- Joined
- Feb 6, 2012

- Messages
- 44

I noticed that all mathhammer posts I have read so far on this and other forums always compute the Expected Value of result of a close combat or ranged attack etc.

I have yet to see a thread which takes into account the VARIANCE

For those not entirely sure what the word means, here is an example.

Suppose we have a unit which has a ranged attack which can wipe out 216 wounds worth of enemy models anywhere on the table top with no saves of any kind allowed. For this attack to work the player must roll 2 sixes on 2 dice (ie. 1/36) chance.

Suppose also that we have another unit which can wipe out 6 wounds of enemy models anywhere on the table top with no saves of any kind allowed. This attack auto hits always.

Using conventional mathhammer we would get that both units do 6 wounds on average. While it is not clear which unit is better (I would tend to say that the second one is), it is clear that these are very different units. We would say that the second units damage output has zero variance (its always 6), while the other unit has a very high variance. (almost always 0, and very rarely 216).

How does this apply to real-life (ie. actual warhammer uints)? Consider our beloved 20 grave guard 5 wide with hand weapon and shield vs 5 frenzied chaos knights charging our grave guard. The mathhammer would tell us that the knights cause 5.6 wounds and we cause 1.2 wounds. We lose by about 4.6. However, we don't need math hammer to figure out that most (if not all) kills we get against the chaos knights will be because of killing blow. Therefore, this combat has an EV of 4.6 but also a high Variance. (if we don't do any killing blows we will get crushed next turn, if we cause say 2 killing blows we will proabably kill the knights next turn).

What does all this mean? In general, it is better to have low variance then high variance. In some situations though high variance tends to favour VC (or any other unbreakable army/unit) over live armies. The reason is simple. Say that on average our unit X loses to our enemies unit Y by 1. If this particular combat would have no variance, we would always lose by 1. However, if the variance was large (ie. the results oscillated a lot), then (for example), the result would be between us winning by 6 and our opponent winning by 8. If we lose by 8 we have now lost 7 more models then expected (from combat res anyway). This is bad but not a disaster for us usually. On the other hand, if our opponent losses by 6 and is not stubborn/steadfast he/she might have a problem. This means that grave guard (for example) are slightly better then mathhammer would have us believe because of their higher variance. It is possible to take variance into account exactly when computing the effectivness of a unit via traditional mathhammer but would be very tedious.

Our wraith's chill grasp attack is very interesting because it is a very low variance attack compared to its regular attacks. Given a particular situation during a battle, we may opt to use one attack or the other not only based on the Expected value but also the need for higher/lower variance, or just whatever we feel like

Our (almost useless I think) Master Strike is even worse then previously thought becaue of it high variance.

I could expand more on the mathhammer but I am getting a little sleepy and don't even know why I wrote all this...

I have yet to see a thread which takes into account the VARIANCE

For those not entirely sure what the word means, here is an example.

Suppose we have a unit which has a ranged attack which can wipe out 216 wounds worth of enemy models anywhere on the table top with no saves of any kind allowed. For this attack to work the player must roll 2 sixes on 2 dice (ie. 1/36) chance.

Suppose also that we have another unit which can wipe out 6 wounds of enemy models anywhere on the table top with no saves of any kind allowed. This attack auto hits always.

Using conventional mathhammer we would get that both units do 6 wounds on average. While it is not clear which unit is better (I would tend to say that the second one is), it is clear that these are very different units. We would say that the second units damage output has zero variance (its always 6), while the other unit has a very high variance. (almost always 0, and very rarely 216).

How does this apply to real-life (ie. actual warhammer uints)? Consider our beloved 20 grave guard 5 wide with hand weapon and shield vs 5 frenzied chaos knights charging our grave guard. The mathhammer would tell us that the knights cause 5.6 wounds and we cause 1.2 wounds. We lose by about 4.6. However, we don't need math hammer to figure out that most (if not all) kills we get against the chaos knights will be because of killing blow. Therefore, this combat has an EV of 4.6 but also a high Variance. (if we don't do any killing blows we will get crushed next turn, if we cause say 2 killing blows we will proabably kill the knights next turn).

What does all this mean? In general, it is better to have low variance then high variance. In some situations though high variance tends to favour VC (or any other unbreakable army/unit) over live armies. The reason is simple. Say that on average our unit X loses to our enemies unit Y by 1. If this particular combat would have no variance, we would always lose by 1. However, if the variance was large (ie. the results oscillated a lot), then (for example), the result would be between us winning by 6 and our opponent winning by 8. If we lose by 8 we have now lost 7 more models then expected (from combat res anyway). This is bad but not a disaster for us usually. On the other hand, if our opponent losses by 6 and is not stubborn/steadfast he/she might have a problem. This means that grave guard (for example) are slightly better then mathhammer would have us believe because of their higher variance. It is possible to take variance into account exactly when computing the effectivness of a unit via traditional mathhammer but would be very tedious.

Our wraith's chill grasp attack is very interesting because it is a very low variance attack compared to its regular attacks. Given a particular situation during a battle, we may opt to use one attack or the other not only based on the Expected value but also the need for higher/lower variance, or just whatever we feel like

Our (almost useless I think) Master Strike is even worse then previously thought becaue of it high variance.

I could expand more on the mathhammer but I am getting a little sleepy and don't even know why I wrote all this...