Where the Diversions go...
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One problem with translating that to the paper doll is that would be nightmarish from a UI perspective. Another is that, while it is mathematically correct, it would be confusing as heck to many players. "I have a 100 dmg AC/20 with a 50% chance to hit the CT. Why does it only show 50 damage?" On average, you would do 50 damage, yes. But that's because you're assuming 0 damage half the time and 100 damage half the time. 0 and 100 are not the same as 50.
Then combine that with all the other weapons and it would be a mish-mosh of confusing overlays. Think about how you would render a situation where you have 4 medium lasers, with hit percentages of 90%, 85%, 80%, and 75% (various +s and hardpoint locations) and damage outputs of 25, 25, 30, and 35 (various +s). Would it be as simple as adding all damage and then multiplying all the percentages? Would that make sense?
Maths don't bother me, but at a certain point, it's just easier to think in one dimension (can I hit?) than it is to factor out averages. Plus, you will NEVER do "average damage". At closest, you'll do median damage. More likely, you'll do a multiple of mode damage. But average? No. An AC/20 with a 40% to hit will never do 40 damage unless it hits a 60% DR target. So representing average damages is not the correct way to represent it.
I didn't say calculate. I said account for, as in the flow of play.
Agreed. I don't even see a need for such a feature considering the amount of new player confusion and Dev work it would introduce. Especially since Imho we can just shoot from the hip with the current data and facing fire table experience like we've always done.
Ymmv
It's not the same at all. Let's say you have four ML (4x25 dmg).
- 50% DR on 100% to hit = 0.5 x 4x25 dmg = 50 dmg
- 50% to hit:
6% of landing all four ML: 100dmg
25% of landing three ML: 75dmg
37% of landing two ML: 50 dmg
25% of landing one ML: 25 dmg
6% of landing no ML: 0 dmg
25% of landing three ML: 75dmg
37% of landing two ML: 50 dmg
25% of landing one ML: 25 dmg
6% of landing no ML: 0 dmg
Knowing that you will do for certain 50 dmg plays very different that knowing that you may do more than or less than that damage.
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And I just realized the first additional wrinkle that makes it uglier still... that probability curve is only accounting for a single level of probability. We're not even including the probability curves for each component in the hit table.
Flip it around though: if I ask "Roughly how much damage can I expect this component to take from this salvo or this called shot" we can generally reason out a good approximation. That's true for every single location, doesn't really involve particularly complicated maths and I literally use it every time I math out my odds of legging a mech. Abstractions aren't meant to give exact numbers, they're meant to give a feel and some brute statistics will give a pretty good feel: 66 damage on a location when I'm firing mlasers? Odds are good it's taking 75 points. If all you're firing is an AC20, the damge is just going to reflect the literal odds of hitting that spot minus the hit base rate.
Sure we'd probably make it optional, but I can promise you that you can read all sorts off of that kind of table.
Sure we'd probably make it optional, but I can promise you that you can read all sorts off of that kind of table.
Yep, that adds another level and you cannot (that I know) calculate at hand many groups of different weapons. But the main difficulty comes when taking into account SRM diminishing returns and (a lot harder) LRM mechanics, in order to have reasonable performance. For example I use two modes: accurate and fast. In the fast one I treat LRM15s as LRM10*1.5 DMG and LRM20s as LRM10*2 dmg, decent as an approximation, but I also can use the accurate one, which takes a lot more time and requires a lot more memory (only if high caliber LRMs are involved).
The problem with brute statistics is that may be misleading and wrong or approximate and good enough. If you need to do 60 dmg with 4xML there is no way you can do it with 50% DR and 100% chance but you may with 0% DR and 50% chance. Both are very different scenarios, and in the last one you actually may want to take the risk, but knowing it's not a good shot.
One problem there is ignoring initial conditions: outside of the first salvo or two, 'mechs relying on Bulwark will tend to have less armour overall because they are getting hit more.
That number is also heavily cherry-picked as in it's literally handing me an underpowered medium as an example and telling me that's representative of the damage statistics across the board.
So yeah, I guess DR has some single turn edge case advantages when you're under gunned. Wait a turn, follow up with another salvo or change my load out and the whole problem vanishes.
