Thinking about BR

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EHamilton
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Thinking about BR

As mentioned yesterday, I've been using BR in order to let players do a bit of customization of their forces for DoW:Battles. Usually that just amounts to allowing a substitution of 3 light infantry for 2 heavy infantry, or something simple like that. I think the BR values do a pretty good job of enforcing fair value on replacements for all the basic troops, even ranged vs melee.

The place where I start to have difficulty is on some of the troops off the exotic creature roster, where it frequently seems like stronger monster troops are underbudgeted relative to the base troop types. I'm currently building a few new units for test purposes. The rules commentary on calculating BR actively encourage a certain amount of formula tweaking to make things "come out right", but I want to make sure I'm doing things correctly before I start to radically changes values on an ad hoc basis.

There are two common causes of BR "feeling" too low:

1. The troops have a very good attack throw, and the BR formula doesn't seem to have any way to account for differences in attack throw quality.

2. The BR is lowered by the extra 1/2 reduction factor for non-sentient troop types.

I'm actually not sure if I'm right about #1; maybe there is some place in the formula that is indirectly accounting for attack throws, and I'm just not recognizing it. So I figured I'd ask here to see if I missed it.

For #2, it's clearly listed in the rules, but there I'm wondering if there's some tactical rule that justifies it in a way I don't appreciate. I've scanned the tactical rules in Battles to see if there's any consequence to using non-sentient troops -- it makes perfect sense to me that there should be -- but I can't find one. They often have extra expenses when taken on campaign, but that shouldn't factor into BR. So I'm feeling like this is a basic disconnect between the fast combat resolution system involving BR (which penalizes hunter and guard monster units heavily) and the full tactical system, which lets them run wild.

Sometimes both of these effects combine together to make a BR calculation feel very wrong to me. The example I asked about a year or so ago was the T-Rex, which is currently "priced" (in BR) at around the same value as a comparable unit of beastman infantry (a bit cheaper than a unit of heavy orcs), but seems substantially more powerful: 6 attacks, better attack throws, better morale, excellent saving throws, and superior armor, with no drawbacks of similar significance.

I think I also singled out the purple worm, which is currently worth BR 0.069, less than four human heavy infantry (0.017 each). When I questioned this before, Alex pointed out some drawbacks to colossal units (bulky, fragile). I can also see some simulationist rationalizations (maybe phlanx/schiltrom might work well at repulsing stupid creatures like purple worms?), but at the end of the day, it's still hard to believe a 15 HD monster is only worth four(!) 0th-level(!!) mercenaries. If I were in a company of 120 normal infantry, I would not want 30 purple worms charging at us -- even if they did have to come in one at a time, and we were drawn up in a shield wall. That would play out as a slaughter in man-to-man.

My first inclination is that I'm just going to remove the 1/2-factor BR penalty for nonsentients, so BR-based Campaigns fast-combat resolution matches up better with the expected man-to-man Core results and tactical Battles results. But I always ask here first, since I often learn that these issues have been given a great deal of thought and that there's a good reason for design decisions that I didn't initially perceive.

Aryxymaraki
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Personally, I'd rather fight the purple worm as a company of light infantry than as heavy infantry, since we could just withdraw away any of its damage and have it be slain by ranged attacks with relative ease. Remember that it has only a single unit hit point and a movement of 1/2/3.

Given how weak it is on the battlefield in Battles, I have no problem with it having a low BR.

As to T-Rexes, not quite so sure on that one. My copy of D@W:C has them at 0.235 BR each, and a unit is 5 T-Rexes, giving the unit a BR of 1.175. This is comparable to a unit of orc light infantry or human light infantry (both at BR 1). 5 T-Rexes have a move of 2/4/6, AC 7, 7 UHP, and 6 attacks at -3+. 120 orc (or human) light infantry have a move of 2/4/6, AC 3, 8 UHP, and 2 attacks at 10+.

