Thanks for the simulation results Dan. UNfortunately you completely failed to address my concerns and I have actually to confirm them somewhat. Although there was an immediately obvious problem with your results, I felt it best to put in the time to do my own simulations and recompose my argument since it's clear that it really wasn't understood first time round. Please read this time.
First though I need to address the simulation because the numbers you've give an immediately bias against low-accuracy/high-DMG weapons.
Thus, over 100,000 battles, Side A wins 54,584 of them. This means the "high ROF" force is 20% more likely to win any given engagement.
The problem is that the damage of these weapons is only inflicted in multiples of three and therefore to destroy your ideal 10 hull ships the high damage weapons need to do 12 points (3 x 4 hits) of damage. 2 out of the 12 points of damage (16.7%) is wasted helping debris clouds expand. For a best case scenario with the hull being a multiple of the damage value (as they are in the high accuracy case where DMG is 1) there is zero wasted damage.
Reproducing this myself this time varying the hull across a range of values (with the weapon number equalling the hull size for simplicity) I get:
1 hull/weapons each: A wins: 70495 (70.50%), B wins: 11680 (11.68%), draws 17825 (17.82%), advantage: 58.81%
2 hull/weapons each: A wins: 52144 (52.14%), B wins: 26830 (26.83%), draws 21026 (21.03%), advantage: 25.31%
4 hull/weapons each: A wins: 38380 (38.38%), B wins: 41883 (41.88%), draws 19737 (19.74%), advantage: -3.50%
4 hull/weapons each: A wins: 59812 (59.81%), B wins: 32533 (32.53%), draws 7655 (7.66%), advantage: 27.28%
5 hull/weapons each: A wins: 52256 (52.26%), B wins: 38031 (38.03%), draws 9713 (9.71%), advantage: 14.23%
6 hull/weapons each: A wins: 44154 (44.15%), B wins: 44903 (44.90%), draws 10943 (10.94%), advantage: -0.75%
7 hull/weapons each: A wins: 56495 (56.49%), B wins: 39168 (39.17%), draws 4337 (4.34%), advantage: 17.33%
8 hull/weapons each: A wins: 51927 (51.93%), B wins: 41608 (41.61%), draws 6465 (6.46%), advantage: 10.32%
9 hull/weapons each: A wins: 46134 (46.13%), B wins: 45779 (45.78%), draws 8087 (8.09%), advantage: 0.35%
10 hull/weapons each: A wins: 54921 (54.92%), B wins: 42041 (42.04%), draws 3038 (3.04%), advantage: 12.88%
11 hull/weapons each: A wins: 51754 (51.75%), B wins: 43401 (43.40%), draws 4845 (4.84%), advantage: 8.35%
12 hull/weapons each: A wins: 47456 (47.46%), B wins: 46190 (46.19%), draws 6354 (6.35%), advantage: 1.27%
13 hull/weapons each: A wins: 54365 (54.37%), B wins: 43218 (43.22%), draws 2417 (2.42%), advantage: 11.15%
14 hull/weapons each: A wins: 51521 (51.52%), B wins: 44560 (44.56%), draws 3919 (3.92%), advantage: 6.96%
15 hull/weapons each: A wins: 48275 (48.27%), B wins: 46596 (46.60%), draws 5129 (5.13%), advantage: 1.68%
16 hull/weapons each: A wins: 53897 (53.90%), B wins: 44156 (44.16%), draws 1947 (1.95%), advantage: 9.74%
17 hull/weapons each: A wins: 51839 (51.84%), B wins: 44969 (44.97%), draws 3192 (3.19%), advantage: 6.87%
18 hull/weapons each: A wins: 48911 (48.91%), B wins: 46653 (46.65%), draws 4436 (4.44%), advantage: 2.26%
19 hull/weapons each: A wins: 53235 (53.23%), B wins: 45000 (45.00%), draws 1765 (1.76%), advantage: 8.23%
20 hull/weapons each: A wins: 51466 (51.47%), B wins: 45709 (45.71%), draws 2825 (2.83%), advantage: 5.76%
21 hull/weapons each: A wins: 49080 (49.08%), B wins: 47141 (47.14%), draws 3779 (3.78%), advantage: 1.94%
22 hull/weapons each: A wins: 52986 (52.99%), B wins: 45523 (45.52%), draws 1491 (1.49%), advantage: 7.46%
23 hull/weapons each: A wins: 51459 (51.46%), B wins: 46031 (46.03%), draws 2510 (2.51%), advantage: 5.43%
24 hull/weapons each: A wins: 49543 (49.54%), B wins: 47012 (47.01%), draws 3445 (3.44%), advantage: 2.53%These results are consistent with all the other variations on the simulation, such as fixed weapon numbers and reduced degredation.
