Rate and Mastery

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Rate and Mastery

Post  Stephen Lincoln on Thu Aug 22, 2013 9:53 pm

I like playing with numbers. This is important. Remember this for a few minutes time. This thread has gone in Random Stuff as it contains my rambling about certain system mechanics but obviously isn't official system mechanics, but it's a slightly more fundamental alteration to a system than just coming up with a new weapon or training is, so it didn't really feel like it belonged in corp culture/player-genned. Without further ado:

Basically, there's some serious synergising going on between the Mastered Weapon training and high-rate weapons. The flat XS-to-damage reward it offers obviously results in significantly more damage output the more attack rolls you get to make (and thus XS you can accumulate) in a single turn. Are you ready for math?

Let's assume you're a specialised character who's normally rocking an AT of 20 and averages an XS of 9. We'll assume you're mastered with whatever you want for this exercise. Now, you can use a dinky weapon that does 2d4 at rate 2, or a big gun that does 2d10 at rate 1. The 2d4 weapon will average 14 damage per hit, and at 2 hits a round scores 28 damage (assuming perfectly average XS and rolls, not factoring in crits, etc). The 2d10 weapon will average 20 damage per hit, but can only fire once a round, so it's already clearly outpaced by the smaller gun, simply because it can fire a single extra time per round (without mastery, the big gun comes out slightly more powerful in terms of raw damage average. Mastery turns that right around and then some). If you introduce armour to the mix, things even out a little - if you give the target 8AV, then the guns become roughly equal in damage to that target. 8AV doesn't seem like a lot by the standards of some Oracle characters, but remember that Tactical Assault Armour is only 6AV! Your target has to be wearing the heaviest armour available and then some before the benefit of doing damage in a single block to overcome armour even achieves parity with the power of just making two shots per round. Add to this the ease with which you can add flat armour penetration to each individual shot (an AP mag, for instance) and the big gun falls behind again. This is just rate 1 compared to rate 2 -the difference is even more severe when you start using rate 3 weapons.

This is a problem apparent even at relatively low powers, but it's not major and it doesn't detract a lot if you don't think about it too much. When you start going to the edge cases, however, things get extreme. For instance, if you start using sniper rifles, as a sniper. For this exercise, we'll compare the AMS Cobra to the newly minted AMS Artemis plasma sniper, using my sniper Stephen for stats. The cobra is a Rate 2 2d6+1 weapon, whereas the Artemis does 2d10+2 at a mere rate 1. Stephen's basic AT with each rifle is at present 22. If he aims for two rounds before firing, he scores a +12 aiming bonus to AT and damage, raising that AT to 34 and giving each extra shot +12 damage. The target has 0AV to contend with. Now there's a very complicated AnyDice script I've written which lives here for anyone who wants to look at it, but the resultant calculation of damage outputs, factoring in the XS on the attack rolls, the chance of the plasma rifle just exploding, bonus from aiming and so forth, works out to look like the following graph (you may want to r-click and view if it's cut off on the right). Also note that throughout the graphs the black lines are for the Cobra at rate 2, the orange for the Artemis, and the blue (when relevant) for the Cobra at rate 1, sacrificing a rate for accuracy).

Aiming for 12, AT34, 0AV, Core

That anomalous dot at 0 for the Artemis is the chance that it just explodes, doing 0 damage to the target (but some damage to Stephen), and the second bump in each curve is where you see critical hit damage.

The damage output of the Artemis is almost doubled by the Cobra, despite the Artemis's individual shots being almost twice as powerful in terms of their basic stats. That discrepancy is rendered negligible by the aiming and mastery bonuses applied to the weapons. When it comes to raw damage, it's all about the rate.

Of course, the Artemis has a considerable advantage over the Cobra in one respect - as a plasma weapon, it ignores armour. A stock Artemis ignores 22AV of armour on a hit. We'll assume that our Cobra is using standard SMART rounds, no AP allowed, to maximise the Artemis's advantage here. What happens when we put them up against a target with 22AV?

