Statistics
Mathematic analysis of Warhammer Fantasy Battle
Preface
After having lost four battles in succession I thought about a mathematical analysis of Warhammer.
The idea was making a statistical analysis of some troop types to determine the best one for a given job.
After doing a lot of computation and playing some battles afterwards I concluded some points:
- Knowing the odds doesn't make you play better, only play more relaxed.
- The list is very funny to read
- To win Warhammer you have to be mean, really mean.
Some facts about Dices
Following are some formulas for calculating odds.
For those of us, who now it already, please skip this chapter.
With a dice you can roll six numbers. So the chance to roll a specific number is 1/6 or 0.166.
In Warhammer the odds are somewhat different because most of the times you have to roll over a given number.
Here the odds are as shown in the table.
| Number to roll | Chance as fraction | Chance as real number |
|---|---|---|
| 6+ | 1/6 | 0.166 |
| 5+ | 2/6 | 0.333 |
| 4+ | 3/6 | 0.5 |
| 3+ | 4/6 | 0.666 |
| 2+ | 5/6 | 0.833 |
| 1+ | 6/6 | 1 |
If you have more as one dice to roll you just multiply the chances.
So, if you need a 4+ to hit and a 3+ to wound you have a chance of 0.5 * 0.333 = 0.1665 or one sixth of the attacks does wound.
Notice: the sequence of the dice rolls is not important.
Destroyed Points in shooting
At first I calculate a number which is very important for the Skaven player.
The points-destroyed-in-shooting-number (PDISN).
It is very easy to imagine that a Skaven general will put the troops with a low number in front of the battleline.
Ok, now how to I calculate this number. First we get a standard bowman. He shoots with BS 4 and S 3.
This bowman shoots e.g. at a stormvermin.
So 4+ to hit, 4+ to wound and the skaven has a light armour which gives him a 6+ save. We get:
1/2 * 1/2 * 5/6 = 0.208.
Only a fifth of the bowmen will kill a skaven and kill 11.5 points (a normal stormvermin).
So we get 0.208 * 11.5 = 2.4 points destroyed per shot.
| Trooptype | P(wound) | P(save) | P(hit) | points | PDISN |
|---|---|---|---|---|---|
| Stormvermin | 1/2 | 5/6 | 1/2 | 8 | 1.7 |
| - with shield | 1/2 | 2/3 | 1/2 | 9 | 1.5 |
| Clanratwarrior | 1/2 | 2/3 | 1/2 | 5 | 0.83 |
| Gutterrunner | 1/2 | 1 | 1/3 | 12 | 2 |
| Slaverat | 1/2 | 1 | 1/2 | 2 | 0.5 |
| - with shield | 1/2 | 5/6 | 1/2 | 3 | 0.63 |
| Plague censer bearer | 1/3 | 1 | 1/3 | 12 | 1.3 |
| Plague monk | 1/3 | 1 | 1/2 | 6 | 1 |
| Poison Wind Globadier | 1/2 | 1 | 1/3 | 10 | 1.7 |
| Warpfire Thrower | 1/2 | 5/6 | 1/3 | 70 | 9.7 |
Now, what do we learn from these numbers?
First, don't let them shoot at your gutterrunners.
This is one of the most expensive troops to get shot at except from a weapon team, but they can take cover near their unit..
Next look at the PDISN of the plague censer bearers.
The skirmishing formation plus their high toughtness helps them to survive.
Buy more slaverats (neek neek).
Now here is the best of all.
Ok, take a look at the numbers for yourself, I don't want to tell you all the things I discovered.
I did the same thing for Lizardmen. Here it is:
| Trooptype | P(wound) | P(save) | P(hit) | points | PDISN |
|---|---|---|---|---|---|
| Skink | 2/3 | 1 | 1/3 | 8 | 1.8 |
| - with shield & javelin | 2/3 | 5/6 | 1/3 | 10 | 1.85 |
| Kroxigor | 1/3 | 2/3 | 1/2 | 50/3 | 1,85 |
| Saurus Warrior | 1/3 | 2/3 | 1/2 | 11 | 1.2 |
| Templeguard | 1/3 | 2/3 | 1/2 | 15 | 1.6 |
Conclusion
Now, what do we learn from he above statistics?
If you play with skaven only buy slaverats and plague censer bearer.
If you play lizardmen be carefull with your skinks.
If you follow this rules you will lose every combat but make yourself some friends (which laugth behind your back).
Now serious. The numbers we just calculated can't tell you what type of troops you should include in your army, but it can tell you which regiment is most vulnerable against shooting.
So this tables only show which troops are most expensive when shot at.
Last updated November 08 2008