The Miniatures War College
Advenio paratus. Egressus melior paratus.
D&D Miniatures strategy and analysis.

February 25, 2005

Damage Efficiency

Last week I talked about a simple way to calculate the "funcitonal damage" that basic attacks can do. I've calculated a spreadsheet of all 313 200pt figures (not 314, King Snurre isn't legal in non-epic or non-extreme formats). So who comes out on top melee wise? Not a suprising list, but not a list that gives insight into the DDM meta-game.

Single AttackFull AttackAttack Average
Fire Giant
25.00
Fire Giant
43.75
Fire Giant
34.38
Frost Giant
21.00
Eye of Gruumsh
37.50
Eye of Gruumsh
28.13
Frenzied Berserker
21.00
Stone Golem
36.00
Frost Giant
27.75
Eye of Gruumsh
18.75
Frost Giant
34.50
Frenzied Berserker
27.75
Stone Golem
18.00
Frenzied Berserker
34.50
Stone Golem
27.00
Orc Champion
16.25
Drizzt, Drow Ranger
30.00
Aspect of Bane
21.75
Hill Giant
16.00
Clay Golem
28.00
Orc Champion
21.25
Aspect of Bane
15.75
Aspect of Bane
27.75
Clay Golem
21.00
Ogre Ravager
15.00
Aspect of Orcus
27.00
Drizzt, Drow Ranger
20.6


Yes, those sure are some big hitters, but how many of them do you actually see in a tournament? Roughly half. Clearly functional damage alone isn't telling the full story. But if we take the functional damage, and divide it by the cost of the figure we get a much more telling table...

Single AttackFull AttackAttack Average
Abyssal Maw
0.75
Eye of Gruumsh
0.85
Abyssal Maw
0.75
Orc Warrior
0.67
Abyssal Maw
0.75
Orc Warrior
0.67
Orc Brute
0.66
Orc Champion
0.67
Orc Brute
0.66
Orc Berserker
0.56
Orc Warrior
0.67
Eye of Gruumsh
0.64
Mountain Orc
0.50
Frenzied Berserker
0.66
Orc Berserker
0.56
Orc Spearfighter
0.50
Orc Brute
0.66
Orc Champion
0.54
Krusk, Half-Orc Barbarian
0.47
Grick
0.60
Frenzied Berserker
0.53
Ogre
0.46
Ogre Ravager
0.59
Mountain Orc
0.50
Half-Orc Barbarian
0.44
Red Samurai
0.58
Orc Spearfighter
0.50


Seen those figures in a tournoment before? I have, except for the Orc Spearfighter (yes, I played against a multiple Ocre Jelly, Grick, Shambeling mound warband, thank goodness for the Gith Renegades ranged attack!).

Where does the Fire Giant stand effeciency wise? 0.21/0.37/0.29 ranking 78/38/53.

So to answer the obvious question of "Why don't we see too many Fire Giant Bands?" The effeciency is just so low that regardless of the skill level, you will likely do better with an Orc Hoard or a Bezerker Band. For goodness sake a Stonechild (0.38) is a better buy!

February 22, 2005

Late Post

My post will be coming this week, possibly thursday or friday. I've got a policical science essay, midterm, a large Computer Science lab, and two smaller ones. All with one less day to boot.

February 15, 2005

Posting Frequency

I will be going to weekly posts unless I get a good backlog of typed up posts. Look for them Tuesday Evenings.

Basic Functional Damage

The basic measure of the offensive capabilities of a Skirmish figure will be what I call "Functional Damage." In other words, averaged over the long run how much damage will my figure be dishing out? For melee and ranged attacks, there are some metrics that can be derived immediately.

Ignoring critical hits and critical misses, the long run damage is the damage per hit times the odds you will actually hit. This is where basing things off of a single d20 makes the math easier than 2d6 or other dice. (d% makes it very easy, but still requires 2 dice). For every number that you can roll to make the hit you have a 5% chance or a probability of 0.05 to connect. From this we can derive an equation based on AC for the amount of damage we can deal...



AttackBonus - AC + 21* Damage
20


The magic number 21 is added so that a +0 will have one chance to hit an AC of 20. For full attacks, it is merely the sum of all of the functional damage for each of the bonuses.

This equation isn't perfect. It starts to break down when the bonus and AC difference approaches 20 and does weird things after then. However, we cannot calculate 17 odd values for each different figure, and we really want one or two numbers (full and single) for each figure. So for simplicity we should pick a reference AC to measure all other attacks against. What number should that be? Well, a nice round number like 21 would make the equation very easy to handle, canceling out the AC and the magic constant.

Now if we pick 21, the actual effective AC will be 20. Why? Well, now we bring in critical hits. When you have only one chance to hit a target it is always going to be a critical and (ignoring immunity to critical hits) is in effect a second chance to hit. So a +0 person swinging at an AC of 20 will do twice it's damage on a 20, and none otherwise. Also, we can conclude that immunity to critical hits is worth about 1 point of Armor Class (ignoring the sneak/death attack benefits).

By picking a reference AC of 20 this breaks down completely below +1 and above +39 to attack. But since ultra-extreme figures do not exist (Regdar, Epic OozeMaster anyone?) and making out of command MongrelFolk the main melee threat will have a predictable outcome the choice will be sufficient.

Next week I will apply the smell test and run this formula through all of the creatures legal in 200 point play: all 314 of them. I won't post all of the results but I will pull out some very interesting observations that have been all but confirmed in the field.