A final issue though is that doesn't really address my point at all either. Yes, reading statistics is a skill, but this is free information that can, for instance, give me an idea of whether it's worth aiming for a side-torso pilot injury, legging a mech or just saving my effort and coring a mech. I can math it, but a rough damage preview, even one with a margin of error bars, can easily save me wasting ammo heat or effort trying to do something I don't need to.
Incorrect, they are getting hit more, but may not necessarily have taken more damage and thus have less armour.
You may have taken 3 ML hits for 15 each with bulwark, thus taking 45 damage and you may have taken just 2 of those with an evasion strategy for 25 each and thus, 50 damage total.
Thus, you took less hits with evasion AND you have less armour as well.
Evasion is bad in cases where you need it most. It degrades and it's weak to powerful enemies with targetting computers and good pilots. You can overkill evasion with accuracy bonuses. Mitigation doesn't care.
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I started thinking about how I would account for calculating probability of kill with layered discrete damage chunks, and realized the “easier” way would be to just write something that applies the attacks in order and Monte Carlo it.
Probability of kill for a precision shot on a damaged mech with a bunch of identical weapons is a lot easier than a generalized case, though.
Let’s say we’ve got a bulwark mech in cover (not Braced) with 30 structure on the CT. I need 3 medium lasers on the CT for a kill. With no evasion, there is a 95% chance the shot lands and an 85% chance each shot hits the CT.
Let’s put the evasion penalty at 15% per stack (probably actually more complicated).
The chance for a laser to miss the CT is 1-(.95-.15*evasion)*.85.
I can afford (lasers fired-lasers needed) misses.
Instead of doing a troublesome summation, I can ask my calculator or spreadsheet for the cumulative binomial distribution for m misses in n trials at my probability for a miss. For 5 lasers, I have a 94.7% chance of two or fewer misses, and a 59.7% chance at 2 evasion. If I’m running a 7 medium laser GRH, I’ve still got an 85% probability of killing a bulwark (but not Braced) target in cover via CT damage at 2 evasion if I burn morale.
See? Mathematical precision!
Edit: you can actually still use this for dissimilar groups of non-missile weaponry with similar to-hit if you just count a bigger weapon as one additional smaller weapon. Your calculation will underestimate your probability of kill, but that’s better than an overestimate.
Probability of kill for a precision shot on a damaged mech with a bunch of identical weapons is a lot easier than a generalized case, though.
Let’s say we’ve got a bulwark mech in cover (not Braced) with 30 structure on the CT. I need 3 medium lasers on the CT for a kill. With no evasion, there is a 95% chance the shot lands and an 85% chance each shot hits the CT.
Let’s put the evasion penalty at 15% per stack (probably actually more complicated).
The chance for a laser to miss the CT is 1-(.95-.15*evasion)*.85.
I can afford (lasers fired-lasers needed) misses.
Instead of doing a troublesome summation, I can ask my calculator or spreadsheet for the cumulative binomial distribution for m misses in n trials at my probability for a miss. For 5 lasers, I have a 94.7% chance of two or fewer misses, and a 59.7% chance at 2 evasion. If I’m running a 7 medium laser GRH, I’ve still got an 85% probability of killing a bulwark (but not Braced) target in cover via CT damage at 2 evasion if I burn morale.
See? Mathematical precision!
Edit: you can actually still use this for dissimilar groups of non-missile weaponry with similar to-hit if you just count a bigger weapon as one additional smaller weapon. Your calculation will underestimate your probability of kill, but that’s better than an overestimate.
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I don't exactly see how you can be so emphatic about this. Evasion has never failed me when I needed it. I literally would never have succeeded any campaigns if it fails as easily as you say it does.
Or are you saying I'm magic? I mean, my mom's been telling me that since I was a kid, so maybe you've just been talking to her.
As for your example, I addressed it in passing by pointing out that the first couple of rounds are an exception. You need a couple of rounds of fire before the statistics will start to assert itself, but when it does it's going to broadly follow the numbers you get through the statistics. The data will be noisy though, so sometimes there'll be outliers in both directions, but that's entirely expected: if statistical probabilities are good enough to guarantee me a Higgs Boson, they're good enough to guide my firing strategy in a computer game.
