Using Mathhammer to Balance your Game

Mathhammer assists Game Design using the 216 System when designed around balanced games, not chasing flavor-of-the-month meta. Using The World That Was as an example, you can see how plateaus in stats ensures no single model dominates on the field.

DISCIPLINE/ACCURACY TABLE
Skill 1 2 3 4 5 6 7 8 9 10 11 12
To Hit 5 5 4 4 4 3 3 3 2 2 2 2

Average Attacks to Destroy Unit: # To Wound/% To Wound
To determine the number of Attacks to destroy a Unit, divided the number of Wounds you want to cause by the percentage chance of causing a Wound. To wipe out a Unit of 5 Dwarf Veterans (5 Wounds), the Orc Warriors (12.5% to cause a Wound) would divide 5 (number in Unit) by 0.125 (percentage to cause wound) for 40 Attacks to destroy the Dwarf Veterans. A Unit of 16 Orc Warriors with two hand weapons can bring 32 Attacks only if they surround the Dwarf Veterans entirely. Orc Warriors with double-hand weapons (20.8% to cause a Wound) would need an average of 24 Attacks (5/.208 = 24) to destroy 5 Dwarf Veterans. That’s almost 2 Rounds of Assault for a Unit of 13 Orc Warriors with double-hand weapons surrounding the Dwarf Veterans that strike last due to reduced Initiative. In both cases the Orcs would be suited to form in Skirmish Formation in order to surround the Dwarf Veterans and bring their numbers to bear. A Unit of Orcs in Ranked Formation can bring 7 Attacks total with corners touching on the sides of the front Orc rank, dropping their survival considerably.

ARMOR SAVE MODIFIER TABLE
Attack Strength
1 2 3 4 5 6 7 8 9 10 11 12
+1 0 0 -1 -2 -3 -4 -4 -4 -5 -5 -6
Roll Modifier

TO WOUND TABLE
Strength 1 2 3 4 5 6 7 8 9 10 11 12
To Wound 5 5 4 4 4 3 3 2 2 2 2 2

Average Damage Output: # Attacks x % To Wound
To determine a Unit’s average damage output, multiply the number of attacks with their equipped weapon (damage output = 1 Wound) by the chance of causing a Wound. The Unit of 16 Orc Warriors with two hand weapons (32 Attacks with 12.5% chance to cause a Wound) will kill 4 Dwarf Veterans on average (32x0.125 = 4) if they can surround the 5 Dwarf Veterans. But that’s not taking into account the Dwarf Veterans’ Rhino Hide saving them 20% of the time. The Unit of 13 Orc Warriors with double-hand weapons (13 Attacks with 20.8% chance to cause a Wound) have chance to slay 2.7 Dwarf Veterans on average (13x0.208), which increased by removing the Dwarf Veteran’s Rhino Hide Save.

CONSTITUTION SAVE “RHINO HIDE” TABLE
Constitution 1 2 3 4 5 6 7 8 9 10 11 12
Rhino Hide Save - -- -- 6 6 6 5 5 5 4 4 4

“RHINO HIDE” MODIFIER TABLE
Attack Strength
1 2 3 4 5 6 7 8 9 10 11 12
- 1 0 0 +1 +1 +1 +1 +2 +2 +2 +3 +3
Rhino Hide Modifier

How about the Dwarf Veterans when they attack the Orc Warriors?

1. Total number of roll results that result in a successful Hit (4+): 4, 5, or 6 = 3 roll results.
2. Total number of roll results that fail the Armor Save (No Save, with 5 Strength Modifier of -2 for Armor Save): 1, 2, 3, 4, 5, 6 = 6 results since no roll is required.
3. Total number of roll results that result in a successful Wound (4+): 4, 5, or 6 = 3 roll results.
4. Multiply results together: (To Hit & Failed Armor Save) 3x6 = 18. (Include Successful Wound) 16x3 = 48.
5. Divide the possible dice rolls (48) by 216 (total number of 3d6 rolls) to determine the percentage chance to cause a Wound: 22% chance of causing a Wound. AND the Orc Warriors lose their Rhino Hide Save (Constitution 4 = 6+ Rhino Hide Save) due to the Dwarf Veterans’ Strength of 4 (-1 Rhino Hide Save modifier).

