Saturday, 10 September 2011
Quantity is quality; a look at basic probability
This post will be concerned with what is called the law of large numbers in mathematics. According to this theory, the larger the sample size, the closer to the expected average (or mean) the results' average should reach. As an example, rolling 2d6 repeatedly has an expected average of 7. However, if there is a small sample size, and you roll snake eyes (which has a very low probability) it will immediately affect the average of the results (and give an impression that the average is lower then 7).
How does all this translate to WH40K? Well, in it's most basic form, the more you are rolling, the less of an impact one bad die roll will have. You should be expecting to achieve results closer to average. Lets look at two weapons: a bs3 shuriken cannon (guardian), and a bs3 missile pod (tau). The missile pod has a probability of 0.5 at glancing a rhino, meanwhile the shuriken cannon is marginally worse (about 0.49). Which one do you think is going to perform better over the course of the entire game? The missile pod should be better, as it has a higher probability, but it rolls less dice (and thus at least in theory would take longer to achieve its expected average). The shuriken cannon, on the other hand, rolls an extra die. This means that one roll, whether good or bad, has less of an impact on the entire results. If the missile pod is rolling well, then it's a good thing, if it has some bad rolls, they will have a larger effect then with the shuriken cannon. At least in theory.
However, this perhaps works better when viewing the army as a whole. An army that rolls lots of dice (like venomspam) will be more reliable in its anti-infantry fire then an army that rolls less dice (e.g. paladins). I have really liked the predictability of my venom spam when it comes to cleaning up infantry. It allows you to better plan your shooting phase, moves etc.. For a strategist, migitating chance is an important factor. Chance is random and cannot be affected. By limiting chance, a player has more control.
This doesn't only hold true in the shooting phase. An army that has a lower model count, will generally suffer more from bad rolls then an army with a high model count. A paladin army will be greatly hindered by a bad ld test or bad armour saves. On the other hand, grey knights msu will be less hindered by the loss of one of its squads to bad armour saves. This has less to do with the law of large numbers, but has a similar mentality. One random event will have less of an impact on your entire game if the procentage of your army affected by that roll is low.
How scientific is all of this? Not very. Just some thoughts and feelings I've been having lately, justified by wikipedia ;).