Look, if it's unfeasible it's unfeasible and I'll accept that. The maths isn't particularly complicated though from what I know, and I literally account for most of it in the flow of my play already: it's just multiplying three, generally fairly simple, fractions and then a whole number. It's easy enough to add enough fire to almost guarantee that you'll destroy a target component (as long as you're not using missiles of course), but what's harder to gauge is whether you'll destroy the CT at the same time, and it's when you're tracking more than one set of probabilities that it gets *mentally* unwieldy: I can do it on a piece of paper just fine.
If it were down to me a simple average would do everything *I* would need it to. Yes, you need a bit of statistical nous to understand that the damage number is a bit of a proxy for the probabilities and you'll need to make a judgement call about what damage is likely to go where due to what weapons you're using, but more than once I've sat there certain that I can take out the component I want to, but then needing to try and repeat the maths for each neighbouring component and then trying to work out likely overflow damage. A simple set of mean averages based on damage output and percentage chances to hit would help me immensely in those cases, actively *lowering* the cognitive load and simplifying my decision making.
I don't think that's an unreasonable thing to ask for, though I'd be happy to accept it if HBS tells me it's not workable.
Colour me interested: I only use simple stats because that's all I've got, but feel free to message me if you're up for elaborating on your methodology here.
The basic problem with Math in terms of complex systems is that it becomes very complex! Duh! Yeah, I know.
The basic problem with Math in BATTLETECH as described in the endless debate between Evasion/Sure Foot and Bulwark 1.0 vs 2.0 constantly revolves around the simple Damage Per Turn equation.
Fire (N weapons for Z damage against Y odds) * (Damage Reduction or Evasion) = X Damage. (Precision Strike Bonus from the Rear)
As has been noted somewhat obliquely earlier... this only works if the target has only one Hit Point count (one damage location). It only works if there is only one OPFOR firing at a single target. Once more than 1 thing fires at a target the formula breaks down. The formula only works in very narrow circumstances. A Firestarter or Grasshopper ML+SL or whatever FOTM build only works well with the right pilots. Or Map; or map and pilots; or map, pilots, and biome. Or RNG! We can talk about the ultimate builds and basically, that is what has been discussed. Repeatedly!
Lost in all of this is the fact that not every mission includes fully buffed King Crabs with AC20++++++++s. Not every Grasshopper has all the ML and SLs with ++++++s. Not every pilot has 9 Tactician for wonderful precision strikes. Not every pilot has perfect Gunnery, Piloting, Guts. Full 10/10/10/10 Pilots with rare +++ weapons, TTS, ARM Mods, Defense Gyros ++++++++, every bell and whistle, etc. Even if they do have all of these things... Resolve changes things up. The map will change things up. The position of the OPFOR will change things up. Range will change things up! Things change! The greatest (insert whatever) is only the greatest when it can actually do the greatest (insert whatever).
Oh, to be certain it is more likely than not that everyone posting here has had some or all of the above. This does not, however, mean that everyone does. Nor does it mean that everyone has all of the above all the time. It most certainly doesn't mean that any discussion should continuously revolve around these things. Edge cases are just that, the edge! The amazing things possible with a Firestarter in the late Campaign game are not even remotely equal to the early Campaign game, it is not even remotely possible in the MP game!
There are literally so many elements that go into a single match that any discussion of 1.2 vs 1.3 Pilot Skills and tactics are moot. They were always moot. They will always be moot. More maths isn't going to help.
You can calculate the binomial, then all combinations for all the different weapon binomials and/or SRM/LRM (with diminishing returns, LRM clustering, global clustering, ...) and at the end filter into the spreadsheet to generate a graph or just a couple of values.
The formula (or formulas) doesn't break down. If you can calculate damage probabilities for one mech in principle you can make it work in all circumstances, for any number of mechs and with different modifiers, skills, ... for each one. That's the easy part.
Yeah, binomials...
You like totally missed my point, The map, biome, opfor, my movement, my weapons, my pilots, my resolve use, my mech design, my choice to fire N weapons, my choice to fire an Alpha, OPFORs see all of the above.
You can not calculate all of these within reason.
OMG it is not a binomial!
It is a multi-dimensional array!
What you can do.... super-pimp GHR is going to get an answer by the AI.
