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Modelling ranged units power - for fun!

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  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    Exarch said:

    I think Eumaies makes a good point about the artillery, which exists in a very different regime to the rest of the units (long ranged, but very weak defensively, low shot count, but with high damage and splash damage). When you exclude the 'monstrous' data points, the only long range (<190m) units left are the artillery.

    When you exclude the monstrous units, all the high ranged data points will be artillery, so the exponential term will be heavily biased towards this unit type. When the long-ranged monstrous infantry are introduced, they appear in a region of the training space conditioned only on artillery, which makes comparison difficult.

    I really like the general approach. I would especially like to see the missile infantry only plot I think, as most of the units within that regime behave much more similarly- the main split there being bow vs powder.</p>

    Yes, but that's actually my point too in a way. Artillery and missile infantry as well as "monstrous" missile infantry should all be of equal value per gold spent on them. The problem is that it's virtually impossible to fit both "monstrous" missile infantry and artillery on the same cost efficiency line if you treat them the same way. This is because they are pushing their range up into the extreme region, and that region has to be assigned high value generation in order to have any chance of making artillery cost efficient. If you don't assign extreme range a very high value, then the kind of mediocre damage output of artillery has no chance to make up for the very poor survivability stats they have.

    You're completely right though that the parametrization alone can't really say which of the two groups are not conforming to the trend. If I fit all at once then bowshapti and jezzails will be the outliers, but that's mainly because there are fewer of them than there is artillery, so artillery is weighted. I would say that the game has been balanced around artillery and archers from day 1 though and that the main outlayers now are more likely to be the more recently introduced "monstrous" missile infantry. They tap into the extreme range but don't really pay the premium that traditional artillery all does. Deck gunners are the exception there because they actually do pay a premium - their stats are very "artillery-like", so intuitively I think they are pretty balanced. The thing that makes them stick out a bit is that they have very long range- and also very accurate AP.
  • eumaieseumaies Senior Member Posts: 4,422Registered Users
    But the point is you haven't actually captured the damage profile of artillery. You're likely wrong in one way or the other, or both, depending on the artillery piece type (bolt vs cannon vs multi-cannon). Accuracy stats have different implications as well that can go in different directions (true of bow vs gun as well, but moreso artillery). You can wave at it and say that one thing cancels out another, but that's just a fancy way of saying the model isn't designed to compare artillery to other ranged units.

    For example you're giving increased weight to range based on fitting on artillery when in fact what's good about the organ gun (which is, nevertheless, an overpriced unit) is the multiple penetrating cannon shots. Maybe that's captured in some kind of raw damage total, but probably it isn't.

    if you took artillery out of your model, on the other hand, since these bowshabti style units are the only other units that sport it, you would probably complain that their ranged advantage isn't being properly accounted for. They might look quite normal, simply because range isn't being associated with cost, at least not at the higher levels of range. Now this could be unreasonable as well, but you're making a choice that you don't want to fit a model like that. You're saying you'd rather have a model that includes artillery, even knowing your stats on them are incomplete, in a way that boost the importance of range, rather than allowing your model to understate the importance of range. Any results stem heavily from your choices.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:

    But the point is you haven't actually captured the damage profile of artillery. You're likely wrong in one way or the other, or both, depending on the artillery piece type (bolt vs cannon vs multi-cannon). Accuracy stats have different implications as well that can go in different directions (true of bow vs gun as well, but moreso artillery). You can wave at it and say that one thing cancels out another, but that's just a fancy way of saying the model isn't designed to compare artillery to other ranged units.

    For example you're giving increased weight to range based on fitting on artillery when in fact what's good about the organ gun (which is, nevertheless, an overpriced unit) is the multiple penetrating cannon shots. Maybe that's captured in some kind of raw damage total, but probably it isn't.

    if you took artillery out of your model, on the other hand, since these bowshabti style units are the only other units that sport it, you would probably complain that their ranged advantage isn't being properly accounted for. They might look quite normal, simply because range isn't being associated with cost, at least not at the higher levels of range. Now this could be unreasonable as well, but you're making a choice that you don't want to fit a model like that. You're saying you'd rather have a model that includes artillery, even knowing your stats on them are incomplete, in a way that boost the importance of range, rather than allowing your model to understate the importance of range. Any results stem heavily from your choices.

