Loggy

They do. If memory serves it's logarithmic: I worked this one out a loooong time ago but can't remember where I saved the numbers...

I'm going to respectfully disagree on point 4, I'm afraid :P I'd observed that some things are disproportionately effective vs unfinished buildings (most notably archers) and siege is unexpectedly bad. This inspired me to work out the specifics, and it's actually a bit surprising. Normally I'd script a lot of the hard work but I'm not really well enough to do that right now, so I opted for more simple reasoning. If I've missed anything blindingly obvious in here, please let me know! Scarab (6h, 12c, x5 vs building) does 117 per hit on a house (30% hack, 5% crush) From this we can work out the anim length modifier: expected dps is 6*5*0.7 + 12*5*0.95 = 78 Therefore scarab's attack interval is 1.5s. On an unfinished house, scarab instead does 48-49 per hit! Too many variables: set scarab crush attack to 0. Scarab now does the expected 31.5 per hit (6*5*0.7). Can't remove house hack armour or scarab attack bonus no longer applies, thanks AoM! Now it does ~16 per hit on the house instead. So what's going on with this? Is it affected by attack bonus or building armour? Increased house hack armour to 60%. Now does 12 per hit (6*5*0.4) on finished, and 16 on unfinished. Increased house hack armour to 80%, and it still does 16 on the unfinished -> building armour does nothing here. If the scarab does 6 crush or pierce instead of 6 hack, it still does 16 (well, somewhere slightly over 16 per hit, but regardless it's close). If the scarab has its attack bonus vs buildings removed, it still does ~16. Now the question is where that 16 per hit actually comes from. Using the KB unit info display I can see the actual damage per hit is 16.2. That would indicate some damage multiplier of 16.2/(6*1.5) = 1.8x As a quick test, I thought I'd look at something I already know the attack interval of from previous experiments: the white tiger, ~1.83s (see https://steamcommunity.com/sharedfiles/filedetails/?id=859012992) Based on this (it has 20h attack) it should do 20*1.83*1.8 = ~65.8 damage per hit on an unfinished house, which is what I observed when trying this. To be sure it's not something specific to houses, I tried on a temple too and got the same result. TL;DR: Units attacking unbuilt buildings ignore any existing damage multipliers and the building's armour, and instead do 1.8x their base damage. So yes, the scarab does significantly less damage to unfinished buildings because its 5x multiplier is voided and its crush damage doesn't have the usual benefit of being more effective.

Urk, as if this problem wasn't already complicated enough without more variables... Thanks though, I'm not all that familiar with the proto.

I can answer a few things alluded to above, and offer a few more musings on the subject. The height bonus is definitely pretty impractical, unlike AoE2's. The threshold to get the bonus means you have to be roughly the height of a sentry tower above your opponent, which makes it fairly unusuable in most standard RM settings. I don't know of a way to measure real height units except maybe via RM script: kbUnitGetPosition seems to always consider the Y coord of any unit to be 0, even for flying units. The only case I haven't tested is ground units sent flying by throw/buck/gore/shockwave, but that wouldn't be terribly practical as a height ruler even if it worked. The game internally tracks health to greater than integer precision: XS scripts can return and output this in more accurate form (kbUnitGetCurrentHitpoints returns a float), but the UI rounds it. I'm not sure exactly what rounding method is used by the interface, but for this reason I've always used custom AI in my investigations into damage and DPS, simply because it can measure damage and time intervals far more accurately and easily than doing it by hand. On a related note, a few years ago I tried to make a script to assess the accuracy increase conferred by the number of consecutive shots by determining hit/miss by calculating the intervals between inflicting damage. I seem to remember having some success, but due to the massive amount of variables at play it's hard to fit it to anything particularly mathematical. Oh, and another obvious factor involved in accuracy is the size of the target: certainly there aren't cases where the humble chariots outrageously miss something as big as a TC, and it's not clear what it is about various buildings which make missing impossible. It's possible this is related somehow to the collision size, or simply that ranged attacks vs buildings never miss. The obvious starting point is probably comparing accuracy of catapults against towers/wall chips and catapults, as the collision size of them is probably fairly similar. For what it's worth, AoE2's system is very simple: if you're any higher than your target, you do more damage (and I think maybe take less?) - but it also affects melee units fighting up hills. I'm fairly sure the amount of height increase doesn't matter either. In any case, it's pretty evident that ES went down a different route for height wars in AoM. Variables that might affect accuracy: Something to explain why archers can't miss large buildings: - Target identity (IE: Unit/Building - which proto tags cause this? Could be anything from Building, BuildingClass, LogicalTypeUnitsNotBuildings, or others...) - Potentially collision area Distance to target - Is this % of max range, or real distance? Target's movement rate vs attacker's track rating Accuracy AccuracyReductionFactor AimBonus Track Rating (does this do anything to attacks vs stationary units?) MaxSpread SpreadFactor VolleyMode (units with multiple projectiles seem to have this tag) What determines the unintentional target that is hit when an attack misses? How is the accuracy of additional projectiles determined? It's clearly a lot lower than the primary ones... It's unclear exactly how dangerous towers/TCs/fortresses are, and how much empowering does to them. What actions reset the consecutive shot bonus? All in all, a lot of questions. Certainly if there's interest I could pull together AI scripts for investigating this stuff as I have done with other things, but I'm unsure exactly what to do, and how relevant it might be to play. My grasp of statistics isn't good enough to understand how you might try to fit multivariate data to some kind of equation, or I would have done this already, as well as address questions like "how much does handaxe REALLY benefit woodcutting due to carry capacity increase" and "when should you build a new storehouse closer to your wood". Accuracy in particular really is a mess due to the masses of variables involved, but I can probably try to see to some basic empirical questions or provide experimental data with the help of a few scripts if it'd help someone. I'm not currently convinced there's a huge amount to gain with regard to actual play from better understanding accuracy. Knowledge is all well and good, but if it's not going to answer real questions that impact play then I'm not sure it's worth the effort to unravel any interactions between all these variables. The kind of questions I see are: How much does pharaoh empowerment/the blessed construction oversight affect building damage against various units? Does forcing a ranged unit to move, or moving out of building range reset the consecutive attack count? This could have micro implications. Is it worth moving certain ranged units closer to their targets in the name of accuracy? Classical Greek heroes and gastraphetes come to mind here. Just how much damage do towers/TCs/fortresses put out at various distances? How much of gain in efficiency is it to task lots of <insert various archer units here> to on one tanky unit like a Greek hero to minimise wasted shots/overkill?