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Spread of common infantry - Archer:2.25 Crossbowman:3 Javelineer:4 Slinger:3
Spread means how inaccurate the shooting becomes at 100m from target. The spread is less when closer than 100m. For example, it is half at 50m. Thus, archer and crossbowman are proportionally the same: 2.25 x 60 / 100 = 3 x 45 / 100 = 1.35
A projectile (arrow / stone / javelin) is considered to hit a infantry when it arrives at radius < 1.5m from target (indeed, a circle). A projectile is considered to hit a calvary when it arrives at the 3m x 6m rectangle of the target (indeed, a rectangle), which is a little larger than the size of two infantry. Dog is smaller, elephant is larger, charriot is larger.
Now, at the beginning of a shoot, after waiting a short initial prepare time (once only), the future location of the target (because it may be walking) is very often precisely predicted, and the projectile is shot there, at a speed around 70m-100m per second, depending on unit. It should mathematically hit the target at the exact position when the projectile lands. Therefore, if the target changed direction during this time, the projectile might miss.
Even if the target did not change direction, the projectile might also miss due to the spread. The exact spread is given by a pair of independent normal random variable at variance of 1m. It is then multiplied by the spread. The result is some sort of 2D normal distribution, but since x and y are independent random variables, the 2D CDF is not circular, but more like a square. It seems super difficult to mathematically calculate the exact probability of it hitting a target. Let's get a rough idea by assuming the 1D case. I don't know how much would it deviate from 2D case, would be great if some mathematician could help.
In the simplified 1D case, I just use some online normal CDF calculator, fixing lower bound at -1.5, upper bound at 1.5, mean at 0, standard deviation at 2.25 x 60 / 100 = 1.35. Archer hits an infantry at 60m with probability 73.35%. After an upgrade of spread (-20%), standard deviation = 2.25 x 0.8 x 60 / 100 = 1.08, the probability is 83.51%.
Crossbowman and slinger hits infantry at 45m with probability 73.35%. At rank 2 spread -20%, the probability is 83.51%. Indeed, exactly same as archer at 60m, coincidentally.
Javelineer hits infantry at 30m with probability 78.87%. At rank 2, the probability is 88.18%.
The best unit would be rank 3 archer plus spread upgrade, at standard deviation = 2.25 x 0.8^3 x 60 / 100, hitting target at 60m with 97%.
Last but not least, when a projectile misses a target, it is not wasted. It will hit some innocent person standing there.
Reference:
https://gitea.wildfiregames.com/0ad/0ad/src/branch/main/binaries/data/mods/public/simulation/components/Attack.js#L714
Maybe worth mentioning, here they have the best preserved example in the world of a manuballista mechanism, from the 1st century AD. I always like to visit these weird unique items in museums, we are all familiar with the Roman semi-cylindrical shields, but not everyone knows there's only one remaining, the scutum from Dura-Europos, at the Yale University Art Gallery: https://artgallery.yale.edu/collections/objects/5959.
Agreed, that's my point. Regarding oppida, I was having them in mind when proposing making more use of palisades (and walls for relevant civs, I seem to remember Gauls had them), this could be combined somehow with "specialised CC". Palisades don't have to enhance turtling too much, just delay some rushes and small attacks.
I think the discussion was that, even when doing that, the player doing the capture would then turn around things instantly, giving too much advantage, and some proper conversion time was being proposed to avoid this. It seemed to me that things were getting unnecessarily complicated, and the base garrison concept would address all issues at once, on top of bringing some control (card ordering) and realism (siege-looking sieges). I'm just proposing it for if someone with modding skills finds the idea interesting and wants to test it, before anything else.