Aiming for 12, AT34, 22AV, Core

By presenting a target with the maximum AV that the Artemis completely ignores and the Cobra suffers the full brunt of, we just barely manage to achieve equal damage outputs. Technically, the cobra is still slightly ahead on average damage, although the median damage is reduced somewhat (42 compared to 48). It takes 22AV to make these weapons roughly equal in power - a level of protection nearly impossible for even Oracle agents to achieve - and taking on high-AV targets is supposed to be the Artemis's specialty.

Say we take Stephen to the extremes of his potential ability, buff his Tactical Firearms to maximum, install reticle eye enhancements, and let him finally take his beloved Advanced Aim training. With two rounds to aim his AT with the guns skyrockets to 43, with a +18 damage bonus from aiming. Against a 0AV target, we get:

Aiming for 18, AT43, 0AV, Core

The Cobra still hugely outperforms the Artemis, as expected. Against a 22AV target, we get:

Aiming for 18, AT43, 22AV, Core

Even against the ridiculous 22AV, the Cobra is now still handily outperforming the Artemis in its specialist role - it's not using any AP, its base damage is still roughly half, but it beats the Artemis in damage to the target by nearly 20 points. It is, in fact, not until we reach a target of 40AV that the Artemis finally, ever so slightly, edges out the Cobra in average damage.

Aiming for 18, AT43, 40AV, Core

In order for the Artemis to be a more useful weapon than the Cobra at these extremes of skill, we have to be shooting at tanks, or cyberlins, or something. This cannot help but feel slightly off to me.

So it seems pretty clear to me that rate and weapon mastery interact in a way which wildly, disproportionately favours high-rate over low-rate weapons (even just between Rate 1 and Rate 2!) And I wondered what might be done to fix this. And the solution that presented itself simple - make the bonus from Mastered Weapon's use of XS inversely proportional to the rate you shoot at. If you want to make several shots, you can't get huge bonuses on all of them - you have to split it up a little. So, you divide the XS by the rate you're firing at to work out your extra damage. Rate 2, XS/2. Rate 3, XS/3. If you make two shots, you'll on average accrue twice the XS of someone making a single shot - so your overall damage bonus from XS across the round stays roughly the same. If you make 3 shots, likewise you'll average 3x the XS, so again you do, on average, the same amount of bonus damage - it's just spread out across your shots. Now instead of being a bonus multiplied by rate, you have effectively a flattish bonus for the whole round. Your average bonus damage actually improves slightly if you sacrifice rate for accuracy, as the bonus to AT translates into bonus damage from XS, and reduced rate means the individual shots get bigger bonuses from that same XS too - which, to my mind, represents slowing down to place precise, accurate shots pretty well, and becomes very desirable when you've got a big chunk of AP to overcome.

If we do this, the graphs start to look quite different.

Aiming for 12, AT 34, 0AV, Revised

Against an unarmoured target, two shots from the cobra is still the best, but that's to be expected. The difference isn't quite so massive anymore, but it's still considerable. What about if we use the 22AV target?

Aiming for 12, AT34, 22AV, Revised

Now the Artemis is clearly significantly more useful against this heavily armoured target than the plain Cobra, doing about double the damage. In fact, the damage expected from the Cobra is improved when Stephen sacrifices a rate to place a single more accurate shot - which is what any good sniper should want to do against a hardened target! And now how about the most extreme example, with a maxed out Stephen taking on a ridiculous 40AV target:

Aiming for 18, AT43, 40AV, Revised

The Artemis outperforms the Cobra by nearly twice as much damage (the weird jaggedness in the lines for the rate 2 cobra shots are down to critical hit mechanics). By experimentation, we can find that with this revised system, at this extreme of aiming and skill, the Artemis started to outperform the Cobra at a mere 13AV:

Aiming for 18, AT43, 13AV, Revised

The mileage you can get out of a good Cobra when you're a goddamn professional is still impressive, but the Artemis still starts to be more useful when engaging targets with an AV you might actually see in real action. All these values are muddied up a bit by the ability to use AP ammunition and, of course, the bonuses from aiming still disproportionately benefit multi-shot weapons to single-shot ones - some tweaking of what exactly those bonuses are and how they're applied to multi-rate weapons might also be appropriate to finish the balancing off, but I've done enough math for today.