@Doctor Machete "easy" is all perspective-based. "I can write it on a whiteboard and say 'just repeat for X times' or write the calculation in a program" is different from "do it in a program and display the output in a clear, meaningful, and understandable way".
From a theoretical perspective, yes, it can be done. From a practical perspective, representing that information in a way that is understandable to everyone (and updated real-time as the player clicks and unclicks weapon systems or changes p-shot locations, etc) is a completely different and arguably pointless exercise.
From a player perspective, to-hit numbers provide all the data that's needed. "Do I have a 'good' (to me) chance of hitting the thing I want to and what do I need to do to give me a 'good' chance of accomplishing the thing I want to do". For some people, 75% is "good enough". For others 90% isn't. Showing anything about damage spreads will just confuse the heck out of most people especially if the damage represented doesn't match up with the damage numbers for the weapons used. I don't care if I have a "good" chance of doing approximately 33 points of damage to a location if, in reality, I have a good chance of doing 25 points of damage and a crappy chance of doing 100. That 33 is misleading and inaccurate and likely to piss people off when they hit but only do 25 damage and don't succeed at what they set out to do (much like how people get pissed when they fire 7 medium lasers with 95% to hit and 3 miss. "ZOMG, that's not 95% hitting, that's less than 66%")
From a theoretical perspective, yes, it can be done. From a practical perspective, representing that information in a way that is understandable to everyone (and updated real-time as the player clicks and unclicks weapon systems or changes p-shot locations, etc) is a completely different and arguably pointless exercise.
From a player perspective, to-hit numbers provide all the data that's needed. "Do I have a 'good' (to me) chance of hitting the thing I want to and what do I need to do to give me a 'good' chance of accomplishing the thing I want to do". For some people, 75% is "good enough". For others 90% isn't. Showing anything about damage spreads will just confuse the heck out of most people especially if the damage represented doesn't match up with the damage numbers for the weapons used. I don't care if I have a "good" chance of doing approximately 33 points of damage to a location if, in reality, I have a good chance of doing 25 points of damage and a crappy chance of doing 100. That 33 is misleading and inaccurate and likely to piss people off when they hit but only do 25 damage and don't succeed at what they set out to do (much like how people get pissed when they fire 7 medium lasers with 95% to hit and 3 miss. "ZOMG, that's not 95% hitting, that's less than 66%")
I don't think you understood me. Yes, you can calculate all of these, and the hardest part are not resolve, pilots, etc... but the main probabilities of the build. And for that binomials are used for most weapons and then specific functions for SRM/LRMs. I never said is nearly enough with binomials. They are just a very small but important part nonetheless.
I didn't say that's easy but "that's the easy part", in the context of other parts of the same problem being way harder.
I don't think it's hard to represent, just a chart, which I think can be very understandable with many builds at the same time. That's if you do the calculation offline, if you want it within the game it could probably made to show for a selected weapons setup during the game the chance of destroying the hit location.
You're right...you did say it was the 'easy part'. And my response was that even as an "easy part", it's nowhere near as easy as you claim and then the other parts are harder still. The chart you've produced is not (from my perspective) meaningful, understandable, or clear. I don't know what you are trying to illustrate, why, or how it applies. I can make assumptions. It looks like you're modelling a bunch of different builds (not sure why) and that you're assuming a 95% chance to-hit attack that will always hit the CT if it connects. Just looking at one line, you might be able to convince me that it was straight-forward in that scenario, but we're not talking about shooting buildings, turrets, or other targets with 1 hit box...we're talking about shooting at targets with up to eight hit boxes all with different percent chances of being hit depending on angle of attack and p-shot. You yourself said:
Keep in mind that this is a discussion about representing this to players during the game so things that impact performance of the calculation would tend to be tossed away in favor of something "cruder" but faster (i.e. plain to-hit numbers instead of complex formulae and graphs). We were (or at least, I was) discussing the issue of "well shit, it's annoying when you go to p-shot a mech and the p-shot goes everywhere except where you said to shoot". I understand that it's maths and probability...and I'm okay with that. It doesn't stop me from being annoyed by it...and no amount of graphs would reduce my annoyance (in fact, having graphs of probable damage-to-component information would likely increase the frustration if the damage application wasn't close to what the graph claimed it might be. "Oh my god. The gorram graph said that I should've been able to get 50 damage to the RT of that Hunchback 4G with a 99% likelihood of success and I only hit it with 25 dmg. AAAARRRRGGGGGHHHHH. Why did I waste my time / attack / whatever? Blah blah blah game bad blah blah blah RNG rigged blah blah".