    Maybe you know something I don't about cannons, if so I will update the model for sure. Are you saying penetrating shots generate extra damage? Cannons have no explosion area. Are you saying cannons have a hidden splash multiplier that I don't know about? As far as I know, I am not cutting anything out that would have helped cannons. Rather the opposite, there is a risk of overkill with high damage single projectiles when it runs out of models it clipped. I assume no wasted damage, so kind of assuming an "optimal" target.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    edited June 11
    Yeah, I did some tests and I should remove cannons. They do indeed exceed their max damage if they get the optimal shot. Boltthrowers, organs and helblaster do not however. Do you know which stat that does that? There is nothing that makes cannons different from bolt throwers in the unit cards or grid, or does it only come from trajectory and bouncing?

    No wonder bolt throwers suck so badly lol.
  • eumaieseumaies Senior Member Posts: 4,422Registered Users

    eumaies said:

    But the point is you haven't actually captured the damage profile of artillery. You're likely wrong in one way or the other, or both, depending on the artillery piece type (bolt vs cannon vs multi-cannon). Accuracy stats have different implications as well that can go in different directions (true of bow vs gun as well, but moreso artillery). You can wave at it and say that one thing cancels out another, but that's just a fancy way of saying the model isn't designed to compare artillery to other ranged units.

    For example you're giving increased weight to range based on fitting on artillery when in fact what's good about the organ gun (which is, nevertheless, an overpriced unit) is the multiple penetrating cannon shots. Maybe that's captured in some kind of raw damage total, but probably it isn't.

    if you took artillery out of your model, on the other hand, since these bowshabti style units are the only other units that sport it, you would probably complain that their ranged advantage isn't being properly accounted for. They might look quite normal, simply because range isn't being associated with cost, at least not at the higher levels of range. Now this could be unreasonable as well, but you're making a choice that you don't want to fit a model like that. You're saying you'd rather have a model that includes artillery, even knowing your stats on them are incomplete, in a way that boost the importance of range, rather than allowing your model to understate the importance of range. Any results stem heavily from your choices.

    Maybe you know something I don't about cannons, if so I will update the model for sure. Are you saying penetrating shots generate extra damage? Cannons have no explosion area. Are you saying cannons have a hidden splash multiplier that I don't know about? As far as I know, I am not cutting anything out that would have helped cannons. Rather the opposite, there is a risk of overkill with high damage single projectiles when it runs out of models it clipped. I assume no wasted damage, so kind of assuming an "optimal" target.
    Feel free to post your DPS assumptions and I can weigh in. The difference in terms of how the units deal damage is obvious - cannons can range from extremely effective penetration of high hp cavalry units to inneffective. Bolt throwers very different since they don't get those benefits and are probably simpler to model.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:

    eumaies said:

    But the point is you haven't actually captured the damage profile of artillery. You're likely wrong in one way or the other, or both, depending on the artillery piece type (bolt vs cannon vs multi-cannon). Accuracy stats have different implications as well that can go in different directions (true of bow vs gun as well, but moreso artillery). You can wave at it and say that one thing cancels out another, but that's just a fancy way of saying the model isn't designed to compare artillery to other ranged units.

    For example you're giving increased weight to range based on fitting on artillery when in fact what's good about the organ gun (which is, nevertheless, an overpriced unit) is the multiple penetrating cannon shots. Maybe that's captured in some kind of raw damage total, but probably it isn't.

    if you took artillery out of your model, on the other hand, since these bowshabti style units are the only other units that sport it, you would probably complain that their ranged advantage isn't being properly accounted for. They might look quite normal, simply because range isn't being associated with cost, at least not at the higher levels of range. Now this could be unreasonable as well, but you're making a choice that you don't want to fit a model like that. You're saying you'd rather have a model that includes artillery, even knowing your stats on them are incomplete, in a way that boost the importance of range, rather than allowing your model to understate the importance of range. Any results stem heavily from your choices.

    Maybe you know something I don't about cannons, if so I will update the model for sure. Are you saying penetrating shots generate extra damage? Cannons have no explosion area. Are you saying cannons have a hidden splash multiplier that I don't know about? As far as I know, I am not cutting anything out that would have helped cannons. Rather the opposite, there is a risk of overkill with high damage single projectiles when it runs out of models it clipped. I assume no wasted damage, so kind of assuming an "optimal" target.
    Feel free to post your DPS assumptions and I can weigh in. The difference in terms of how the units deal damage is obvious - cannons can range from extremely effective penetration of high hp cavalry units to inneffective. Bolt throwers very different since they don't get those benefits and are probably simpler to model.
    I wonder if it has to do with them being different "missile canisters" or something. I know handmaidens for example fire missiles and they have max penetration = 2 now. The damage is "consumed" I believe because I have never seen a maiden kill two chaos knights in one shot but they can kill 2 grails in one shot quite often. As far as I know BTs probably work the same. They do more damage and can kill slightly more models when penetrating multiple models, but I have never seen them exceed their max damage of 600 per volley. I have always assumed cannons were the same, they have much more damage per volley and that's enough potential to kill some 12 models per volley. When I tested under optimal conditions I managed to kill 16 CK in one shot though (1800 damage and max volley is about 1200), so that would imply that they work differently. That's way above what penetration would give... so maybe that's a different missile canister that doesn't work by penetration, but rather by animation? Otherwise there ought to be some kind of "splash multiplier" that generates extra damage.