The net effect of this change to the mastered weapon rule is to reduce how dangerous mastered high-rate weapons are. There's no change to the damage potential of weapons that were already rate 1. It was already plainly obvious to most of us that the absolutely optimum way to max your damage was to master your guns and fire as often and as wildly as possible. Those guns would be back on an even keel with their more powerful but slower counterparts, and in many circumstances you're even rewarded by sacrificing rate to take a more accurate shot, a situation which almost never would have arisen in the core system. It serves to make the difference in damage due to a weapon's basic stats compared to another more relevant again, rather than having that difference be almost immediately rendered trivial compared to the benefit of mastery.

And most importantly, it gives Stephen a good reason to take the Artemis on missions. By making his other rifle less powerful, mind you, but still.

TL;DR
Adopting a new mastered weapon system where your XS bonus to damage is divided by the rate you are firing it stops high-rate weapons being obscenely powerful compared to low-rate big guns and seriously alleviates bizarre artefacts of the system at the extreme ends of the scale.
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Re: Rate and Mastery

Post  Tansai Kay on Thu Aug 22, 2013 11:55 pm

I've been doing some poking around on this, and this system reduces the damage output of a mastered cougar (AT 20 vs AV 5) to ~8, and these aren't exactly unusual conditions. I worry that this could be a sweeping wide change based on an extreme example.
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Re: Rate and Mastery

Post  Stephen Lincoln on Fri Aug 23, 2013 1:25 pm

Tansai Kay wrote:I've been doing some poking around on this, and this system reduces the damage output of a mastered cougar (AT 20 vs AV 5) to ~8, and these aren't exactly unusual conditions. I worry that this could be a sweeping wide change based on an extreme example.
See this graph for what the damage output of a cougar in mastered states looks like -  the rate reductions assume you are sacrificing rate for accuracy, giving an increased AT. This is an instance where you're rewarded for sacrificing shots for accuracy by increased damage - and after all, AV5 is comparatively high for a pistol weapon to be dealing with. If you remember that you can take AP smart mags as well, that drops the AV to an effective 3 (I'm sure you're capable of playing with the variables in the script to test the changes). But yes, this is a change which will generally reduces the power of high-rate weapons. You must remember that Weapon Mastery effective gives a rate 3 weapons three times the bonus it gives a rate 1 weapon - it's basically three times as valuable. That's a really huge discrepancy.

If you look at this graph, you'll see that the average damage output of a mastered cougar firing at full rate in core (generally I assume profession is applicable for all tests, and again I'm using stats for Stephen as if he was equally good at light weapons as tactical weapons) is actually slightly better in raw damage than getting the maximum normal aim bonus with the Artemis' single shot. Which is normally three rounds of aiming. If you assume a full aiming bonus for the Cougar, too, it's damage output soars to almost double what the Artemis can do, over the same length of time. Even with the revised system (remember that for the rate 1 weapons there's no difference to mastery so the values for core are still applicable to them) the aimed Cougar has slightly better damage output than the aimed Artemis. The sniper has to sink a bunch more XP into trainings specialised for sniping before his damage output starts to be appreciably better than the cougar. And then the Cougar's damage will fall off appreciably against an armoured target (let's say AV5), but it is a pistol class weapon against AV5, which in context is a relatively good AV (and you start to get into the range where losing rate for bonus AT works out for you, not featured in the graph, and there are other armour penetrating options available which will still improve your damage somewhat).

Basically, high-rate weapons become the most effective things to use against unarmoured or lightly-armoured targets (as they're meant to be) and low-rate weapons become the option of choice against a single heavily-armoured target. This increases weapon specialisation and it does do so by just making high-rate weapons less powerful, but they were already ludicrous.