Anyway... this forum has seen more than its share of probability and RNG discussions and how bad humans are at comprehending the implementation and expression of such things. I wouldn't blame @Havamal or any other mod for banging their head against a wall and then ripping out the probability / RNG comments into their own thread and leaving the "After playing with the ability beta, I think I'm going to put <this> kind of lance together for these situations" kinds of comments. (and I apologize for adding more than a few comments to the probability / RNG discussion instead of taking it to a different thread).
Keep in mind that this is a discussion about representing this to players during the game so things that impact performance of the calculation would tend to be tossed away in favor of something "cruder" but faster (i.e. plain to-hit numbers instead of complex formulae and graphs). We were (or at least, I was) discussing the issue of "well shit, it's annoying when you go to p-shot a mech and the p-shot goes everywhere except where you said to shoot". I understand that it's maths and probability...and I'm okay with that. It doesn't stop me from being annoyed by it...and no amount of graphs would reduce my annoyance (in fact, having graphs of probable damage-to-component information would likely increase the frustration if the damage application wasn't close to what the graph claimed it might be. "Oh my god. The gorram graph said that I should've been able to get 50 damage to the RT of that Hunchback 4G with a 99% likelihood of success and I only hit it with 25 dmg. AAAARRRRGGGGGHHHHH. Why did I waste my time / attack / whatever? Blah blah blah game bad blah blah blah RNG rigged blah blah".
Anyway... this forum has seen more than its share of probability and RNG discussions and how bad humans are at comprehending the implementation and expression of such things. I wouldn't blame @Havamal or any other mod for banging their head against a wall and then ripping out the probability / RNG comments into their own thread and leaving the "After playing with the ability beta, I think I'm going to put <this> kind of lance together for these situations" kinds of comments. (and I apologize for adding more than a few comments to the probability / RNG discussion instead of taking it to a different thread).
I find it's best to just have a general idea of the math, but not worry about it too much.
Instead you look at the nature of something.
It's like the classic RPG trope of armour that reduces damage by a flat amount (say 5 or 10) and armour that reduces damage by a percentage (15%).
One has the nature of being extremely powerful against low damage, high rate of fire weapons. The other, gives a general reduction.
So what can we do knowing this "nature of the two things"?
Well, in a game with lots of machineguns, doing rapid low damage, the flat amount armour might be amazing. In a game where even the weakest weapon does 10,000 points of damage, a 10 damage reduction is not very exciting.
When you look at the nature of mitigation against evasion in Battletech, you realise you have a similar issue with evasion. When you need it most, against the most accurate or dangerous enemies or when you make the biggest mistakes, that's when evasion is at it's worst. This is the nature of evasion. It's weaker against 8 crappy enemies, than 3 nasty ones as well. So there is complexity.
I don't like the nature of a thing, that gets worse the more I need it. So I favour mitigation. Doesn't mean I won't also use evasion, but it's nature is that of something that is not reliable, even if a better defense is "probable". It's that one time things go really wrong that ends a campaign.
Not 50 other missions where you took generally more damage.
Instead you look at the nature of something.
It's like the classic RPG trope of armour that reduces damage by a flat amount (say 5 or 10) and armour that reduces damage by a percentage (15%).
One has the nature of being extremely powerful against low damage, high rate of fire weapons. The other, gives a general reduction.
So what can we do knowing this "nature of the two things"?
Well, in a game with lots of machineguns, doing rapid low damage, the flat amount armour might be amazing. In a game where even the weakest weapon does 10,000 points of damage, a 10 damage reduction is not very exciting.
When you look at the nature of mitigation against evasion in Battletech, you realise you have a similar issue with evasion. When you need it most, against the most accurate or dangerous enemies or when you make the biggest mistakes, that's when evasion is at it's worst. This is the nature of evasion. It's weaker against 8 crappy enemies, than 3 nasty ones as well. So there is complexity.