    Interesting regardless, I am learning something today. Would be grateful if anyone knows this for sure!
  • eumaieseumaies Senior Member Posts: 4,422Registered Users
    Yeah it's complex. They can definitely exceed their max damage when used well (e.g. side shots in particular), though I do agree in general your model is probably pretty kind on damage total for them and moreso for bolt throwers.

    I also don't know exactly how accuracy and calibration works for different units, and would have to test scenarios to see how it plays.
  • ParmigianoParmigiano Posts: 750Registered Users

    eumaies said:

    eumaies said:

    But the point is you haven't actually captured the damage profile of artillery. You're likely wrong in one way or the other, or both, depending on the artillery piece type (bolt vs cannon vs multi-cannon). Accuracy stats have different implications as well that can go in different directions (true of bow vs gun as well, but moreso artillery). You can wave at it and say that one thing cancels out another, but that's just a fancy way of saying the model isn't designed to compare artillery to other ranged units.

    For example you're giving increased weight to range based on fitting on artillery when in fact what's good about the organ gun (which is, nevertheless, an overpriced unit) is the multiple penetrating cannon shots. Maybe that's captured in some kind of raw damage total, but probably it isn't.

    if you took artillery out of your model, on the other hand, since these bowshabti style units are the only other units that sport it, you would probably complain that their ranged advantage isn't being properly accounted for. They might look quite normal, simply because range isn't being associated with cost, at least not at the higher levels of range. Now this could be unreasonable as well, but you're making a choice that you don't want to fit a model like that. You're saying you'd rather have a model that includes artillery, even knowing your stats on them are incomplete, in a way that boost the importance of range, rather than allowing your model to understate the importance of range. Any results stem heavily from your choices.

    Maybe you know something I don't about cannons, if so I will update the model for sure. Are you saying penetrating shots generate extra damage? Cannons have no explosion area. Are you saying cannons have a hidden splash multiplier that I don't know about? As far as I know, I am not cutting anything out that would have helped cannons. Rather the opposite, there is a risk of overkill with high damage single projectiles when it runs out of models it clipped. I assume no wasted damage, so kind of assuming an "optimal" target.
    Feel free to post your DPS assumptions and I can weigh in. The difference in terms of how the units deal damage is obvious - cannons can range from extremely effective penetration of high hp cavalry units to inneffective. Bolt throwers very different since they don't get those benefits and are probably simpler to model.
    I wonder if it has to do with them being different "missile canisters" or something. I know handmaidens for example fire missiles and they have max penetration = 2 now. The damage is "consumed" I believe because I have never seen a maiden kill two chaos knights in one shot but they can kill 2 grails in one shot quite often. As far as I know BTs probably work the same. They do more damage and can kill slightly more models when penetrating multiple models, but I have never seen them exceed their max damage of 600 per volley. I have always assumed cannons were the same, they have much more damage per volley and that's enough potential to kill some 12 models per volley. When I tested under optimal conditions I managed to kill 16 CK in one shot though (1800 damage and max volley is about 1200), so that would imply that they work differently. That's way above what penetration would give... so maybe that's a different missile canister that doesn't work by penetration, but rather by animation? Otherwise there ought to be some kind of "splash multiplier" that generates extra damage.

    Interesting regardless, I am learning something today. Would be grateful if anyone knows this for sure!
    "Max damage" has nothing to do with the total that would result from collateral. So if bolt throwers could somehow collateral enough models to exceed that number, they would. That number is simply damage. If all 3 shots hit 1 entity, how much damage.

    Divide damage by 3, that is how much each bolt will do, that will kill each model with less hp than that. Then the damage it did was just how many models did it hit. Bolt throwers struggle to hit enough models, cannons have a wider projectile.

    In some sense Jezzails are just overpowered bolt throwers, but they don't have the collateral that many units in their price range have.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:

    Yeah it's complex. They can definitely exceed their max damage when used well (e.g. side shots in particular), though I do agree in general your model is probably pretty kind on damage total for them and moreso for bolt throwers.