February 9, 2005

Passing a phase

As a brief review, where have we come in our tale? First, I addressed why you would want to make a warband with a large number of figures. There are many valid reasons, but the reason with the most effect on the game is to create Overactivation. Overactivation is such a big deal you want to use it or protect against it, mostly by using more figures. The problem is, large warbands rarely finis a game inside of an hour, and too many games are called on time. It is so reliable that many warbands plan to win on time rather than outright. Then, I looked briefly at a recommended solution to drop the warband limit to 8 figures, and concluded that it really won't address the cause of the large numbers of creatures, just limit the impact.

So what, you may ask, is my idea to fix the problem? Well, it has to address reliable overactivation. I feel that it doesn't need to eliminate overactivation but if you can't predict and rely on it's location in the phase order you will play differently, and instead play based on tactical advantage rather than back-loading all of your effective pieces. My solution is also based on my recommendation when R&D asked for suggestions for tournament format changes back in August of 2004. It is, however, a bit different.
Passing a Phase - When it is your turn to activate two creatures you may instead choose to pass your activations and your opponent will activate two more creatures. You may only do this when the number of creatures with activations remaining your opponent controls is greater than the number of creatures with activations remaining you control. If you both have the same number of creatures with activations remaining you may also pass, but only if you did not act first in the round. If you have more creatures with activations remaining or you have the same number and you activated first in this round, you may not pass.

A slight change on act/defer. There isn’t as much mental math, and I hope it is a rule that is stated more simply. But like Assault/Plunder there are many small nuances that may need to be explained.

First and foremost, it allows you to interrupt overactivation blocks of your opponent. This is because you can judiciously pass activations and make your opponent activate two more creatures when he was hoping to hold them off until later. So there may be multiple overactivation blocks during the round but their location and size is not entirely predictable or reliable. Hence, you can bring a 6 figure band against an 11 figure band and not be looking down the wrong side of a 5 to 7 figure activation, unless you really want to.

Second, the tie rule preserves the decision made by the initative winner to play or to react. This may require some mnemonic, like an arrow pointing to who must act on equal figures. But if you win initiative you still have (for the most part) the power to say "I go last."

This also preserves the initiative rule impact of a few creatures, Tactics from the Moon Elf Fighter, Ryld Argith's Improved Initiative, and all four creatures with Dual Activation. Moon Elf can still cause an overactivation of his own. Ryld's control of initiative still means something. And finally, Dual Activation still provides for minor abuse. This last one needs some clarification: since the rule asks you to look for "creatures with activations remaining" you don't count the choker twice, and after he moves once he still counts. Hence you can use dual activation to gain a slight overactivation or battle one.

Finally there is one quirk, I call it an off by one error. If one band has an odd number of figures it can always be activating last against a band with even numbers. But the impact is very slight: an underactivated block, i.e. only one activation. This slightly improves the value of dual activation, but since it encourages specific figures or a smaller warband, it seems ok to me.

This may not be as cut and dried as the 8 figures rule, but in my opinion it addresses the cause of the warband bloat rather than addressing the symptom.

February 7, 2005

Long Games and Reducing the Warband Limit.

As I addressed previously, the advantages of overactivation and the need to defend against it are what are driving the large size of the warbands we see today. But what impact does this have on the game? A very bad one.

The analysis in the following two paragraphs I first saw posted by Guy Fullerton, the WOTC NetRep for D&D Miniatures. I will paraphrase it since I am to lazy to find the original post on the WOTC boards.

The crux of the argument revolves around the assertion that the number of activations in a game is relatively fixed. If it takes you 30 seconds to a minute per move, and you spend 10 minutes setting up your warband and tiles in a game, then you have between 50 and 100 activations per game. For simplicity let's split the difference and say there are 75 activations. If both players bring a 11 figure warband to the table, and each loses one figure a round, then when time is called for the round there is one figure left on the board (22 + 20 + 18 + 16). This activation number may be a bit aggressive, and is probably closer to the 50 activations per round in the 200 point game since most games get called between the third and fourth round. So 60 seems to be a reasonable middle for the calculation.

Now, if the warband limit was dropped down to, say 8 figures (like it was in Extreme) then the numbers get a little better. Instead of calling time during turns 3 and 4, you call time between turns 5 and 6 (16 + 14 + 12 + 10 + 8). It is also likely that more games will win on victory in that case because of victory accelerators like assault/plunder points and enhanced damage and also that the speed of figure removal tends to increase as the game goes on. [Guy Fullerton, massive paraphrase]

This solution is reminiscent of what they have done with MTG when they first sanctioned play. The rules originally required 40 card decks, but constructed decks require 60 cards (smaller is better in magic). As a consequence nearly all constructed decks run at the 60 card limit. This wasn't done to deal with the speed of the game, but to deal with degenerate combos. The problem is that it failed. They had to resort to other techniques like banning cards to break combos, like the Pros-Bloom decks in Mirage block and anything that effectively uses the Tolarian Academy.

Changing the numbers around in MTG alone didn't address the core of the combo problems (that some cards should have never been printed the way they were). Similarly I don't think that reducing the warband limit will address the core cause of large warbands in the current environment. The only way to counter or create reliable overactivation is to bring large quantities of figures. Almost all warbands will just bring 7 or 8 figures (like is done in Extreme), and minions and summons will again become a viable way to create overactivation.

Next I will propose a solution, somewhat radical, that will address reliable overactivaiton and reduce the incentive to bring large numbers of creatures.