See for instance the blackbird's semi-auto mode - without aiming, it's just better than the Artemis. With aiming, it's more than twice as good.

I have to go like right now or I might have posted some more but I'm sure you can see the point. Basically, the Cougar shouldn't get to be equally effective against all sorts of targets, there are still ways to mitigate higher APs if you're using a cougar and it makes sense that the high-power weapons should be the options of choice against armoured enemies, okay bye
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Re: Rate and Mastery

Post  Stephen Lincoln on Fri Aug 23, 2013 1:36 pm

P.S. I'm pretty sure that anydice does integer division and always rounds down so if you allow the XS to be rounded up after rate division rather than down you'd actually see a reasonable improvement in average damage output for the higher-rate weapons - I will look into seeing how I can do this with anydice later, can probably hack it by changing the division to (XS + RATE - 1) / RATE if you fancy looking at it while I'm gone
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Re: Rate and Mastery

Post  Stephen Lincoln on Fri Aug 23, 2013 1:44 pm

double P.S. ignore the comment that says add aiming damage bonus directly to the weapon base damage, I took it out into the bonus damage value in order to accurate calculate plasma AP in our revised AP system
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Re: Rate and Mastery

Post  Fenris on Fri Aug 23, 2013 3:39 pm

Looking at the graph, with your changes, one shot from the plasma sniper rifle is doing significantly more damage than being shot 3 times with a pistol, which to me at least, doesn't make sense. Being shot more times should do more damage. And the only point at which the damage levels get close to each other is when you spend 3 rounds aiming, which seems unfeasible when you are in the middle of a fire fight.
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Re: Rate and Mastery

Post  Stephen Lincoln on Sat Aug 24, 2013 2:31 am

Negative reaction and some discussion is making me explore alternative systems for changing how Mastered Weapon works. I've been tinkering with scripts and testing different numbers for like three hours since coming home. I'm not going to post any of the math and my findings this evening because SO TIRED but seriously. You would not believe how complex my microprogram has to get in order for me to adequately test multiple different solutions at a time.
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Re: Rate and Mastery

Post  Stephen Lincoln on Sat Aug 24, 2013 3:16 pm

Alright, let's establish our baseline character rather than just vaguely using stats from mine so we've got a decent ground to do comparisons on. Since we're talking about mastered weapon we're always going to be talking about a specialist in their particular field, so let's go with this:

A relevant attribute (in our case Perception) of 11. They went for a high but not maximal perception to begin with and have a couple of perception enhancements.
A relevant weapon skill of 8 - it's their best skill and their profession, to boot.
They have the Mastered Weapon training in whatever weapon they're using.
They don't have any other trainings or special properties relevant to their ability to shoot guns.
They're using a standard, normal damage version of their weapon, with no particular special mods or properties.

This means that their basic AT with their weapon will be 19.

Now I came up with a couple of other modifications to the system. Don't worry, you'll be pleased to know that I automatically discounted anything that involved dividing by 3 - hopefully dividing by two is acceptable, though. I have been furiously anydicing them to see how they play out. In this post I'm going to be comparing three different sets of mechanics - the first will be the core mechanics, where mastered weapon and aiming behave exactly as they normally do. The second is a revised version where only the first shot (or if you prefer, you choose which shot, for slightly more flexibility when it comes to handling shields) gets the full benefit of mastery and aiming - all the other shots you make in the round with that weapon only get half the benefit (aiming bonus is halved, halve XS before applying to damage). The final revision is a system where the benefit of mastery and aiming ONLY applies to a single shot in a given round, and other shots made get no benefit from them.