    I also don't know exactly how accuracy and calibration works for different units, and would have to test scenarios to see how it plays.

    I just tested to increase cannon damage by 50%, which is far too much, but in any case I can weaken the range-exponent to improve the fit a little but over all it's not possible to get as good over all fit anymore. This because cannons start to look OP and organ sink through the floor, BTs also drop etc. The outliers don't move that much tho since they are earlier on the exponent. Ratlings are not affected at all.



    So with such a "buff" for cannon extra damage the over all fit just gets worse.
  • eumaieseumaies Senior Member Posts: 4,422Registered Users
    Yeah i'm not saying cannons necessarily deserve max boost like that, but it's just a complexity.

    I still think leadership should be factored in here.

    On Ratlings, I wonder how accuracy is being modelled. They are great units no doubt, but their damage output can vary alot as a function of accuracy and calibration distance. A number of ranged units are like that in terms of whether they work well at full range vs closer range. Part of what makes ranged units hard to model.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:

    Yeah i'm not saying cannons necessarily deserve max boost like that, but it's just a complexity.

    I still think leadership should be factored in here.

    On Ratlings, I wonder how accuracy is being modelled. They are great units no doubt, but their damage output can vary alot as a function of accuracy and calibration distance. A number of ranged units are like that in terms of whether they work well at full range vs closer range. Part of what makes ranged units hard to model.

    Yeah, just wanted to test the influence at maximum throttle to see what we're dealing with. It does bring down the jezzails a little tho, but not near enough to merge the artillery and jezz/bowshapti populations.

    I also tested some cannon balls and BTs by having them shoot at stacked foot heroes and it appears that both actually does deal full damage to every model they clip. Maybe it's only missiles from infantry like heroes and generals that get exhaused and use penetration mechanics? I would have thought BTs did. In this case it seems to only be a matter of BT projectiles being extremely bad at clipping things. I wonder what controls that, according to twwstats they have the same projectile size and no explosion. Guess the cannons fire a bit flatter but not that much. Maybe it's a bounce physics on the cannon ball doing it, or there's something hidden. BTs really look lack-luster when comparing like this, especially the DWF BT seems to fire with a higher trajectory.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:


    On Ratlings, I wonder how accuracy is being modelled. They are great units no doubt, but their damage output can vary alot as a function of accuracy and calibration distance. A number of ranged units are like that in terms of whether they work well at full range vs closer range. Part of what makes ranged units hard to model.

    I use a rather soft scaling for accuracy because I have to assume somewhat "optimal targets", otherwise things like archers would do nothing while powder would do everything... so both ratlings and jezzails being up there at least shows that the accuracy treatment isn't responsible.
  • Cukie251Cukie251 Posts: 916Registered Users
    Yeah I was going to say, are you 100% certain organ guns don't penetrate as well? From experience they penetrate very heavily which is part of the reason they eat cav for lunch. Worth checking out.

    Also it may be because the cannon ball "rolls" (jumps may be a more accurate term) retaining an active hitbox longer wheras bolts just stick in the ground.
  • eumaieseumaies Senior Member Posts: 4,422Registered Users

    eumaies said:


    On Ratlings, I wonder how accuracy is being modelled. They are great units no doubt, but their damage output can vary alot as a function of accuracy and calibration distance. A number of ranged units are like that in terms of whether they work well at full range vs closer range. Part of what makes ranged units hard to model.

    I use a rather soft scaling for accuracy because I have to assume somewhat "optimal targets", otherwise things like archers would do nothing while powder would do everything... so both ratlings and jezzails being up there at least shows that the accuracy treatment isn't responsible.
    I’m not sure what you mean. My point is Ratlings do nowhere near their damage potential at max range.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:

    eumaies said:


    On Ratlings, I wonder how accuracy is being modelled. They are great units no doubt, but their damage output can vary alot as a function of accuracy and calibration distance. A number of ranged units are like that in terms of whether they work well at full range vs closer range. Part of what makes ranged units hard to model.

    I use a rather soft scaling for accuracy because I have to assume somewhat "optimal targets", otherwise things like archers would do nothing while powder would do everything... so both ratlings and jezzails being up there at least shows that the accuracy treatment isn't responsible.
    I’m not sure what you mean. My point is Ratlings do nowhere near their damage potential at max range.
    Sure. What I mean is that cal area ranges from like 0.5 to 10, that's a factor 20 so you can't just scale that linearly. Something with a large cal area will still do well vs a unit in tight formation, but not vs a single entity... on the other hand, you want to reward say a Great cannon over a Carronade because it has better accuracy and that makes it a better cannon. So a soft scaling has to be used, which would correspond to that you assume that units are used vs targets they are good vs.
  • ystyst Posts: 6,054Registered Users
    This is still magically conjuring numbers out of thin air. Somehow jezz score a "meta" value of 1300 and waywatch at 1100.