The primary differences are in potential formation (T-Rexes are always IM, orc infantry are always IF, human infantry can be LF or FF) and in ranged potential (the light infantries can attack at range with one attack at 10+). I don't think this is adequate compensation, and on a battlefield, I would definitely rather have the unit of T-Rexes than the unit of orc infantry. (The human infantry might potentially open up more tactical options, but I'm pretty sure the tactical option of 'charge until they're dead' is the only one the T-Rexes need.)

EHamilton
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The problem with purple worms isn't just that they are valued below infantry, but that they are valued so vastly below infantry. Currently a BR of 0.069 suggests that it takes about 15 purple worms to equal a single unit of light infantry, when it seems to me that the answer should be around half that.

If you want to do an apples-to-apples comparison on speeds -- to avoid the "I just kite them to death with ranged units" issue -- then you could compare the purple worm to a unit of (short sword) goblin light infantry, with BR 0.5 and identical movement. (Or with spears, actually, since the BR calculation assumes spears aren't being thrown.) An equivalent BR gives you 7 purple worms. That'a total of 7 uhp (vs 6 for the goblins), and every other category (AC, morale, attacks, attack throws, saving throws) isn't even close. (Edit: AC values are close, identical in fact.)

I will happily fight a tactical battle where I get seven purple worms and my opponent gets one light goblin company!

But doubling the BR for purple worms (i.e., removing the BR penalty for non-sentient troops) would make for a much more balanced fight of 3 worms vs 1 goblin company. Here the goblins are more durable, but the worms have better armor and an extra attack, so it could swing either way. Again, this just indicates that the tactical rules themselves really need to be imposing some kind of operational penalty for using non-sentients, to justify having this additional modifier in the BR calculation (which already accounts for things like relative speeds and the power of ranged attacks pretty well). Otherwise this is exactly the kind of imbalance we'd expect to discover between the two combat resolution systems.

EHamilton
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After reflecting on this a little more, I actually think that the BR ratio might be correct, at least relative to the classic D&D man-to-man rules. If I imagine a normal Core Rules battle between a single purple worm and 17 goblins (the balanced ratio suggested by the BR values), I actually think the goblins have a very solid chance of winning. The worm can't eat/sting more than two of them per round, and a third of the goblins will be hitting it successfully (hitting on 14+), knocking off about a hit-dice worth of damage with each hit (assuming spears at 1d8). That means that the purple worm will lose about a third of its total hit points per round. And even as it swallows them, they'll still be stabbing it from the inside!

In a narrow tunnel, where it can methodically eat goblins one row at a time, the odds would be more even. But in an open battlefield, where they mob it and attack all together, the goblins probably carve it up by the fourth round, losing less than half their number. Maybe the third round, if they make an opening charge with their spears.

That still leaves the discrepancy between the BR result and the tactical Battles result. But it suggests that maybe the BR result is the more sensible one. Maybe the worms shouldn't be buffed in BR, but nerfed at the tactical scale. So now I'm undecided as to what to do.

Jard
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Isn't ACKs-style cleaving supposed to factor into the calculations though? Can't remember purple worm's stats off the top of my head, but it's got to be able to kill at least 2 or 3 per round.

bobloblah
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In the man-to-man rules it's very dependant on positioning, as spreading out (quite sensible when fighting a Purple Worm!) prevents Cleaving.

EHamilton
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I'd see this as another instance of how fighting underground in close quarters really favors a single strong combatant, and fighting outdoors favors a larger number of weak combatants. Purple worms are big enough that I *think* 17 goblins could find cleave-free attack formations against one, at least when using spears. I'm visualizing about six goblins spread out evenly in melee contact along the 80 foot length of the worm, each with a back row of 2 spear goblins using reach to attack it, just out of cleave range.

But arguably something like a purple worm should receive a longer cleave range, just to avoid getting picked to death by miserable little runts like this. In that case, we'd be back to "BR makes it too weak, and Battles gets it right".

Alex
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Great discussion.

It's exceptionally difficult to make a BR system that can stand up to the many variables that can exist in a game like ACKS. As the comments above show, even a tactical variable such as the amount of space available to fight in can make a huge difference.