I don't like the nature of a thing, that gets worse the more I need it. So I favour mitigation. Doesn't mean I won't also use evasion, but it's nature is that of something that is not reliable, even if a better defense is "probable". It's that one time things go really wrong that ends a campaign.
Not 50 other missions where you took generally more damage.
@scJazz The calculation I performed pulls variables from different columns. So Armor+Structure remaining (presumably) on CT, %chance to hit, %chance to hit location, #evasion stacks, damage per weapon, target damage reduction, and number of weapons fired can be changed on the fly. You just update the columns to describe whatever your situation is, it'll give you the probability of precision shotting a CT and scoring a kill. I don't want to put the work in to make it account for every weapon in the game, but it will certainly account for all of the known variables that go into the to-hit and damage calculation.
In no way do I want or expect a probability of kill widget added to the game. Anyone who really wants one can write their own spreadsheet. I mainly wanted to demonstrate that it is possible to calculate the volume of fire needed to overcome a combination of Evasion and Bulwark, to a certain level of certainty. And write the thing to make sure I wasn't overlooking anything.
I also don't care if a smarter AI makes targeted salvage harder to get, the game will become boring more quickly if the AI is a pushover. I also think the game will become monotonous if the optimal thing to do is jump around in cover all the time with Bulwark pilots. It's why I want Breaching Shot/Sensor Lock and Multishot/Ace Pilot types to be more useful.
In no way do I want or expect a probability of kill widget added to the game. Anyone who really wants one can write their own spreadsheet. I mainly wanted to demonstrate that it is possible to calculate the volume of fire needed to overcome a combination of Evasion and Bulwark, to a certain level of certainty. And write the thing to make sure I wasn't overlooking anything.
I also don't care if a smarter AI makes targeted salvage harder to get, the game will become boring more quickly if the AI is a pushover. I also think the game will become monotonous if the optimal thing to do is jump around in cover all the time with Bulwark pilots. It's why I want Breaching Shot/Sensor Lock and Multishot/Ace Pilot types to be more useful.
The graph shows the X chance for doing Y damage to the CT with a Precision Shot at 95% base chance and from the front. But the base chance is not fixed, you can put any value to account for evasion; the Precision Shot can be set at different levels of skill (or with no PS), and instead CT can be the head or leg, and then compare different builds. If I want to go for headcapping, which is the most efficient build? the graph doesn't solve that, because there are a lot more variables than just chance to hit and damage, but no doubt it's a tool to help with.
Also even if you're not interested in the least for this specific purpose I think you overlook that if you can generate a chart like this then you could with little modification generate data for very different uses, like showing eight different values, one for each hit location like you say. For example, to know if it's more likely to destroy the LL than the LA when aiming at the LL for a specific opfor build, taking into account his evasion, damage reduction, mech armor, internal structure, your accuracy (skills/TTS/modifiers), ... All of these parameters are mostly adding/substracting/multiplying from the input parameters or the output results, that's why I haven't implemented them, because you can easily do it by memory. If opfor has three chevs I'll set 65% base chance instead of 95%, if it's bulwarked I'll just assume I need double damage, but they could be added to the UI as well.
Performance is not a problem at all if an approximation is good enough. So it could be done ingame without issues, even with mostly very high accuracy, because performance only suffers in specific cases. Most calculations could be perfectly accurate, simplifications only would need to be done with custom LRM boats and some custom very high alpha brawlers with varied weapons.
I you think you'd be frustrated by the stats then these can baked, same the game does to mitigate frustration. Problem solved. Things like doing 25 damage when you expect 50 with 99% chance should still happen but be extremely rare.
Then, the builds I'm modelling are extracted from a planner which for me is useful in itself, more accurate and less cumbersome than the mech bay version and I've been using it since a long time. I don't care at all about the mech bay stats, although it has got much better than at the beginning. So I don't need to generate specific data to feed the chart. On the contrary I can use the chart to compare already existing build setups in a way it suits my preferences. Which build would grant me more chances to headcap, a more heavier SRMs or perhaps lighter ones but adding an extra LL (for example)?
I like minmaxing but not exactly playing with minmaxed builds (a bit of that too sometimes but not most of the time) but the process itself of minmaxing and testing the results I like way more.