As explained in previous threads
, the random damage in the game is based on the number of hits in a round, which in turn forms a binomial distribution
. My personal theory is that people don't have a good intuitive feel for how this distribution behaves, especially since the average number of hits or misses are both usually small, around 2-3. Since the number of possible values is small, this leads to large swings in actual observed damage, very different to what one would see with a normal distribution
, the smooth behaviour of which most people seem quite familiar with.
Technically speaking, the binomial distribution of damage values that we see is usually skew
(asymmetrical around the mean) and platykurtic (with negative kurtosis
, ie. with the damage values tending to swing around quite a lot). The fact that the distribution isn't always the same but depends on the number of swings and the probability of hitting, is in itself confusing.
Further, people don't usually have a good intuitive feel for skew distributions, and are even more unfamiliar with distributions that are platykurtic. The binomial distribution of hits will be skew whenever the probability to hit is not 0.5 (when it is 0.5 then the distribution will be symmetrical about the mean). It will also have zero kurtosis, like the normal distribution, only when the probability to hit is 78.87% or 21.13%; at 80% and 20% it will have slightly positive kurtosis of 1/4n, but at the commonly used values used in the game the kurtosis will be negative, going as low as -2/n when the chance to hit is 50% (where n is the number of swings).
As previously discussed
, one way to "fix" this is to increase the total number of swings, while reducing the damage per successful hit, since the binomial distribution will tend to the normal distribution as the number of events increases. We then have units like the Cuttle Fish, lots of little hits, much less unpredictable total damage. And guess what, people can actually make their own campaigns to implement custom units like this -- Custom Elvish Fighter, does 1-20 damage: same average damage, same standard deviation, but very different observed behaviour.
But I think one of the unique features of Wesnoth would be lost if we did that. Making every fight into a clash of normally distributed damage values would pretty much remove an important feature of the strategy in the game. The role of the probability to hit is huge, since it determines the shape of the damage distribution, not just its mean. Making all damage distributions have the same shape would pretty much mean we might as well go to the deterministic damage model, where every fight results in the average damage (so a unit doing 5-4 damage and 50% chance to hit will always do 10 points of damage). A large part of the strategy in the game, and an important reason that this game has longevity, is this large influence of terrain on how battles go, not just the average damage. Let's not lose that.
Getting back to EP's original point, I still think making the default gold 150 instead of 100 would reduce the initial luck factor without detracting from the rest of the game. It has been pointed out that in certain matchups the choice of recruitment is critical, which means that in games where the factions of the other players is not known up front, a bad choice of initial recruiting can lose the game straight away. I think this is a much more serious issue than how damage is calculated -- an unlucky assumption of what to recruit initially can lead to an unretrievably bad position, before the units have even started engaging
. Clearly the popularity of the no-fog clan is testament to why this is a bad thing.
This quote is not attributable to Antoine de Saint-Exupéry.