I'm going to be posting links to a lot of graphs - for brevity's sake, remember that weapons used at Rate 1 are completely unaffected by these changes and so I'll only ever show lines for this situation as using the core rules, because otherwise it's just cluttering the legend. It is also worth noting that these changes de-obsolete vital shot when using weapons at Rate 2 or higher, but for these calculations I have not attempted to include the effects of optimal use of vital shot because it is highly dependent on AT and AV and very difficult to work out intuitively and exhaustive by trial and error. Instead, I assume that when taking the secondary shots, our shooter takes the maximum vital shot penalty he can without going under AT20, as this is an easy heuristic to use and will always give you better damage without sacrificing any chance to hit. When the AT is already 20 or less, we don't bother using it at all. Keep in mind though that using a few points of vital shot can most certainly bump up the expected damage in many of the examples we're about to look at.

First of all, let's take a look at how the cougar fares under these changes. We can see that in core, it has an average damage output of about 41, falling to ~32 using the half-bonus revision and ~23 using the single-shot revision. Despite the changes, it always has a (at least slightly - remember vital shot, it definitely helps in this situation) better raw output than a snap shot from the PR95, but it's not as good as getting a full aiming bonus in with that sniper rifle (although remember that such requires a full three rounds of aiming, so over the four rounds taken by the PR95 to take a shot, the Cougar can get in four full rounds of firing, pumping raw output to more than double the PR95's potential in the same space of time). If we instead look at engaging a "moderately" armoured target at AV5, the cougar's damage has dropped a lot in all cases, falling to 11 for the single-shot revision, although again vital shot can improve that significantly. We start to approach the situation where a fully aimed PR95 shot is actually comparable to four full rounds of cougar-shooting, too. Bumping up to a heavily-armoured AV10, the Cougar's damage is considerably fallen but still roughly comparable to an aimed PR95 shot if four rounds of shooting are considered. Increase the AV much more and it becomes definitely preferable to use the PR95 against the high-AV target than to just plink away with a cougar, which is presumably the sort of situation we want the rules to create.

There will be more to come, but I have to wash up and pack things. Feel free to comment or whatever in the meantime, I will try and respond to points raised in my subsequent posts.
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Re: Rate and Mastery

Post  Admin on Sun Aug 25, 2013 10:58 am

Perhaps we could say that a Mastered shot requires the use of a free action, to represent the focus and concentration needed to pull it off? That would limit a character to one per round, though I would also knock together some trainings to up that to two, since that is certainly something worth 10XP.
Just thinking about some narrative justifications for some changes. Thanks for the number crunching, I look forwards to the next edition.
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Re: Rate and Mastery

Post  Stephen Lincoln on Sun Aug 25, 2013 12:25 pm

After discussion on IRC I arrived at a version with the following details:

1. Mastered Weapon only gives one attack in a round at full bonus and the other attacks have their XS bonus to damage capped by your relevant weapon skill. This was generally considered easier to do than dividing anything and it has a much smaller effect on the lower end of the scale (ATs in the 10-20 sort of spectrum) than it does at the ridiculous sniper end, where the majority of my problem is.

2. Aim bonuses only apply to one attack in a round at full bonus and the other attacks have the aim bonuses halved. This doesn't really affect many people at all (they're very fond of pointing out that nobody bothers to aim in a firefight), but it is necessary to stop the Cobra being so absolutely dominant in the field of sniping.

These changes still mean higher-rate weapons get more benefit out of Masted Weapon and aiming bonuses, but it's no longer by 2-3 times as much. This is what these changes do to the math (as always, remember the changes don't affect Rate 1 weapons so they're always given as using Core rules):

Comparison of Cougar, Cobra, and Kronos against AV0
Three rounds of aiming assumed when aiming specified. It's worth noting that Generic Shootman can actually get slightly improved damage by taking 3-point vital shots on the last 2 rate of his cougar shooting, and a 7-point vital shot on his second Cobra shot - by giving up some of the AT for the flat damage bonus you reduce your XS but also decrease the likelihood that some of your XS was wasted by going over the cap, giving you better overall damage, at least until the increased odds of missing start to offset this. I won't be taking this into account in the graphs I make, as the exact value varies depending on the AV you're shooting at.