The non-sentient penalty exists because, in repeated playtests of D@W:B, we found that non-sentients had some particular vulnerabilities that could be exploited on the battlefield even if they weren't immediately apparent in a mechanical sense. For example, how is the purple worm being controlled? Is it charmed? A simple Dispel Magic will release it from the enemy's control, or a Charm Monster take it over. Does it have creature handlers? A Fireball could kill its handlers, even if it leaves the purple worm alive. And so on. Such decisions tend to emerge in play of D@W:B, but they cannot appear in the context of D@W:C abstract system, so I tried to "build" them into the BRs.

James K
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That squares with the historical approach to dealing with elephants (the closest historical analogue), which tended to focus on killing the handlers or stampeding them back onto their own army rather than killing them outright.

bobloblah
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Legolas disagrees with you.

EHamilton
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If flaming war pigs cause panicked elephant stampedes, then I assume flaming war elephants would cause panicked purple worm stampedes, right?

I do not want to be the way of a purple worm stampede.

EHamilton
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I've noticed a third situation where BR feels too low, in addition to the two given above: Troops where a creature's alternate attack is stronger than the standard attack in mass combat, due to the way cleave factors are weighted, but where the BR seems to be calculated off the primary attack.

An example of this is the minotaur. Currently I calculate the BR of a company of 60 minotaurs as 4.1 based on the bite/gore combo (4.09=3*3*1.09*0.929*0.68*4/6), but as 6.1 based on the use of a 1d10 weapon (and the minotaur +2 damage bonus), which gives 6.13=3*3*1.09*0.929*0.68*6/6.

The value in the table (0.077 per minotaur) seems to be based on the weaker attack mode, rather than the stronger one (which would give 0.1 per minotaur). Although even then it doesn't quite match up perfectly, since I would get 0.067 instead of 0.077 -- so maybe this value was tweaked by hand and the current rating is intentional.

Or as a third possibility, maybe I'm doing something wrong in the BR calculation, since it's got a lot of fiddly math bits in it!

bobloblah
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I hate to say this, but I'm getting the impression that the only way you are going to be sure about a lot of these is by doing extensive play testing, and I don't mean white room scenarios.

Aryxymaraki
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Out of curiosity, did you include the charging bonus for gore?

(The minotaur description doesn't mention it, but they do have "natural weapons suitable for charging" as described under the charge monster special ability, I think they should benefit from it, and I'm curious if including that benefit would change the numbers to line up better.)

EHamilton
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Based on the explanations in Chapter 8 of Battles, it looks like only cavalry and chariot units get to use their charge attacks in a mass battle. There are plenty of spear-armed infantry units that don't get to use charge attacks, so I would guess that minotaurs don't get them either. But I'm not really sure how this works, to be honest.

Also, if charging prevents the use of the bite attack -- not sure on this either -- then it basically balances out, since ACKS uses the BX 1d6/1d6 sequence. Losing the bite is equivalent to gaining double damage on the gore. (This is different from the minotaur in later D&D editions, which has a weaker bite and a better charge.)

If both a charge and a bite can be combined, that would increase max gore/bite damage by a factor of half again (i.e., from 4 to 6 unit attacks), equal to attack with a great axe. That amounts to increasing BR from 4.1 to 6.1 regardless of assumed attack mode -- which would mean that the current BR for minotaurs is definitely too low.

I assume Alex can check and confirm whether or not that's true.

Aryxymaraki
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My assumption was that gore and bite can be combined on a charge, with only the gore dealing double damage.

The Melee Value in Combat Multiplier of the complicated BR formula (Battles page 93) counts the maximum damage dealt during a charge (which is given as 3 for a unit of humans with spears).

My assumption is that the gore would work the same as the spear; because they have a weapon well-suited for charging, instead of going from 4 to 6 attacks, they'd still have four attacks but would do an extra point of damage on the first successful charge attack in a round. (This is the same rule as humans armed with spears; Battles page 20.) Though apparently only Formed Foot (or any mounted) qualify for this bonus, and minotaurs using natural weapons would not normally be FF.

So in summary, I don't know what I'm doing, I'm just kind of saying things.

EHamilton
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I'm pretty sure that human foot units only get a charge bonus if they are in FF formation.

