (shock-retreat-inducing) melee damage usually happens in the not-giants-and-dragons typical case.  Still, I could definitely see averaging in typical-case melee attack sequence.

Another thought is that BR is currently very coarse-grained, and going even beyond 0.25 increments to, say, multiplying BR by 10 and rounding to nearest (eg Greataxe Furies -> 18 points, dwarven plate crossbowmen -> 91 points)  would bring it closer to a nice clean wargamey point-buy system.  Smoothing granularity, however, is likely to reveal more edge cases and breakpoints (which isn't necessarily a bad thing as long as you know to look for them).

In any case, I have no illusions about building a perfect point-buy system.  We saw Starmada attempt this, and it turned out to be a mess.  I'm just looking for "generates fun games, works well in play."  BR as it exists is probably a reasonable starting point for this.

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