We can see that the cougar is only moderately affected by the change, and is still much more dangerous than either of the sniper rifles in a single round of shooting. In the meantime the Cobra outshoots the Kronos in both capacities against this lightly armoured target.

Cougar, Cobra, and Kronos again AV5
AV5 is basically the turning point for snap shooting. At AV5, it becomes more desirable to fire wildly at things with the Cobra than the Cougar; the crossover for the Cobra vs. the Kronos is AV6. But at AV5, they all do approximately the same damage. It seems reasonable to me that AV5 - which, by the system core, is supposed to be relatively heavily armoured, that's the second best armour available in core right there - is a sensible place for it to start being more desirable to use the big guns than the pistols. This is of course going to be thrown off ever so slightly by AV reductions due to the new focus fire action, although I've just realised I can actually relatively easily extend my script to account for that. Oh well. Later.

Cougar, Cobra, and Kronos against AV11
AV11 is the turning point when a fully-aimed Kronos shot becomes better than a fully-aimed round of fire from the Cobra. This is, for reference, a better AV than the example Malenbrach given in Core, but it's still the kind of AV we would realistically see in the field on someone other than ourselves (although it doesn't take into account the ability to use AP rounds, which bump that value up to 13/14. Still feasible, I guess).

Cougar, Cobra, and Kronos against AV14 max spec.
In this example I just look to see what the results are for someone who has basically maximal skill without being a telepath. Effective perception is bumped to 15 (10 + 3 enhancement + 2 from the reticle eye (I know there are other enhancements that can apply but sod it)), skill is at 10, and aiming can be up to +18. Because of the higher AT involved the cougar has suffered a bit more from the changes, but judicious use of vital shot can actually bring the expected damage there much closer to the core cougar again. In the meantime, it's AV14 where the turning point between aimed Cobra and aimed Kronos is now, AV16/17 when ap rounds are involved. That's pretty extreme, but an AV we might actually see on something extremely heavily armoured - like a vehicle or Boss Alpha Malenbrach or something - so it still gives an actual incentive to carrying around the Kronos for engaging very high AV targets for this theoretically maximised Stephen.

Admin wrote:Perhaps we could say that a Mastered shot requires the use of a free action, to represent the focus and concentration needed to pull it off? That would limit a character to one per round, though I would also knock together some trainings to up that to two, since that is certainly something worth 10XP.
Based on my extended investigations if you start restricting mastered shot too heavily it starts to seriously mess with the pistols and light-tac end of the spectrum - even just halving the XS on secondary shots was causing people to be unhappy with the damage outputs down there. Using the capping system at least alleviates the impact the change has on the low-end. I feel it can justified in a similar way - assuming Mastered Weapon is supposed to represent your incredible precision, it seems fair to say you can only put that exceptional focus into one shot, and you're still more accurate with your others but not to the same extent. Of course we could play around with this - it may that people are more accepting of a change which has a relatively large impact if they're allowed to use a free action to alleviate it, although personally I'd want to avoid a situation where it's effectively possible to start using the cobra as in core again (by being able to get two full mastered shots a round) since that just once again makes it better for pretty much any sniping activity you care to name, even with the aiming system change.

If anyone wants me to punch scripts and run numbers on a particular variant they come up with, let me know, and I'll do my best. Right now, must get back to packing.
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Re: Rate and Mastery

Post  Stephen Lincoln on Sun Aug 25, 2013 12:37 pm

P.S. In my latter example the maximal Stephen actually has the Cobra vs. Kronos turning point at AV19 when using vital shot, and - incredibly - has created a situation where two hands one weapon is a training that is actually useful for increasing your damage, whereupon optimal use increases the turning AV to 21.

Something I'd really like to do is change THOW so it reads "if you only make a single attack with a weapon in a round, double the bonus to damage you get from taking vital shots", and maybe rename it. Boom, suddenly it's actually useful for people who specialise in using just one very powerful weapon again, letting them get (dependent on circumstances) up to ten extra points of damage on a single shot. Doesn't only have to apply to light and tac weapons, either. Anyway. Packing. That.
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