Although I agree that if there's any good time to make an exception and allow charge damage for an IF unit, it's when that unit is full of creatures with the heads of angry bulls.

EHamilton
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I figured out why I was getting 4.1 instead of 4.5, and a bunch of other small discrepancies. It was a mistake in how the spreadsheet was doing the ratio of rounded to unrounded attacks.

Alex
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I am afraid I don't follow your Minotaur BR calculation.
BR = (Unit AC) x (uhp/8) x (Morale Multiplier) x (Speed Multiplier) x (Formation Multiplier) x (Combat Multiplier) / 6

Unit AC: 3
UHP: 24
Morale Modifier: 1.253
Speed Multiplier: 0.929
Formation Multiplier: 0.675
Combat Multiplier: (3.97/4) * 4 = 3.97

This leads to 0.0779 per creature, 4.67 per unit (rounded to 4.5).

The BR is for unarmed and unarmored minotaurs. If you equip them with weapons and armor they will have a superior BR.

EHamilton
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One more example, and this one is leaving me completely baffled: ghouls seem to have a much higher BR than I'd anticipate. Currently ghouls are at 0.289, which means that a full company of them would be BR 34.68. That's even better than wyverns (the highest BR units I've used in a playtest), and wyverns are basically ultra-fast flying ghouls, since poison/paralysis use such similar rules. That can't be right, can it?

The base unit has stats that would only give it a BR of around 2, so clearly almost all of the additional rating comes from paralysis. But even given ghouls a tactical modifier of 1.0 (human-level sentience), I only get a special attack bonus of 10.0, which would put them around BR 12.0 (or around 0.1 per ghoul).

I can't even make a guess as to why this is such a large discrepancy.

A couple of side questions/notes:

1. Frequently when I multiply out the BR per troop by the size of a company (as above), I get an unrounded answer. This even happens when the unit is just a single creature (i.e. a giant roc is 20.53). Why are these rounded off to the nearest 0.5, like human and demihuman troops? This is really obvious with skeletons (120 * 0.005 = 0.6) and zombies (120 * 0.01 = 1.2), but there are many other examples. Those nice round numbers for skeletons and zombies make me wonder if I am missing some rule about certain types of companies having fewer than 120 troops (maybe just 100, to give those values).

2. Confusingly, giant roc is actually used as an example of how to use rounding, and is given a BR of 16 in the text on page 95 of Battles -- which is quite different from the value of 20.53 in Campaigns. My own attempted calculations suggest that it should be around 20.

3. The special attacks section of the table on page 95 is labeled "Special Defense", and the special defenses section is labeled "Special Attack".

Alex
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The published Battle Rating for Ghouls is entirely wrong.
- I wrongly assigned them a Special Attack BR bonus of 1,750 instead of 1,000 for their paralyzing touch
- I wrongly assigned them a Special Defense BR bonus as if they were immune to normal weapons, which they are not.
The correct BR for Ghouls is 0.099 per creature, or 12 per company.

The correct BR for Giant Rocs is 20.5, according to my spreadsheet. I do not see any evident errors in the spreadsheet. The example on p.95 of D@W:B is not correct because a Giant Roc's BR without its flight is 7, not 2.5.

I don't understand your question about BR rounding. Could you re-phrase it?

EHamilton
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For the BR rounding issue, my expectation was that every full (company-sized) unit would have an BR that was rounded to the nearest half-integer, since the rounding happens before dividing by the number of troops in a company. So the effect of multiplying the per-troop BR of a man-sized troop by 120 should always give a number that ends in .0 or .5.

Some of the troops give unit-size BR values that haven't been rounded. For example, 120 zombies (BR 0.01 per zombie) would give a unit with BR 1.2, which isn't rounded down to 1.0 like I would have expected. If it had been rounded to 1.0 before dividing, as seems to be for all human/demihuman/beastman troops, the BR per zombie would be 0.008 instead (really 0.008333333...).

And in other news, it's really easy to misspell "beastman" as "bestman", which makes me visualize a gnoll in a tuxedo giving a wedding toast.