5 Dwarf Veterans have an average damage output of 1.1 Orcs. (5 Attacks x 22% chance to Wound.) The 5 Dwarf Veterans kill 1 Orc Warrior on average, but will require an average of 72 Attacks to destroy 16 Orc Warriors with two hand weapons. (16 Wounds to cause divided by 22% to cause a Wound or 16/.22 = 72.72) That’s 5 Rounds of Assault to wipe out 16 Orcs. The 5 Dwarf Veterans would require an average of 36 Attacks to destroy 13 Orcs with double-hand weapons (13/.22 = 36) for 4 Rounds of Assault.

Points per Wound: Damage Output/Unit Cost
To determine Unit effectiveness, divide cost of the Unit by average damage output.
5 Dwarf Veterans (80 points) with hand weapons (average damage 1.1) cost 72 points per unsaved Wound against the Orc Warriors.
16 Orc Warriors with two hand weapons (80 points) with an average damage output of 4 shows each Wound cost 20 points per unsaved Wound. (80/4 = 20).
13 Orc Warriors with double-hand weapons (78 points with average damage 2.7) cost 28.8 points per unsaved Wound.

Divide these numbers by the cost of a Wound of the Unit being Assaulted.
A Dwarf Veteran costs 16 points.
16 Orc Warriors with two hand weapons cost 1.25 points per unsaved Wound against Dwarf Veterans.
13 Orc Warriors with double-hand weapons cost 1.8 points per unsaved Wound against Dwarf Veterans.
16 Dwarf Veterans cost 14 points per unsaved Wound against Orcs with two hand weapons.
16 Dwarf Veterans cost 12 points per unsaved Wound against Orcs with double-hand weapons.

Dwarf Veterans are highly effective until they are overwhelmed in numbers. The Dwarf have survivability on their side – being able to take a hit – while the Orcs have the weight of numbers that can be brought to bear against their opponent. A Unit of 5 Dwarf Veterans can stand toe-to-toe against a Unit of 13 to 16 Orc Warriors and survive for a couple of rounds, if not hold the line until reinforcements arrive.

10 Dwarf Veterans can take out a Unit of 10 Orcs before the Orc reinforcements arrive.

No Plan Survives the Battlefield
Using the 216 System assists in ensuring Game Balance for the players who choose your Game to invest time and money. This System also provides Game Developers the tools needed to balance their Game and determine which Units need tweaking before release. Just remember this does not take into consideration the unexpected events or circumstances that occur on the battlefield. We cannot plan for every outcome, no matter how hard we try. However, a balanced System will ensure flexibility and fairness for every participant in your Game.

Alternative 216 Systems

Numerous games in Historical, Fantasy, and Science Fiction wargames exist using the 216 System. Below are examples of these systems

Alternative Ranged To Hit Chart using 216 System

For example, a Discipline of 6 when rolling against a Discipline of 3 would need to roll a 2+ to Hit. A Discipline of 3 when rolling against a Discipline of 6 would need a 6+ to Hit. A Discipline of 4 when rolling against a Discipline of 3 would need a 3+ to Hit. A Discipline of 5 when rolling against a Discipline of 6 would need a 5+ to Hit.

For example, a Discipline of 6 when rolling against a Discipline of 3 would need to roll a 3+ to Hit. A Discipline of 3 when rolling against a Discipline of 6 would need a 5+ to Hit. A Discipline of 4 when rolling against a Discipline of 3 would need a 3+ to Hit. A Discipline of 5 when rolling against a Discipline of 6 would need a 4+ to Hit.

For example, Strength 6 rolling against Constitution of 3 would need to roll a 2+ to Wound. Strength 3 when rolling against Constitution 6 would need a 6+ to Wound. Strength 4 when rolling against Constitution 5 would need a 5+ to Wound. Strength 5 when rolling against Constitution 4 would need a 3+ to Wound.

Note: these systems in low point costs Armies allow an Avatar to dominate the battlefield while the Rank-and-File are relegated to watching the heroics. Unless that is the goal of the game, be cautious of imbalance when using these 216 System alternatives.