By these figures its obvious that waste damage and not the "early weapon damage" distribution is what accounts for the cast majority of the advantage of the high-accuracy weapons in this simulation. Furthermore, in cases where there is no waste damage (hulls values of 3, 6, 9...) at the lower end of the scale (where your "early damage" effect should be most pronounced) the high damage configurations are actually slightly more effective. When I simulate high ROF instead of high accuracy (which you were actually doing), the difference between the high-ROF and the high-DMG configurations is less than 1% across the entire range when the shot wastage is eliminated.
In other words the "early weapon damage" effect is simply undetectable, if it exists at all.
Waste damage is a real effect but the damage needed to kill a hull would probably be spread randomly across a largish range of values and we would expect the waste damage typically to be about half between the maximum and the minimum. And, as I pointed out in the earlier post, when the sample size increases (more hull hits in this case) the error due to the distribution reduces (in this case the wasted damage becomes a smaller portion of the increasing hull damage requirements).
Altogether the simulation results are really just confirming my point that the Starmada combat however is purely a matter of statistical distribution in a fairly narrow range (more likely about 10%) of effect between best weapon configuration and the worst. Other game related factors such as limited choice through weapon bearing or ability to selectively focus enough weapon fire to cripple an enemy are for the most part going to further flatten the advantage.
... just as high ROF is more valuable than high DMG because it makes it more likely that some hits will be scored earlier, so too is ACC 3+ more than twice as valuable as ACC 5+.
What you are actually observing is that in the Combat resolution equation (ROFxACCxIMPxSHLDxDMG) factors at the start are slightly more valuable than those at the end. Why? Predominantly because they allow finer grain resolution in the final product and therefore less waste damage and a flatter distribution. If we swap the damage dice multiplication step and the ROF steps at the start and the end of the equation (we'll call it virtual projected future damage) then damage becomes the "best" factor instead for no reason thatn because it's at the start of the calculation.
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And that brings me (finally) back to my original point:- none of the core weapon factors have any meaning beyond the minor effects due to their position in a lossy statistical process. Specifically they don't interract with the target stats except in the most trivial way.
When state "RoF is the best stat" there was a chorus of agreement from almost everyone else. If you pointed out that DMG is actually more cost effective due to the cost bias then everyone would probably agree with that as well. Either way, though, the concensus is that there's only one optimal way of selecting weapon stats, anyone who takes anything differently is playing a (marginally) suboptimal configuration.
But it would be the same even if you succeeded in finding a perfect cost/benefit balance between the stats. There's still no good reason for anyone to select more than a single stat to use.
What's lacking from the strategic mix is the concept of weapons that are better in certain circumstances but not others. For example nobody in this thread has said anything like "ROF is good against small craft, but DMG is better against large ones".
Compare this with Full Thrust. In that game basic beam weapons are defined with accuracy and dice number matched against shields. The system is generally simpler because there are only two or three basic steps in combat resolution - takea handful of dice at the outset and resolve them against accuracy and shields, but it's no less stategically deep that Starmada because even though Starmada has more combat steps to handle each of 3 (ROF, IMP, DMG) weapon statistics they don't contribute anything. There's no reason to utilise more than one stat. Combine them into a since weapon dice product and you don't lose any strategic options or subtleties.
For example:
The "best against target type X" effects you're trying to get out of raw RoF/Imp/Dam are modelled with weapon traits like Piercing, Anti-Fighter, etc. If Impact bothers you so much, do what many people do and just set it to 1 for all weapons.
actually makes this argument. I'm not arguing against the special rules but where they are actually recognised as doing the "job" of a core mechanic (IMP) which itself is not used by "many people" then there's obviously something amiss.