    $700 deck gun scores 900 points.
    $900 jezz scores 1300 points.

    Like do a real dmg and range chart with proper solid number instead of completely, randomly assigning numbers that r irrelevant. Pretty much any guns in game will significantly outdps jezz comes their range. I mean thats basically just 2 shots or so to cover 150m ish distance there +50% every single volley thereafter at $600 vs $900
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  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    yst said:

    This is still magically conjuring numbers out of thin air. Somehow jezz score a "meta" value of 1300 and waywatch at 1100.

    $700 deck gun scores 900 points.
    $900 jezz scores 1300 points.

    Like do a real dmg and range chart with proper solid number instead of completely, randomly assigning numbers that r irrelevant. Pretty much any guns in game will significantly outdps jezz comes their range. I mean thats basically just 2 shots or so to cover 150m ish distance there +50% every single volley thereafter at $600 vs $900

    It's not only about dps. If you only care about dps, Ratlings are your guys.
  • eumaieseumaies Senior Member Posts: 4,422Registered Users

    yst said:

    This is still magically conjuring numbers out of thin air. Somehow jezz score a "meta" value of 1300 and waywatch at 1100.

    $700 deck gun scores 900 points.
    $900 jezz scores 1300 points.

    Like do a real dmg and range chart with proper solid number instead of completely, randomly assigning numbers that r irrelevant. Pretty much any guns in game will significantly outdps jezz comes their range. I mean thats basically just 2 shots or so to cover 150m ish distance there +50% every single volley thereafter at $600 vs $900

    It's not only about dps. If you only care about dps, Ratlings are your guys.
    But the point with ratlings is you are giving them credit for range that is not their effective range.

    It’s fine but it’s part of why they’re an outlier.

    And low leadership units are not getting credit for that weakness.
  • Disposable HeroDisposable Hero Posts: 3,697Registered Users
    eumaies said:

    yst said:

    This is still magically conjuring numbers out of thin air. Somehow jezz score a "meta" value of 1300 and waywatch at 1100.

    $700 deck gun scores 900 points.
    $900 jezz scores 1300 points.

    Like do a real dmg and range chart with proper solid number instead of completely, randomly assigning numbers that r irrelevant. Pretty much any guns in game will significantly outdps jezz comes their range. I mean thats basically just 2 shots or so to cover 150m ish distance there +50% every single volley thereafter at $600 vs $900

    It's not only about dps. If you only care about dps, Ratlings are your guys.
    But the point with ratlings is you are giving them credit for range that is not their effective range.

    It’s fine but it’s part of why they’re an outlier.

    And low leadership units are not getting credit for that weakness.
    They are not that inaccurate, at Max range they are more accurate than he archers at like 150 meters, so vs units that's not bad, it's only vs single entities they need to be closer.

    The problem with ratlings is that I am not 100% sure the dps calculation its right, I used generalconfusions info on adding 0.33 sec per shot in the salvo to get the right reload time. I can try to look into that tomorrow.

    Adding ld I should do.
  • eumaieseumaies Senior Member Posts: 4,422Registered Users

    eumaies said:

    yst said:

    This is still magically conjuring numbers out of thin air. Somehow jezz score a "meta" value of 1300 and waywatch at 1100.

    $700 deck gun scores 900 points.
    $900 jezz scores 1300 points.

    Like do a real dmg and range chart with proper solid number instead of completely, randomly assigning numbers that r irrelevant. Pretty much any guns in game will significantly outdps jezz comes their range. I mean thats basically just 2 shots or so to cover 150m ish distance there +50% every single volley thereafter at $600 vs $900

    It's not only about dps. If you only care about dps, Ratlings are your guys.
    But the point with ratlings is you are giving them credit for range that is not their effective range.

    It’s fine but it’s part of why they’re an outlier.

    And low leadership units are not getting credit for that weakness.
    They are not that inaccurate, at Max range they are more accurate than he archers at like 150 meters, so vs units that's not bad, it's only vs single entities they need to be closer.

    The problem with ratlings is that I am not 100% sure the dps calculation its right, I used generalconfusions info on adding 0.33 sec per shot in the salvo to get the right reload time. I can try to look into that tomorrow.

    Adding ld I should do.
    If you want to post some of the dps' we could also test how well they approximate actual damage, for example at full and half range.
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