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

June 28, 2005

Basic Functional Hit Points

Calculating a simple means to give a linier value to the damage output of a figure was to me a straightforward task (see my previous post on Basic Functional Damage). Calculating a value for durability was not nearly as straightforward as I had hoped. I had many failed formulas that I was unsatisfied with, but I will spare you the details. Ultimately what I decided to do was what Guy suggested in a similar thread on the WOTC message boards: convert AC and other durability factors into an equivalent amount of HP. Factors I need to consider are AC, Morale (level and fearless), and Conceal. And the command rating of a commander can contribute to the functional HP of a figure incrementally. For simplicity rally is not considered.
  • First, I only take half of the printed HP value of the base. This is the only "Guaranteed" HP you have.
  • Next, I multiply the remaining half by the figures level/save, and divide by 20.
  • For Fearless creatures, I consider their level to be 20, effectively giving the other half of their HP.
  • Next I take the AC of the figure, subtract a normalized attack bonus, and divide by 20 to get the hit percentage, and then multiply that by the figures HP.
  • Finally I take the conceal percentage, multiply that by the functional HP at this point, and add it again.
The one item I had the most concern about what to use for the normalized attack bonus. I finally settled on +10. Why +10? Only one createure has an AC lowere than 10, the oddball Ochre Jelly has an AC of 4. But the lowest AC you will see in serious play is AC 10, and you will see it in the CG Inspired Frenzy band. My reasoning was that the lowest AC should offer no additional "functional HP." This also gives a baseline for a number, factoring in Fearless and ignoring Burnout that gives the Frenzied Berserker 90 Functional HP.

From this, we can derive the following formula, for what I shall call "Basic Functional Hit Points"

HP *(Save + 2*AC)*19 + Conceal
4020

For creatures without the Conceal ability Conceal = 1
For Fearless creatures Save = 20

What results does this give us? The top 10 are...


FigureFHP
1Large Silver Dragon240
2Fire Giant196
3Stone Golem189
4Frost Giant175.5
5Thaskor175
6Aspect of Bane174
7Large Red Dragon171.88
8tZombie White Dragon162.5
8tAspect of Nerull162.5
10Vrock155.25

June 21, 2005

How Many Rounds to Play?

I've noticed that the available rules for sanctioning really don't include a table any more for "how many rounds to play for x # of players." This is especially useful for events like the qualifiers and pre-releases with top-2^n knockout rounds. The premise was to show how many rounds to play and guarantee all of the no loss and one loss players a spot in the knockout rounds, and making the two loss crowd depend on early and solid wins (mostly for game win % and strength of opposition tie breakers).

That seems to be a simple enough standard to derive a solution from. In a Swiss format assume perfect point groups, ignore ties, and ignore a degenerate case where the top players all play each other in early rounds, and a chart can be derived. But since I am a computer scientist and not a mathematician I wrote a program to get my answer the brute force way (python 2.4 source code available here).

The first chart matches my memory of my days in MTG, some poor schmuck (wasn't me) signed up as the 213 player just before registration closed and forced a 9th round at one qualifier I was at.

PlayersRounds
4-81
9-102
11-163
17-244
25-405
41-646
65-1287
129-2128
213-?9

But this table was predicated on top 8. D&D Miniatures has recently gone to top 4s, and the guarantee of making it in with only one loss ramps up the required rounds quicker.

PlayersRounds
41
5-83
9-104
11-165
17-326
33-527
53-968
97-1609
161-?10

The bizarre thing is that it doesn't make the tourney go any quicker round wise, in some cases (like at 33 players) it makes the tourney go a round longer! But when the prizes are only given to the top four, the upshot is that if you go to the break rounds you are guaranteed a prize. Otherwise top four prizes and a top 8 means you have one do-or-die round, even if you played the tourney perfect to this point.

June 14, 2005

Figureing out the Golaith Barbarian: How Good is the Re-Rolled Attack?

The Goliath Barbarian, with it's reroll attack ability, poses a rather interesting number crunching problem when analyzing the statistics of a warband, just how good is it's ability? Clearly the piece is worth more than the +10/+5 (20) that is listed on the card, but just how much more? This is also useful to star wars players, since you can spend a force point to re-roll an attack roll you missed on.

To answer this question, I am going to resort to what amounts to applied elementary probability and statistics, and if it makes your head hurt just skip down to the chart. I call it elementary because I don't do this stuff for a living and it makes sense to me, therefore it can't be all that difficult. What I did was convert the "roll needed" to hit to a probability of hitting, at a simple 0.05 probability per side that can hit. Then I squared that probability to get the odds that I will miss twice. Once on the normal attack and once on the re-roll. The rest of the probability, split basically 50/50 is the odds I hit on the normal roll or the re roll. But I just calculated those together. Then I figured what an equivalent "hit number" would be for those odds, the difference between the two is the benefit from using the re-roll. Here is a chart summarizing the numbers.

Roll
Needed
2x Miss
Odds
Effective
Roll Needed
Net
Bonus
200.09819.050.95
190.19017.201.80
180.27815.452.55
170.36013.803.20
160.43812.253.75
150.51010.804.20
140.5789.454.55
130.6408.204.80
120.6987.054.95
110.7506.005.00
100.7985.054.95
90.8404.204.80
80.8783.454.55
70.9102.804.20
60.9382.253.75
50.9601.803.20
40.9781.452.55
30.9901.201.80
20.9981.050.95


Armed with this information we have our answer, about +3/+4 on most attacks. Against a Large Silver dragon it's like having a +14/+5 attack (+13/+5 if buffed). Against an Orc Champion it's +10/+10 (+13 on a single attack), against an Ogre Ravager it's +10/+10 or +14 on a single attack. Against a Frenzied Bezerker it's +10/+8, not so special there. Between the primary and secondary attacks it is most effective against ACs between 15 and 23, i.e. most of the beaters!

Here is a quick comparison chart for a Goliath re-rolling an attack against a particular AC.

Primary

Secondary
30+11

25+6
29+12

24+7
28+13

23+8
27+13

22+8
26+14

21+9
25+14

20+9
24+15

19+10
23+15

18+10
22+15

17+10
21+15

16+10
20+15

15+10
19+15

14+10
18+15

13+10
17+14

12+9
16+14

11+9
15+13

10+8
14+13

9+8
13+12

8+7
12+11

7+6

June 6, 2005

A Balanced Solution to the CE Hordes: Making CE "Hate" Miniatures

Even with he banning of the Drider the CE bands are still running roughshod over most of the field. While not 100% dominating they are shaping the field in that only skilled play or another CE band will be a reliable way to beat them. DeathKnell was supposed to provide LE the minis it needed to be on top, but the old big stick standbys are still ruining the LE fun.

What is really needed is minis that are decent to OK for their faction but are ones CE would just hate to see. However they cannot strictly be better than the other minis or else we have merely set a new standard for minis.

Honor Guard
Lawful Good; 24 points; Made up (1/1, Uncommon) Humanoid (Human)
Level: 6
Speed: 6
AC: 15
HP: 55
Melee Attack: +11/+6 (5)
Courage against Evil (Gains Fearless if this mini can see an Evil Enemy)
Chaotic Bane (Melee Attack +2, Melee Damage +10 against Chaotic)

Against a LG band, A Warforged Hero is strictly better. Against a LE/CG band the Hero is slightly better. Against CE? Load up your warband! The Honor guard dislikes chaos and evil, but it just hates chaos and evil.