Going on to my main argument against the IMP stat (which is a specific example of the general problem of wepaon stats) I ran another series of simulations to test the relative effectiveness of IMP over ROF and DMG against low an high shields, this time using the full core Starmada rules (including the extended dice rules and misses on a '1'):
Low Shield: high-ROF vs high-IMP:
Fully simulating 100000 battles:
Ship A hull: 10, shield: 1, weapons 10 [accuracy: 4+, ROF: 5, IMP: 1, DMG: 1]
Ship B hull: 10, shield: 1, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
A wins: 5082 (5.08%), B wins: 29 (0.03%), draws 94889 (94.89%), advantage: 5.05%
A: 2.08 damage per round, B: 2.09 damage per round
Low Shield: high-IMP vs high-DMG:
Fully simulating 100000 battles:
Ship A hull: 10, shield: 1, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
Ship B hull: 10, shield: 1, weapons 10 [accuracy: 4+, ROF: 1, IMP: 1, DMG: 5]
A wins: 3601 (3.60%), B wins: 4945 (4.95%), draws 91454 (91.45%), advantage: -1.34%
A: 2.08 damage per round, B: 2.08 damage per round
High Shield: high-ROF vs high-IMP:
Fully simulating 100000 battles:
Ship A hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 5, IMP: 1, DMG: 1]
Ship B hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
A wins: 49639 (49.64%), B wins: 48148 (48.15%), draws 2213 (2.21%), advantage: 1.49%
A: 0.26 damage per round, B: 0.25 damage per round
High Shield: high-IMP vs high-DMG:
Fully simulating 100000 battles:
Ship A hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
Ship B hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 1, IMP: 1, DMG: 5]
A wins: 47748 (47.75%), B wins: 46961 (46.96%), draws 5291 (5.29%), advantage: 0.79%
A: 0.34 damage per round, B: 0.29 damage per roundSo across the entire range of shield values (1-5) the differential between the performance of a weapon configuration that favours high-ROF, high_IMP or high DMG is barely in a 3.5% range. with ROF being the best in all cases and barely a 1% difference between DMG and IMP regardless of the target shielding. All this, of course ignoring, the waste damage effect which uniformly favours ROF and accuracy.
Starmada doesn't exist in isolation. There's been a 30 year history of starship construction/combat games (TCS was published in 1981) and plenty of other genre wargames in the last half century. A lot of them include some rules for weapon penetration and armour as a general mechanism and, across the board, they all have a major effect on the relative effectiveness of different weapons on different targets.
For example Brilliant Lances used two basic varieties of of beam weapons, particle accelerators and lasers. The PAs did a lot of damage compared with lasers but it was fully reduced by armour whereas lasers had a penetration modifier that reduced the effectiveness of the armour for reducing damage. The penetraction factor typicall about 1/10, in other words (after cost balancing) there was approximately a 300% differential each way between high penetration weapons and low penetration weapons in their effectiveness against high and low armoured targets. Predecessors costed armour on an exponential scale or made penetration rolls on multiple dice for a bell curve but always with a major differential in the circumstantial performance.
Modern dice bucket games need to rely more on linear effects. 40K has a step threshold system simply adding a strength value to a dice roll and matching it against and armour value. As a consequence some weapons cannot damage some targets (which is a major design issue but not an absolute limitation); selecting a mix of weapons (or even ignoring high strength weapons to focus on victory conditions) does therefore become an important factor in the core game strategy. Plenty of wargames over the decades have implemented similar mechanisms but always with a clear effect.
My own current Starmada variant is to replace the existing "IMP multplies dice" mechanic with an alternative: IMP + d6(extended) >= (shield x 2). The numbers have selected so there's a reasonable range of values using the (non-linear) extended dice mechanism, but a IMP 1 weapon can still damage a shield 5 (doubled to 10) ship on rare occasions. Simulating this I get the following results:
Shield 0: high-ROF vs high-IMP (alternative impact rule):
Fully simulating 100000 battles:
Ship A hull: 10, shield: 0, weapons 10 [accuracy: 4+, ROF: 5, IMP: 1, DMG: 1]
Ship B hull: 10, shield: 0, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
A wins: 99902 (99.90%), B wins: 0 (0.00%), draws 98 (0.10%), advantage: 99.90%
A: 2.50 damage per round, B: 0.50 damage per round
Shield 0: high-IMP vs high-DMG (alternative impact rule):
Fully simulating 100000 battles:
Ship A hull: 10, shield: 0, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
Ship B hull: 10, shield: 0, weapons 10 [accuracy: 4+, ROF: 1, IMP: 1, DMG: 5]
A wins: 63 (0.06%), B wins: 99675 (99.67%), draws 262 (0.26%), advantage: -99.61%
A: 0.50 damage per round, B: 2.48 damage per round
...
Shield 5: high-ROF vs high-IMP (alternative impact rule):
Fully simulating 100000 battles:
Ship A hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 5, IMP: 1, DMG: 1]
Ship B hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
A wins: 3532 (3.53%), B wins: 96421 (96.42%), draws 47 (0.05%), advantage: -92.89%
A: 0.04 damage per round, B: 0.13 damage per round
Shield 5: high-IMP vs high-DMG (alternative impact rule):
Fully simulating 100000 battles:
Ship A hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 1, IMP: 5, DMG: 1]
Ship B hull: 10, shield: 5, weapons 10 [accuracy: 4+, ROF: 1, IMP: 1, DMG: 5]
A wins: 85507 (85.51%), B wins: 14018 (14.02%), draws 475 (0.47%), advantage: 71.49%
A: 0.14 damage per round, B: 0.04 damage per roundthe damage values vary by orders of magnitude, high-RoF and high-DMG have a 5:1 advantage over high-IMP weapons when used against low shield targets, but against targets with high shield ratings the high_IMP weapons have a 3:1 advantage over the alternatives.
The core rules of Starmada's weapon combat mechanics are the worst of both worlds, they simply lack that strategic dimension of many systems without benefitting from the streamlined simplicity of others. Applying parsimony to game design means that mechanics that have little or no effect should probably be dropped. Starmada is either intended as a game where design, deployment, skill and often luck make a difference over a short number of turns, in which case the effects of single volley need to make a significant difference, or it's a game where ships line up on opposite sides and the players roll buckets of dice until the "marginal percentages accumulate over the course of a game". You cannot have it both ways. I don't seriously believe that the argument from percentages is anything other than an excuse. Anyone who has played any reasonable amount of wargames will recognise Section 4.3 as being fairly typical in describing a mechanism in which IMP is intended to be used to counter shields, and it's my belief that this is the mechanism that was actually intended as well as likely what many players actually believe happens. Your own argument:
Granted, against a ship with zero shields, there is no difference between IMP and DMG. However, assuming the ship has shields, the same theory applies: high IMP weapons are more likely to cause some damage, and are therefore more effective. The higher the target's shields -- and thus the greater the disparity between less damage more often and more damage less often -- the more pronounced the effect...
basicaly confirms your own mistaken belief that a mechanic relating IMP and shields exists and IMP is "more effective" (your words) whereas in fact it gives less than a one percent advantage. After saying that (as the designer) I don't think that you can reasonably argue that the absence of any such relationship is not a design flaw.
The problem I suspect is that the baby's been thrown out with the bathwater. In adopting the universal dice multiplying mechanism the numerical interaction between IMP (formerly PEN) and shields familiar in other games was dropped. At first it looked to me like an elegant game mechanic without any need for an arithmetical comparison or table lookup step but it was self-defeating, by removing the connection you removed the actual interraction and therefore any value for having a seperate IMP parameter.
As has been demonstrated by some of the previous posts, the mechanisms are not actually well enough understood by the designers and, on the tabletop, they are buried too deeply in the die rolling sequence and behind special rules for the players to have noticed either. For this reason you can ignore the problem and keep the game as it currently exists, but it doesn't alter the fact that there's a major block of the rule system that doesn't make any positive contribution to the game in the manner that was intended. At the least it offers an opportunity for game improvement even if everyone is currently happy in their blissful ignorance.</r>